# Molecular Clouds in the Second Quadrant of the Milky Way Mid-plane from
l$=$104$.\\!\\!^{\circ}$75 to l=119$.\\!\\!^{\circ}$75 and
b=$-$5$.\\!\\!^{\circ}$25 to b=5$.\\!\\!^{\circ}$25

Yuehui Ma Purple Mountain Observatory and Key Laboratory of Radio Astronomy,
Chinese Academy of Sciences, 10 Yuanhua Road, Nanjing 210033, China
University of Chinese Academy of Sciences, 19A Yuquan Road, Shijingshan
District, Beijing 100049, China  Hongchi Wang Purple Mountain Observatory and
Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, 10 Yuanhua
Road, Nanjing 210033, China  School of Astronomy and Space Science, University
of Science and Technology of China, Hefei, Anhui 230026, China  Chong Li
Purple Mountain Observatory and Key Laboratory of Radio Astronomy, Chinese
Academy of Sciences, 10 Yuanhua Road, Nanjing 210033, China  University of
Chinese Academy of Sciences, 19A Yuquan Road, Shijingshan District, Beijing
100049, China  Lianghao Lin Purple Mountain Observatory and Key Laboratory of
Radio Astronomy, Chinese Academy of Sciences, 10 Yuanhua Road, Nanjing 210033,
China  School of Astronomy and Space Science, University of Science and
Technology of China, Hefei, Anhui 230026, China  Yan Sun Purple Mountain
Observatory and Key Laboratory of Radio Astronomy, Chinese Academy of
Sciences, 10 Yuanhua Road, Nanjing 210033, China  Ji Yang Purple Mountain
Observatory and Key Laboratory of Radio Astronomy, Chinese Academy of
Sciences, 10 Yuanhua Road, Nanjing 210033, China

(Accepted February 18, 2021)

###### Abstract

We have studied the properties of molecular clouds in the second quadrant of
the Milky Way Mid-plane from l$=$104$.\\!\\!^{\circ}$75 to
l$=$119$.\\!\\!^{\circ}$75 and b$=-$5$.\\!\\!^{\circ}$25 to
b$=$5$.\\!\\!^{\circ}$25 using the 12CO, 13CO, and C18O $J=1-0$ emission line
data from the Milky Way Imaging Scroll Painting project (MWISP). We have
identified 857 and 300 clouds in the 12CO and 13CO spectral cubes,
respectively, using the DENDROGRAM + SCIMES algorithms. The distances of the
molecular clouds are estimated and the physical properties like masses, sizes,
and surface densities of the clouds are tabulated. The molecular clouds in the
Perseus arm are about 30$-$50 times more massive and 4$-$6 times larger than
the clouds in the Local arm. This result, however, is likely biased by
distance selection effects. The surface densities of the clouds are enhanced
in the Perseus arm with an average value of $\sim$100 M⊙ pc-2. We selected the
40 most extended ($>$0.35 arcdeg2) molecular clouds from the 12CO catalog to
build the H2 column density probability distribution function (N-PDF). About
78% of the N-PDFs of the selected molecular clouds are well fitted with log-
normal functions with only small deviations at high-densities which correspond
to star-forming regions with scales of $\sim$1-5 pc in the Local arm and
$\sim$5-10 pc in the Perseus arm. About 18% of the selected molecular clouds
have power-law N-PDFs at high-densities. In these molecular clouds, the
majority of the regions fitted with the power-law correspond to molecular
clumps of sizes of $\sim$1 pc or filaments of widths of $\sim$1 pc.

Galaxy: structure — ISM: clouds — radio lines: ISM — stars:formation — surveys
— turbulence

††journal: ApJS

##  1 Introduction

Molecular clouds are the birthplace of stars. They are the coldest and densest
part of the turbulent and multi-phased interstellar medium (ISM). Since
discovered by Wilson et al. (1970), the CO molecule becomes the most widely
used tracer of molecular clouds in the Milky Way and the galaxies. Because of
the high abundance of the CO molecule in the ISM, the low-J transitions of
12CO are usually optically thick, whereas those of 13CO and C18O are
relatively more optically thin and therefore can be effectively used to trace
the regions of molecular clouds at higher densities. The knowledge of the
distribution and physical properties of molecular clouds in the Milky Way
mainly comes from large-scale surveys of the rotational transitional emission
from CO and its two isotopologues 13CO and C18O toward the Galactic plane
(Burton et al., 1975; Scoville & Solomon, 1975; Gordon & Burton, 1976; Burton
& Gordon, 1978; Solomon et al., 1987; Dame et al., 2001; Heyer et al., 2001;
Roman-Duval et al., 2010; Rice et al., 2016; Miville-Deschênes et al., 2017).
The masses of molecular clouds lie in the range from a few tens of solar
masses to about 106 M⊙, while the sizes vary from $\sim$10 to 150 pc. The
typical velocity dispersion of molecular clouds revealed by the surveys is
$\sim$1 km s-1. The most massive molecular entities ($>$ 104 M⊙) are called
giant molecular clouds (GMCs), which have complex and hierarchical structures
that can be further divided into clouds, clumps, and cores (Blitz & Williams,
1999). The cloud mass function (CMF) is found to follow a power-law
distribution of exponents in the range from $\sim-$1.4 to $\sim-$2.2 (Blitz,
1993; Kramer et al., 1998). A power-law scaling relation exists between the
cloud size and the velocity dispersion with an exponent of 0.38-0.5 (Larson,
1981; Solomon et al., 1987). There also exists a power-law correlation between
the mass and size of molecular clouds, $M\propto R^{h_{M}}$, where $h_{M}$
depends on the inner density distribution of the molecular clouds (Kauffmann
et al., 2010a, b).

The hierarchical structure and the power-law behavior of the CMF and the
$\sigma_{v}-r$ relation of molecular clouds are found to be the outcomes of
large-scale turbulence in various numerical simulations ignoring self-
gravitation (Vázquez-Semadeni & García, 2001; Padoan & Nordlund, 2002;
Federrath et al., 2009). However, gravity is found to play an important role
in the dynamics of the molecular clouds on small scales ($<$ 1 pc) (Larson,
2003; di Francesco et al., 2007). Numerical simulations including gravity at
the early evolutionary stage of molecular clouds also successfully recovered
the mass and density distribution of molecular clouds (Vázquez-Semadeni et
al., 2007). It is valuable to investigate the statistical properties and
equilibrium states of molecular structures with surveys of molecular clouds
that have high sensitivity, good spatial resolution, and wide sky coverage at
the same time. This kind of surveys are capable of providing a sample of
molecular clouds at different evolutionary stages in different environments
and at different Galactocentric distances. It is also important that this kind
of surveys allow us to investigate the physical properties and the scaling
relations of molecular clouds in a high dynamic range of scales from the
molecular cores to the GMCs.

The ongoing Milky Way Imaging Scroll Painting (MWISP) project (Su et al.,
2019) provides us a good opportunity to study the statistical properties of
molecular clouds. For this investigation, first we need to decompose the
molecular line emission into individual clouds. For this pourpose we used the
DENDROGRAM 111https://dendrograms.readthedocs.io (Rosolowsky et al., 2008) and
SCIMES222https://scimes.readthedocs.io (Colombo et al., 2015) algorithms.
Colombo et al. (2015) have made detailed comparison of the performance between
the DENDROGRAM+SCIMES algorithm and other algorithms such as CPROPS
(Rosolowsky & Leroy, 2006) and ClumpFind (Williams et al., 1994) frequently
used for the automatic identification of extended structures in spectrometric
data. They found that CPROPS and ClumpFind tend to overdivide the emission of
molecular gas. Other traditional algorithms, like GAUSSCLUMPS (Stutzki &
Guesten, 1990) and FELLWALKER (Berry, 2015), are more suitable for the
identification of clumps or cores.

The probability distribution function of H2 column density (N-PDF) of
molecular clouds is a useful statistical tool to investigate the underlying
physics that influence the structure of the molecular clouds. A log-normal
behavior of the N-PDF has been predicted in theoretical studies (Vazquez-
Semadeni, 1994; Padoan et al., 1997; Klessen, 2000) and is attributed to the
supersonic turbulence in molecular clouds. Some following observations have
confirmed the existence of the log-normal N-PDFs in relatively quiescent
molecular clouds (Goodman et al., 2009; Kainulainen et al., 2014). Log-normal
plus high-density power law tail or pure power-law distributions of the
N-PDFs, have been observed in active star-forming regions with dust extinction
or emission data (Kainulainen et al., 2009; Schneider et al., 2013; Tremblin
et al., 2014; Benedettini et al., 2015; Lombardi et al., 2015; Stutz &
Kainulainen, 2015). However, Alves et al. (2017) propose that the
completeness, i.e., the last closed contour, has a significant influence on
the shape of N-PDFs and they conclude that, above the completeness limit,
there is no observational evidence for log-normal N-PDFs in molecular clouds.
The results of Tassis et al. (2010) also challenge the one-to-one
correspondence between the shapes of the N-PDFs and the underlying physics in
molecular clouds, as log-normal N-PDFs are observed in their modeled clouds
without supersonic turbulence.

In this work, we use the DENDROGRAM+SCIMES algorithms to extract molecular
clouds in the second quadrant of the Milky Way mid-plane from
l$=$104$.\\!\\!^{\circ}$75 to l=119$.\\!\\!^{\circ}$75 and
b=$-$5$.\\!\\!^{\circ}$25 to b=5$.\\!\\!^{\circ}$25 using the 12CO and 13CO
datasets from the MWISP project and study their physical properties. The
observations are introduced in Section 2 and the results are presented in
Section 3. We discuss the properties of the N-PDFs of a selected sub-sample of
molecular clouds in Section 4 and make a summary in Section 5.

##  2 Observations

We have observed the 12CO , 13CO , and C18O $J=1-0$ line emission toward the
Galactic plane with a sky coverage of 15°$\times$10°from
l$=$104$.\\!\\!^{\circ}$75 to l=119$.\\!\\!^{\circ}$75 and
b=$-$5$.\\!\\!^{\circ}$25 to b=5$.\\!\\!^{\circ}$25\. The observation is part
of the MWISP project, which is an unbiased simultaneous survey of the $J=1-0$
transitional emission of the three isotopologues of carbon monoxide toward the
Galactic plane visible from the northern hemisphere. The detailed
observational information and the data processing procedure of the MWISP
project are introduced comprehensively in Su et al. (2019). Here we only give
a brief description of the observations and the dataset used in this work. The
observations were taken from 2012 March to 2018 October using the Purple
Mountain Observatory (PMO) 13.7 m millimeter-wavelength telescope located at
Delingha, China. The half-power beam width (HPBW) of the telescope is around
52$\arcsec$ and 50$\arcsec$ at 110 GHz and 115 GHz, respectively, and the
pointing of the telescope has an accuracy of about 5$\arcsec$ during all the
observational epochs. The telescope is equipped with a nine-beam
Superconducting Spectroscopic Array Receiver (SSAR) (Shan et al., 2012). A
two-sideband Superconductor-Insulator-Superconductor (SIS) mixer works as the
front end of the receiver. The 12CO , 13CO , and C18O $J=1-0$ line emission
data are obtained simultaneously with the 12CO $J=1-0$ line emission being
covered by the upper sideband while 13CO $J=1-0$ and C18O $J=1-0$ lines by the
lower sideband. The backend of the receiver is a Fast Fourier Transform
Spectrometer (FFTS) with a total bandwidth of 1 GHz and 16,384 frequency
channels, providing a spectral resolution of 61 kHz per channel which
corresponds to a velocity resolution of 0.17 km s-1 at 110 GHz. The antenna
temperature is calibrated according to $\rm{T_{mb}=T^{*}_{A}/\eta_{mb}}$
during observation, where the $\eta_{mb}$ is the main beam efficiency and its
value can be found in the annual status report
333http://english.dlh.pmo.cas.cn/fs/ of the PMO-13.7 m millimeter telescope.

In the MWISP project, the survey area is divided into individual cells of size
of 30$\arcmin\times$30$\arcmin$. For each cell, the observations were made in
the position-switch on-the-fly (OTF) mode along the directions of Galactic
longitude and Galactic latitude. The scanning rate is 50$\arcsec$ per second,
and the dump time is 0.3 s. The data products of the MWISP survey are
automatically pre-processed after observation. The pre-processing includes the
rejection of prominent bad channels, subtraction of a first-order baseline
from every spectrum, and the combination of the spectra obtained at different
times for the same sky position. The final data are regrided into
30$\arcsec\times$30$\arcsec$ pixels in the directions of Galactic longitude
and latitude. The required standard for the median RMS noise level in the
MWISP project is below $\sim$0.5 K per channel at the 12CO $J=1-0$ line
wavelength and below $\sim$0.3 K at the 13CO $J=1-0$ and C18O $J=1-0$ line
wavelengths.

##  3 Results

###  3.1 Overall Distribution of Molecular Gas

The average spectra of the 12CO , 13CO , and the C18O $J=1-0$ line emission
over the total surveyed area are presented in Figure 1. The molecular gas
traced by 12CO $J=1-0$ line has three main velocity components that are
centered at $\sim-52$, $\sim-35$, and $\sim-$10 km s-1, respectively, while
there are only two velocity components, $-52$ and $-10$ km s-1, in 13CO
$J=1-0$ line. There is also some 12CO emission contained in the velocity range
from $-$115 to $-75$ km s-1, not visible in the total spectrum since it is
confined in small regions. For clarity, we inserted in Figure 1 the average
spectrum of the 12CO line at the positions where the 12CO emission is detected
in the velocity range from $-$115 to $-75$ km s-1. The 12CO , 13CO , and C18O
line emission is considered being detected at a position only when its
spectrum show at least five, four, and three contiguous channels,
respectively, with intensities above 2$\sigma_{\rm{RMS}}$. The C18O emission
in the region is too weak to be identified in the average spectrum. However,
it clearly emerges in the average spectrum of the positions where the C18O
$J=1-0$ emission is above the detection criterion (see inset in Figure 1). The
spikes at $\sim 34$ and $\sim$45 km s-1 in the 12CO spectrum and at $\sim-75$
and $\sim$10 km s-1 in the 13CO spectrum are residual bad channels not
properly removed from the automatic reduction pipeline, and so are the spikes
at $\sim-127$, $\sim-110$, $\sim-23$, and $\sim 60$ km s-1 in the C18O
spectrum. The bump in the velocity range from $-40$ to $-17$ km s-1 in the
13CO spectrum is caused by wavelike baselines in the spectra.

Figure 1: Average spectra of the 12CO , 13CO , and C18O $J=1-0$ line emission
in the surveyed region. The black, blue, and red lines correspond to the 12CO
, 13CO , C18O spectra, respectively. The spikes at $\sim 34$ and $\sim$45 km
s-1 in the 12CO spectrum and at $\sim-75$ and $\sim$10 km s-1 in the 13CO
spectrum are due to bad channels, and so are the spikes at $\sim-127$,
$\sim-110$, $\sim-23$, and $\sim 60$ km s-1 in the C18O spectrum. The left
zoomed-in panel is the spectrum of the 12CO spectra averaged over the spatial
pixels that show emission in the velocity range from $-$115 to $-75$ km s-1 in
at least five contiguous channels with intensities above 2$\sigma$. The right
zoomed-in panel is the average spectrum of C18O line emission of all positions
that have at least three contiguous channels with intensities above 2$\sigma$.
The green line represents the 3$\sigma$ noise level of the average spectrum.
Figure 2: Color-coded intensity maps of the 12CO emission in different
velocity ranges. Red, green, and blue colors correspond to the 12CO integrated
intensities in the velocity ranges from $-$27 to 20, $-$75 to $-$27, and
$-$115 to $-75$ km s-1, respectively. The integrated intensity thresholds are
1.5 times $\sqrt{N}\sigma\delta v$, where N is the number of velocity channels
in the integrated velocity range, $\sigma$ is the RMS noise per velocity
channel, and $\delta v$ is the width of the velocity channel. The orange
ellipses show the extents of the supernova remnants (Green, 2014, 2017) in the
region. The H II regions and the H II region candidates in the WISE catalog
(Anderson et al., 2014) are indicated with blue and magenta circles,
respectively. The corresponding names of the H II regions in the Sharpless’
catalog (Sharpless, 1959) are shown with yellow letters, while the names of
the supernova remnants are shown in red. Some active star-forming regions,
like NGC 7822, are indicated with black letters.

Figure 3: (a) L$-$v diagram of 12CO emission. The red dashed lines are the
l$-$v curves of the Local, Perseus, and Outer spiral arms derived from model
A5 from Reid et al. (2014). The black dashed lines are the location of the
spiral arms derived from CO and HI observations (Weaver, 1970; Cohen et al.,
1980), which are used as the arm traces in Reid et al. (2016). (b) B$-$v
diagram of 12CO emission. The contours in the two panels start at 1.5$\sigma$
and then increase to 0.7 times the emission peak in seven steps with the same
intervals. The red squares and the green circles in the panels are the
positions of the molecular clouds identified by (Du et al., 2016) and (Sun et
al., 2015), representing the Outer arm and the New (OSC) arm, respectively.

The spatial distribution of the molecular gas in different velocity ranges in
the region is shown in Figure 2. The integrated intensity of 12CO emission in
velocity ranges from $-27$ to 20, $-75$ to $-27$, and $-115$ to $-75$ km s-1
are indicated with red, green, and blue colors, respectively. In the observed
portion of the outer Galaxy, more negative local standard of rest (LSR)
velocity corresponds to farther distance. The nearby molecular gas shown in
red color spreads over all the observed Galactic latitude range. The most
distant gas, shown as the blue color, only distributes at positive Galactic
latitudes which may be a result of the warp of the gas disk of our galaxy
(Westerhout, 1957; Wouterloot et al., 1990). Several well known molecular
clouds are located in this region, such as the nearby Cep GMC, shown in red in
Figure 2, the GMC complex NGC 7538 and the Cas GMC, shown in green. The Cep
GMC is a low-mass star-forming region, while the NGC 7538 complex is the
birthplace of massive stars. The detailed analysis of the physical properties
of Cas GMC was presented in our previous work Ma et al. (2019).

Figure 3 shows the position velocity distribution of the 12CO emission along
the directions of the Galactic longitude and latitude. Within the span of
Galactic longitude covered by this work, spiral arms of the Galaxy are
identified as continuous curves in the l-v diagram. The red dashed lines in
Figure 3 shows the projected l-v positions of the Local, Perseus, and the
Outer arms that are derived according to the fitted log-periodic spirals of
these arms in Reid et al. (2014), which are based on the measured parallaxes
of maser sources in high-mass star-forming regions and the Galactic rotation
constants from their model A5. The black dashed lines are the l-v locations of
the Local, Perseus, and Outer arms from the CfA CO observations (Cohen et al.,
1980), which are presented in figures 8 and 9 in Reid et al. (2016) and are
used as the spiral arm traces in the Bayesian distance estimator program in
Reid et al. (2016). Therefore, the previously known kinematic anomaly, which
can be inferred from the large discrepancy between the kinematic distances and
the luminosity/parallax distances of massive star-forming regions (Xu et al.,
2006), of the Perseus spiral arm, is shown in Figure 3 as the separation
between the red and black dashed “Perseus” lines. There exists a velocity
shear between the east and west parts of the Perseus arm, divided by the
shell-like structure located at $l=111\arcdeg,v=-45$ km s-1, which corresponds
to the NGC 7538 complex. The molecular gas to the east of the NGC 7538 complex
is mainly concentrated at $-$37 km s -1 while the gas to the west of the
complex mainly at $-$52 km s -1, which is the reason for the two peaks
observed at these velocities in the 12CO spectrum shown in Figure 1. The
spiral arms in this region can be seen clearly in also the b-v diagram in
Figure 3. The velocity dispersion of the molecular gas in the Local arm is
getting broader from south to north, which is caused by the fact that the
majority of the gas in the Local arm is located at Galactic latitudes above b
= 0°. The velocity of the molecular gas in the Perseus arm is gradually blue-
shifted along the south to north direction, as can be seen from Figure 3. Sun
et al. (2015) and Du et al. (2016) identified hundreds of molecular clouds in
the “New” arm, which is the extension of the Scutum-Centaurus arm in the outer
Galaxy (OSC arm), and the Outer arm using the MWISP data. The locations of
those clouds that fall in the region observed in this work are shown with
green circles and red squares, respectively. Some of the identified clouds are
indiscernible in our position-velocity diagrams, which is caused by the broad
latitude range used in the integration.

###  3.2 Statistics of 12CO , 13CO , and C18O Emission in Different Spiral
Arms

According to the l-v distribution of the 12CO emission and the spiral arm
traces, the molecular gas in the observed region can be divided into three
layers, the Local arm layer (from $-$27 to 20 km s-1), the Perseus arm layer
(from $-75$ to $-27$ km s-1), and the Outer$+$OSC arm layer (from $-$115 to
$-$75 km s-1). Each layer can be further divided into three kinds of masks
based on the detection of the 12CO , 13CO , and C18O emission. Mask 1 is
defined to be the regions where 12CO emission is detected. Mask 2 is the
regions where both 12CO and 13CO emission are detected, while Mask 3 is the
region where the emission from all three kinds of isotopologues is detected.
According to this definition, the Mask 1 regions contain the Masks 2 and 3
regions, while the Mask 2 regions contain Mask 3 regions. The 12CO , 13CO ,
and C18O line emission is considered being detected at a position only when
their spectra show at least five, four, and three contiguous channels,
respectively, with intensities above 2$\sigma_{RMS}$. Figure 4 presents the
spatial distribution of Masks 1-3 in the three velocity layers. 12CO and 13CO
emission is detected in all the spiral arms, while the C18O emission is only
detected in very few pixels of the first two layers, corresponding to the
densest part of active star-forming regions like the Cep GMC and NGC 7538
complexes. The total numbers and the percentages of the detection of 12CO ,
13CO , and C18O emission are presented in Table 1. The 13CO emission is
detected among 22.2% pixels with 12CO detection in the Local arm, while this
percentage is 24.1% in the Perseus arm and only 3.8% in the Outer$+$OSC arm.
The C18O emission is detected among only about 0.31% pixels with 12CO
detection in the Local and Perseus arms. We calculated the physical
properties, such as the excitation temperature, optical depth of the 13CO and
C18O emission line, and the column density of the three isotopologues of the
molecular gas for each pixel in Masks 1-3 in the Local and Persues arms. Since
the pixel number with good detection within the masks 2 and 3 regions in the
Outer+OSC arms are too small, their physical properties are not calculated.
The column density of 12CO molecule is directly converted from the H2 column
density using the abundance ratio [H2/12CO ] = 1.1$\times 10^{4}$ (Frerking et
al., 1982), while the H2 column density is obtained by multiplying the
integrated intensity of the 12CO emission by a conversion factor X${}_{\rm
CO}=2.0\times 10^{20}$ cm-2 (K km-1)-1 (Bolatto et al., 2013). The excitation
temperature of each pixel in each Mask and velocity layer is calculated using
the peak brightness temperature of 12CO in the corresponding velocity range of
that Mask, using eq. 1 in Li et al. (2018). The optical depth of 13CO and C18O
in Masks 2 and 3 are derived using the peak intensities of the 13CO and C18O
emission in the corresponding Masks and velocity ranges, using eqs. 2 and 3 of
Li et al. (2018), respectively. The column densities of 13CO and C18O for the
Local, Perseus, and Outer$+$OSC arms are calculated from the 13CO and C18O
integrated intensities in the corresponding velocity ranges using eqs. 5 and 6
in Li et al. (2018). The statistics of the physical properties such as
excitation temperature, optical depth, and column density of Masks 1-3 are
summarized in Figure 5 and Table 1.

It can be seen from Table 1 that the median excitation temperatures of Mask 1
in the four arms lie in the range from 6 to 8 K, while those of the Mask 2
regions are relatively higher, lying in the range from 8 to 10 K, which are
typical for molecular clouds where the gas is self-shielded from the
interstellar radiation field. The range of the excitation temperatures in the
Local and Perseus arms is quite large, from about 4 K to 47 K, indicating that
large differences in the physical conditions and excitation of the gas are
present within the molecular clouds at the spatial scales resolved by the
MWISP survey. The densest regions, Mask 3, which correspond to the active
star-forming regions like the Cep GMC, NGC 7822, L1188, and the NGC 7538
complex in the Local and Perseus arms, have much higher excitation
temperatures, with the median values from 15 to 19 K. This is expected in
regions where star formation is active since the new-born stars warm up their
envelopes. Moreover, the radiation emitted by already formed stars, expecially
if they are massive, can warm up their surrounding. The optical depth of 13CO
emission, $\tau_{\rm{13CO}}$, is less than 1 in most regions and has a median
value in Mask 2 of about 0.3 for both the Local and Perseus arms. However, it
reaches as high as 1.5 in some pixels, which may be small regions such as
clumps or cores. The density in these regions can be much higher than that in
the more diffuse part of the molecular clouds and consequently, the optical
depth of the 13CO lines increases so that the lines become optically thick.
The C18O emission is optically thin both in the Local and the Perseus arms,
but, on average, the pixels in the local arm have a C18O optical depth a
factor of two higher than those in the Perseus arm. For the Local and Perseus
arms, the distribution of N12CO has a shape similar to that of N13CO. However,
the median column densities of 12CO molecules is reduced by a factor of
$\sim$3 in the Outer$+$OSC arm compared with those in the Local and Perseus
arms. This indicates that there is less material in the Outer$+$OSC arms of
the Milky Way, the most external arms, than in the other two more internal
arms. The column density of C18O molecule in the Perseus arm is greater than
that in the Local arm by a factor of $\sim$1.5.

Figure 4: Spatial distributions of molecular gas in different Masks in the
three velocity layers. Blue, green, and red colors correspond to the regions
where 12CO , 13CO , and C18O emission is detected, respectively. Top, central
and bottom panels correspond to the Local, Perseus, and Outer$+$OSC arms,
respectively. The velocity ranges corresponding to each of the arms are given
in the bottom right corner of each panel. The color compositions of the sky
coverages of Masks 1-3 are shown in the lower-left corner of the bottom panel.

Figure 5: Histograms of (a) excitation temperature in Mask 1 regions, (b)
optical depth of 13CO emission in Mask 2 regions, (c) optical depth of C18O
emission in Mask 3 regions, (d) column density of 12CO emission in Mask 1
regions, (e) column density of 13CO emission in Mask 2 regions, and (f) column
density of C18O emission in Mask 3 regions in different arms. The colors of
the four arms are indicated in the upper-right corner of each panel.

Table 1: Statistical properties of molecular gas in the four arms of the
Galaxy

Arms | Mask | Pixel | Area | $T_{ex}$ | $\tau_{{}^{13}CO}$ | $\tau_{C^{18}O}$ | $lg(N_{{}^{12}CO)}$ | $lg(N_{{}^{13}CO})$ | $lg(N_{C^{18}O})$
---|---|---|---|---|---|---|---|---|---
Name | Name | Num (Per) | (deg2) | (K) |  |  | $\rm{(cm^{-2})}$ | $\rm{(cm^{-2})}$ | $\rm{(cm^{-2})}$
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
Local | Mask 1 | 658940 (29.01$\%$) | 45.760 | 4.05-44.71 (7.31) | … | … | 15.89-18.52 (17.10) | … | …
| Mask 2 | 146517 (6.45$\%$) | 10.175 | 4.79-44.71 (9.83) | 0.07-7.18 (0.33) | … | … | 14.04-17.03 (15.17) | …
| Mask 3 | 2106 (0.09$\%$) | 0.146 | 5.65-43.57 (14.89) | … | 0.04-0.88 (0.14) | … | … | 14.31-16.06 (15.02)
Perseus | Mask 1 | 285143 (12.56$\%$) | 19.802 | 3.94-47.26 (7.08) | … | … | 15.85-18.76 (17.10) | … | …
| Mask 2 | 68766 (3.03$\%$) | 4.775 | 4.71-47.26 (10.58) | 0.07-2.19 (0.28) | … | … | 14.16-17.25 (15.27) | …
| Mask 3 | 950 (0.04$\%$) | 0.066 | 7.01-47.26 (18.72) | … | 0.02-0.36 (0.09) | … | … | 14.35-16.13 (15.22)
Outer$+$OSC | Mask 1 | 5387 (0.23$\%$) | 0.374 | 4.23-14.74 (5.82) | … | … | 15.83-17.71 (16.76) | … | …
| Mask 2 | 203 (0.00$\%$) | 0.014 | … | … | … | … | … | …
| Mask 3 | 1 (0.00$\%$) | 0. | … | … | … | … | … | …

Note. — Col. 1: name of the arm. Col. 2: mask used, the definition of the
masks is given in Sect. 3.2. Col. 3: number of pixels with good detection
following the criteria explained in Sect. 3.1, in parenthesis the percentage
of the good pixels with respect to the total observed pixels is given. Col. 4:
total angular size of pixels with good detection. Col. 5: range and median
value (in parenthesis) of the excitation temperature. Cols. 6-7: ranges and
median values (in parenthesis) of the optical depths of 13CO and C18O
emission, respectively. Cols. 8-10: ranges and median values (in parenthesis)
of the column density of 12CO , 13CO , and C18O , respectively.

###  3.3 Catalogs of 12CO and 13CO Molecular Clouds

####  3.3.1 Decomposition of the 12CO and 13CO Emission into Individual Clouds

With the 12CO and 13CO line emission data, we identify distinct 12CO and 13CO
clouds in the surveyed region using the DENDROGRAM plus the SCIMES algorithms.

In practice, the dendrogram algorithm is memory consuming when the dataset
used is large. We smoothed the width of the velocity channels of 12CO and 13CO
data into 0.5 km s-1, resulting in new 12CO and 13CO datacubes with median
noise levels of 0.31 and 0.17 K, respectively. Before the implementation of
the DENDROGRAM algorithm, only those voxels within at least two consecutive
velocity channels with intensities higher than 2$\sigma$ are selected and all
other velocity channels are masked. The majority of the noise channels are
removed under this criterion, but some contiguous bad channels were not
removed. Nonetheless, if we set a higher noise threshold or broader velocity
coverage, real signal could be removed. The DENDROGRAM algorithm is then
implemented to the noise-masked and velocity-smoothed 12CO and 13CO datacubes.
The minimum difference between two separate “leaves” in a dendrogram tree is
set to be 3$\sigma$, and the bottom threshold for detection is 2$\sigma$. The
minimum voxel number of an individual “leaf” is set to be 50, corresponding to
3.7 consecutive pixels along each of the l-b-v axes. The above settings
corresponding to molecular cloud of size of 0.5$\times$0.5 and 1.6$\times$1.6
pc2 for distances of 1.0 and 3.0 kpc, respectively, and velocity range of 1.8
km s -1. We use “volume” as the clustering criterion for the SCIMES algorithm.
As a result, a mask cube that records the l-b-v positions and a catalog that
contains the physical information of the output clusters are generated. The
output “clusters” are taken to be individual clouds in this work. Since some
of the bad channels that produce spurious spikes in the spectra (see Figure.
1) still exist in the masked and smoothed data, they may cause false
identification of molecular clouds. Therefore, after the cloud identification,
we performed a manual check for each identified cloud to further ensure the
identified molecular clouds are real structures and not caused by bad
channels. We carried out molecular cloud identification on 12CO and 13CO data
separately, and cross-matched the two resulting catalogs. If more than 85%
voxels of a 13CO molecular cloud can be assigned to a single 12CO cloud, then
the 13CO cloud is considered to match to the 12CO cloud. As 13CO usually
traces the denser part of a molecular cloud, we find that one 12CO cloud
usually contains several 13CO clouds.

A total of 857 molecular clouds have been extracted from the 12CO $J=1-0$
data, while 301 molecular clouds have been extracted from the 13CO $J=1-0$
data. The molecular clouds that have centroid velocities in the velocity
ranges from $-115$ to $-75$, $-75$ to $-27$, and $-27$ to $20$ km s-1 are
assigned to the Outer$+$OSC, Perseus, and Local arms, respectively. The total
numbers of 12CO molecular clouds in the Local, Perseus, and Outer$+$OSC arms
are 440, 399, and 18, respectively, while the corresponding numbers of 13CO
molecular clouds are 176, 124, and 1. The 13CO cloud in the Outer$+$OSC arm is
found to be artificial, which is caused by bad velocity channels, therefore,
is removed in the final catalog. According to the result of cross-matching,
279 13CO molecular clouds have counterparts of 12CO clouds. The name of the
matching 12CO cloud for each 13CO cloud is given in the final catalog (see
Table 3 in Section 3.4). Figures 6 and 7 present the demonstrations of the
outlines of the 12CO and 13CO molecular clouds in the Local arm, respectively.
The results of clouds identification in the Perseus and Outer$+$OSC arms are
shown in the Appendix, Figures 20-22.

Figure 6: Demonstration of the outlines, as the output of the SCIMES
algorithm, of the identified 12CO molecular clouds in the Local arm in (a) l-b
space and (b) l-v space. Different colors in the two panels correspond to
different molecular clouds. The background image in panel (a) is the
integrated intensity of 12CO in the velocity range from $-27$ to $20$ km s-1,
while that of the panel (b) is the l-v diagram integrated along the Galactic
latitude from b=$-$5$.\\!\\!^{\circ}$25 to b=5$.\\!\\!^{\circ}$25\.

Figure 7: Same as Figure 6, but for 13CO clouds.

####  3.3.2 Distance estimation

Distance is critical for the calculation of the physical parameters of
molecular clouds. For the 12CO clouds with centroid velocities less than $-27$
km s-1, which are beyond the Local Arm, we adopted the kinematic distances
derived using a flat Galactic rotation curve, which is a good approximation
for the outer Galaxy, with a solar galactocentric distance of $R_{0}$ = 8.34
kpc and a rotation velocity of $\Theta_{0}$ = 240 km s-1 (Reid et al., 2014).
Since we are looking toward the outer Galaxy, our distance estimate is not
affected by the near or far ambiguity. For the nearby clouds, the peculiar
motion of the gas and the internal velocity dispersion of molecular clouds may
lead to large uncertainty in the estimation of the distances based on the
kinematic method. Therefore for these clouds, we use an alternative method to
estimate the distance. For molecular clouds within 2 kpc, we looked for the
position of sharp steepening in the 3D reddening map within the projected area
of each cloud to determine their distances. We used the three-dimensional map
of dust reddening up to 5 kpc produced by Green et al. (2019) with the
parallaxes from Gaia DR2 catalog and the stellar photometry from Pan-STARRS 1
and 2MASS.

The public Python package “dustmaps” is used to query the reddening map of
Green et al. (2019). We have queried a region of the “median” dust reddening
cube with the same pixel size and spatial extent as our CO datacube, which
contains dust reddening along each line-of-sight from distance modulus from 4
mag to 18.725 mag in steps of 0.125 mag. For each 12CO cloud, we derive the
average dust reddening within the projected boundary of the cloud at different
distance modulus, such as panel (a) in Figure 8. The distance of the molecular
cloud is considered to correspond to the distance modulus where there is a
sharp increase of the reddening curve, which also corresponds to a local
maximum of the derivative of the reddening-distance modulus curve, defined as
the dust reddening density. In practice, we use two methods to determine the
“step” in the average reddening-modulus curve of each cloud. The first method
is to determine the distance modulus that corresponds to the minimum of the
second derivative of the reddening versus the distance modulus, as indicated
by the blue dashed line in panel (b) in Figure 8. The second method is to
derive the modulus at which the cross-correlation between the integrated
intensity map and the reddening density map reaches the maximum, as indicated
by the red dashed line in panel (c) in Figure 8. For molecular clouds that
have large angular sizes, such as the Cep GMC in Figure 8, the distances
estimated by the two methods are consistent within 0.25 mag distance modulus.
In this case, the averaged value from the two methods is adopted. For
molecular clouds of small angular size, the distances obtained by the two
methods are usually inconsistent. In this case, we choose the modulus found by
the first method. However, in practice, for some clouds there are multiple
“steps” or no “step” in the reddening-modulus curves. When there are multiple
“steps” in the reddening-modulus curve, we check the average 12CO spectrum of
the cloud and match each step with different velocity components with the rule
of more negative velocity corresponding to larger distance. For those clouds
that no obvious “step” in the reddening-modulus curve is found, the cloud
distance is not assigned. Figure 8 is given as an example of the distance
estimation. We have manually checked the figures for each of the 440 12CO
clouds in the Local arm to estimate their distances. Finally, there are 267
out of the 440 nearby 12CO molecular clouds with distance assigned by using
the extinction method.

In summary, we estimated the distances of the molecular clouds of the Local
arm with the 3D-extinction method, while for the clouds in the Perseus and
Outer$+$OSC arms, we used the kinematic method. The distances of the 13CO
clouds are taken to be that of their counterpart 12CO clouds. For the 13CO
clouds that do not have counterpart 12CO clouds, distances are not assigned.
The relationship of cloud distance with their centroid velocity and the
corresponding histograms are given in Figure 9. As shown in Figure 9, the
molecular clouds in the Local arm are mainly concentrated at two distances,
$\sim$250 and $\sim$750 pc with small dispersions, while the distances of the
molecular clouds in the Perseus arm distributed in a wider range from $\sim$2
to $\sim$6 kpc with the peak at $\sim$3.7 kpc. This different distribution of
cloud distances in the two arms could be related to the different methods used
to derive distance for the two arms. The molecular clouds in the Outer$+$OSC
arms are located in the distance range from $\sim$6 to $\sim$9 kpc without any
concentration. Very few molecular clouds are located in the interarm regions.

Figure 8: Example of distance estimate of molecular clouds using the 3D dust
maps from Green et al. (2019). (a) Average reddening versus distance modulus
of the Cepheus GMC. The blue dashed line shows the distance of the Cepheus
GMC. (b) Dust reddening density, $\Delta E(B-V)/\Delta d$, versus distance
modulus. The blue dashed line marks the distance modulus that corresponds to
the maximum of the $\Delta E(B-V)/\Delta d$ value. (c) Variation of the cross-
correlation between the reddening density map and the 12CO integrated
intensity map of the cloud. The red dashed line shows the distance modulus
that corresponds to the maximum of the cross-correlation. (d) 12CO intensity
map of Cepheus GMC integrated within the PPV mask resulting from the SCIMES
algorithm. (e) Dust reddening density map at the distance modulus indicated by
the blue dashed line in panel (b). (f) Dust reddening density map at the
distance modulus as indicated by the red dashed line in panel (c). (g) Average
spectrum of 12CO emission within the projected boundary of Cepheus GMC. Figure
9: Relationship between the centroid velocities and the distances of the 12CO
clouds. The upper and right panels show the statistics of the centroid
velocity and the distance, respectively. We adopt the extinction distances for
the clouds with velocities $v>-27$ km s-1 and the kinematic distances for the
clouds with velocities $v<-27$ km s-1.

###  3.4 Physical Properties of the Identified Molecular Clouds

The statistical properties of molecular clouds in our Galaxy can provide
insight into understanding their formation, evolution, and environments (Dobbs
et al., 2014). In this section we derive the physical parameters of the
identified 12CO and 13CO clouds.

####  3.4.1 Physical parameters

The centroid position and the velocity dispersion of the identified molecular
cloud are given by the DENDROGRAM+SCIMES algorithms directly, which are
defined as the brightness temperature-weighted first and second moments within
the p-p-v mask of the cloud, respectively (Colombo et al., 2015).

The effective radius of a cloud is derived as the geometric mean of the major
and minor axes of the cloud given by the algorithm, and then deconvoluted with
the HPBW of the PMO-13.7 m telescope,

$R_{eff}=\frac{1}{2}d(\theta_{a}\theta_{b}-\theta_{beam}^{2})^{1/2}$ (1)

where $\theta_{a}$, $\theta_{b}$, are the fitted FWHM along the major and
minor axes of the cloud, and $\theta_{beam}$ is the HPBW of the PMO-13.7 m
telescope, and d is the distance to the cloud. This method means that we
approximate a molecular cloud to a Gaussian ellipsoid, and its projected area
is an ellipse.

The total intensity and the exact area, in units of square arcseconds, of each
cloud are tabulated in the output table of the DENDROGRAM algorithm, which can
be used to calculate the averaged column density of a cloud as follows,

$N_{0}(H_{2})=N_{tot}/num_{p}.$ (2)

where $N_{tot}$ is the total column density of molecular hydrogen, and
$num_{p}$ is the total pixel number of a cloud that can be obtained through
dividing the exact area of a cloud by the pixel size of the data.

For the molecular clouds extracted from the 12CO $J=1-0$ data, the total H2
column density was derived in the same way described in Section 3.2 using the
formula

$N_{tot}=X_{\rm CO}I_{\rm CO},$ (3)

where $I_{\rm CO}$ is the 12CO intensity integrated over the total area of the
cloud and X${}_{\rm CO}=2.0\times 10^{20}$ cm-2 (K km-1)-1 (Bolatto et al.,
2013) is the conversion factor. For the molecular clouds extracted from the
13CO data, we used a different method to derive the total H2 column density
that takes into account the estimate of the gas excitation temperature, the
13CO optical depth, and the variation of the 12C/13C abundance ratio with the
galactocentric distance. In particular, assuming the 13CO molecules are under
the Local Thermodynamic Equilibrium (LTE) condition, the total H2 column
density of the 13CO clouds can be calculated according to

$N_{tot}=A\times 2.42\times
10^{14}\frac{\tau(^{13}CO)}{1-e^{-\tau(^{13}CO)}}\\\
\frac{1+0.88/{T_{ex}}}{1-e^{-5.29/T_{ex}}}I_{{}^{13}CO},$ (4)

where $A$ is a constant related to the abundance ratio to convert the 13CO
column density to H2 column density, $T_{ex}$ is the excitation temperature,
$\tau(\rm{{}^{13}CO})$ is the optical depth at the peak intensity of the 13CO
emission within the boundary of a 13CO cloud, and $I_{\rm{{}^{13}CO}}$ is the
total 13CO integrated intensity. The constant $A$ is the product of the
abundance ratio [12C/13C] = 6.21$d_{GC}$ \+ 18.71 (Milam et al., 2005) and
H2/12CO = $1.1\times 10^{4}$ (Frerking et al., 1982), where $d_{GC}$ is the
cloud distance from the Galactic center. The excitation temperature is
calculated according to Eq. 1 in Li et al. (2018), using the peak intensity of
the 12CO emission within the boundary of the 13CO cloud, while the optical
depth of the 13CO emission is according to Eq. 3 in Li et al. (2018).

The cloud mass, either for the 12CO clouds or the 13CO clouds, is eventually
obtained through

$M=N_{tot}d^{2}\Omega\mu m_{H},$ (5)

where d is the cloud distance, $\Omega$ is the solid angle of each pixel, and
$\mu$ = 2.8 is the atomic weight per molecular hydrogen.

The surface densities and number densities of the clouds are derived as
follows,

$\Sigma=M/(\pi R_{eff}^{2})$ (6) $n(H_{2})=3M/(4\pi R_{eff}^{3}\mu m_{H}).$
(7)

The dynamical state of a molecular cloud is characterized by the virial
parameter, which measures the ratio of the internal kinetic energy to the
gravitational energy. In the literature, there are different forms of the
virial parameter. In this work we follow the definition of Bertoldi & McKee
(1992)

$\alpha_{\rm vir}=\frac{5\sigma_{v}^{2}R_{eff}}{GM},$ (8)

where G is the gravitational constant, $\sigma_{v}$ is the velocity
dispersion. Theoretically, the critical value of $\alpha_{\rm vir}$ for a non-
magnetized isothermal hydrostatic equilibrium sphere is 2 (Kauffmann et al.,
2013). A cloud with a virial parameter above or below the critical value will
eventually dissipate or collapse when not considering other physical
mechanisms beside its self-gravity and internal pressure. We have derived the
virial parameters for each $\rm{{}^{12}CO}$ and $\rm{{}^{13}CO}$ cloud.

All above derived physical parameters of 12CO and 13CO clouds are tabulated in
Tables 2 and 3, respectively. In Table 2 and Table 3, we have listed a total
of 857 12CO molecular clouds and 300 13CO molecular clouds, respectively.
However, the physical parameters, such as effective radius, mass, surface
density, number density, and virial parameter, are only presented for the 684
12CO molecular clouds and 274 13CO molecular clouds that have assigned
distances. The histograms of the physical parameters for the distance-assigned
12CO and 13CO clouds are presented in Figures 11 and 12, respectively, and we
also used the distance assigned clouds as the sample to study the scaling
relations in Section 3.5.

Table 2: Properties of 12CO clouds

Name | l | b | $\theta_{a}$ | $\theta_{b}$ | PA | $v_{lsr}$ | $\sigma_{v}$ | $d$ | $R_{eff}$ | $N_{0}(H_{2})$ | $Mass$ | $\Sigma$ | n | $\alpha_{\rm vir}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| $\arcdeg$ | $\arcdeg$ | $\arcsec$ | $\arcsec$ | $\arcdeg$ | (km s-1) | (km s-1) | (kpc) | (pc) | (cm-2) | (M☉) | (M☉ pc-2) | (cm-3) |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | (15)
MWISP G104.767-03.132-041.32 | 104.767 | -3.132 | 204 | 55 | 93 | -41.32 | 1.08 | 3.73 | 2.21 | 6.5e+20 | 520.0 | 33.8 | 166 | 5.7
MWISP G104.780+02.258-002.08 | 104.780 | 2.258 | 200 | 79 | 95 | -2.08 | 0.49 | … | … | 3.3e+20 | … | … | … | …
MWISP G104.790+01.372-048.22 | 104.790 | 1.372 | 109 | 40 | 162 | -48.22 | 0.62 | 4.32 | 1.55 | 5.5e+20 | 244.2 | 32.4 | 228 | 2.8
MWISP G104.815+01.257-007.89 | 104.815 | 1.257 | 206 | 101 | 127 | -7.89 | 0.74 | … | … | 4.8e+20 | … | … | … | …
MWISP G104.827+00.885-001.44 | 104.827 | 0.885 | 182 | 149 | 75 | -1.44 | 1.16 | 0.23 | 0.22 | 5.1e+20 | 4.8 | 32.7 | 1655 | 70.1
MWISP G104.833+00.155-065.87 | 104.833 | 0.155 | 354 | 152 | 55 | -65.87 | 1.33 | 5.91 | 7.82 | 7.7e+20 | 8169.8 | 42.5 | 59 | 2.0
MWISP G104.845-01.155-013.37 | 104.845 | -1.155 | 224 | 195 | -161 | -13.37 | 1.27 | 0.24 | 0.29 | 7.4e+20 | 8.5 | 31.9 | 1199 | 64.0
MWISP G104.860+02.192+001.67 | 104.860 | 2.192 | 274 | 147 | -165 | 1.67 | 0.53 | … | … | 5.5e+20 | … | … | … | …
MWISP G104.863+01.003-050.03 | 104.863 | 1.003 | 111 | 90 | 124 | -50.03 | 1.05 | 4.48 | 2.51 | 5.6e+20 | 722.7 | 36.5 | 158 | 4.4
MWISP G104.894+03.260-011.29 | 104.894 | 3.260 | 616 | 367 | 62 | -11.29 | 2.47 | … | … | 1.2e+21 | … | … | … | …
MWISP G104.913+02.753-024.20 | 104.913 | 2.753 | 607 | 412 | 106 | -24.20 | 0.82 | 1.73 | 4.93 | 9.8e+20 | 4327.6 | 56.6 | 125 | 0.9
MWISP G104.922+02.575-002.77 | 104.922 | 2.575 | 450 | 246 | 122 | -2.77 | 2.14 | … | … | 4.8e+20 | … | … | … | …
MWISP G104.950+01.082-058.92 | 104.950 | 1.082 | 146 | 45 | 126 | -58.92 | 1.31 | 5.26 | 2.37 | 3.6e+20 | 254.7 | 14.4 | 66 | 18.4
MWISP G104.978+01.130-007.80 | 104.978 | 1.130 | 136 | 53 | -152 | -7.80 | 0.51 | … | … | 3.8e+20 | … | … | … | …
MWISP G104.983-02.678-042.50 | 104.983 | -2.678 | 301 | 79 | 123 | -42.50 | 1.20 | 3.82 | 3.34 | 8.0e+20 | 1117.6 | 31.8 | 103 | 5.0
MWISP G104.985+02.011-020.40 | 104.985 | 2.011 | 409 | 272 | -169 | -20.40 | 2.23 | 1.73 | 3.29 | 1.6e+21 | 5038.7 | 148.2 | 492 | 3.8
MWISP G104.998+00.735-054.11 | 104.998 | 0.735 | 221 | 55 | 175 | -54.11 | 0.77 | 4.82 | 2.99 | 4.3e+20 | 587.6 | 20.9 | 76 | 3.5
MWISP G105.057+02.266-002.05 | 105.057 | 2.266 | 287 | 101 | 159 | -2.05 | 0.43 | 0.35 | 0.34 | 3.3e+20 | 7.6 | 20.7 | 659 | 9.5
MWISP G105.090+02.907-014.19 | 105.090 | 2.907 | 238 | 123 | -140 | -14.19 | 1.77 | … | … | 6.2e+20 | … | … | … | …
MWISP G105.094+01.123-047.81 | 105.094 | 1.123 | 496 | 281 | -176 | -47.81 | 1.90 | 4.27 | 9.11 | 1.4e+21 | 21978.9 | 84.3 | 101 | 1.7
MWISP G105.094-04.029-046.86 | 105.094 | -4.029 | 82 | 62 | 68 | -46.86 | 1.90 | 4.18 | 1.64 | 7.0e+20 | 521.1 | 61.4 | 408 | 13.1
MWISP G105.098+00.853-047.35 | 105.098 | 0.853 | 132 | 99 | 133 | -47.35 | 1.05 | 4.23 | 2.72 | 6.5e+20 | 781.2 | 33.6 | 135 | 4.5
MWISP G105.142+00.322-069.25 | 105.142 | 0.322 | 192 | 119 | -140 | -69.25 | 1.16 | 6.20 | 5.32 | 9.9e+20 | 5337.9 | 59.9 | 122 | 1.6
MWISP G105.151+03.434-009.98 | 105.151 | 3.434 | 212 | 84 | 152 | -9.98 | 0.53 | 0.24 | 0.19 | 1.3e+21 | 13.9 | 129.2 | 7631 | 4.3
MWISP G105.151-01.327-016.15 | 105.151 | -1.327 | 168 | 30 | 158 | -16.15 | 1.04 | … | … | 4.0e+20 | … | … | … | …
MWISP G105.153-00.170-010.70 | 105.153 | -0.170 | 145 | 48 | 145 | -10.70 | 0.70 | … | … | 3.9e+20 | … | … | … | …
MWISP G105.155+02.907-009.07 | 105.155 | 2.907 | 171 | 105 | 70 | -9.07 | 0.62 | … | … | 4.6e+20 | … | … | … | …
MWISP G105.212+00.698-061.54 | 105.212 | 0.698 | 120 | 51 | 178 | -61.54 | 0.92 | 5.48 | 2.37 | 4.0e+20 | 445.7 | 25.2 | 116 | 5.2
MWISP G105.212-01.181-014.72 | 105.212 | -1.181 | 222 | 85 | -174 | -14.72 | 0.90 | 0.65 | 0.50 | 6.7e+20 | 30.4 | 38.0 | 822 | 15.5
MWISP G105.230+00.787-052.97 | 105.230 | 0.787 | 263 | 93 | -173 | -52.97 | 1.14 | 4.71 | 4.19 | 7.7e+20 | 3044.2 | 55.1 | 143 | 2.1
MWISP G105.231+00.479-051.08 | 105.231 | 0.479 | 124 | 71 | 68 | -51.08 | 1.50 | 4.54 | 2.38 | 4.7e+20 | 585.4 | 32.8 | 150 | 10.6
MWISP G105.247-00.284-034.00 | 105.247 | -0.284 | 98 | 67 | 176 | -34.00 | 0.66 | 3.07 | 1.38 | 7.6e+20 | 313.4 | 52.1 | 411 | 2.3
MWISP G105.262+01.329-009.19 | 105.262 | 1.329 | 392 | 187 | 152 | -9.19 | 1.21 | … | … | 7.8e+20 | … | … | … | …
MWISP G105.275+00.360-011.72 | 105.275 | 0.360 | 219 | 114 | 120 | -11.72 | 0.67 | … | … | 5.9e+20 | … | … | … | …
MWISP G105.276-03.925-042.92 | 105.276 | -3.925 | 80 | 58 | 117 | -42.92 | 1.16 | 3.83 | 1.43 | 4.8e+20 | 216.8 | 33.9 | 259 | 10.2

Note. — The source name is defined under the MWISP standard. According to the
MWISP standard for nomenclature, molecular clouds are named after their
centroid positions and velocities. Specifically, the names start with “MWISP”
and then contain the spatial coordinates of the molecular clouds accurate to
three decimal places and the centroid velocities accurate to two decimal
places. The accuracy is set according to the pointing accuracy and the
velocity resolution of the PMO-13.7m telescope. Columns 2$-$6 give the
centroid positions, the intensity-weighted major and minor axes, and the
position angles of the clouds. The centroid velocity, the velocity dispersion,
and the distance of the clouds are presented in columns 7$-$9\. Columns
10$-$15 list the effective radius, average column density, mass, surface
density, number density, and the virial parameters of the clouds,
respectively.

This table is available in its entirety in machine$-$readable form in the
online material.

Table 3: Properties of 13CO clouds

Name | l | b | $\theta_{a}$ | $\theta_{b}$ | PA | $v_{lsr}$ | $\sigma_{v}$ | $d$ | $R_{eff}$ | $T_{ex}$ | $\tau_{{}^{13}CO}$ | $N_{0}(H_{2})$ | $Mass$ | $\Sigma$ | n | $\alpha_{\rm vir}$ | Name of matching 12CO cloud
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| $\arcdeg$ | $\arcdeg$ | $\arcsec$ | $\arcsec$ | $\arcdeg$ | (km s-1) | (km s-1) | (kpc) | (pc) | (K) |  | cm-2 | (M☉) | (M☉ pc-2) | cm-3 |  |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18)
MWISP G104.794+03.498-008.57 | 104.794 | 3.498 | 199 | 85 | 114 | -8.57 | 1.04 | … | … | … | … | … | … | … | … | … | …
MWISP G104.806+00.169-052.16 | 104.806 | 0.169 | 153 | 104 | 154 | -52.16 | 0.74 | 4.63 | 3.30 | 12.6 | 0.4 | 1.3e+21 | 3767.9 | 110.1 | 364 | 0.5 | MWISP G105.389+00.275-052.19
MWISP G104.829+02.795-024.17 | 104.829 | 2.795 | 283 | 145 | 91 | -24.17 | 0.57 | 1.73 | 1.99 | 10.1 | 0.7 | 2.5e+21 | 991.6 | 79.5 | 435 | 0.8 | MWISP G104.913+02.753-024.20
MWISP G104.967+01.333-000.91 | 104.967 | 1.333 | 261 | 109 | 82 | -0.91 | 0.55 | 0.41 | 0.39 | 10.2 | 0.6 | 1.3e+21 | 29.3 | 60.3 | 1675 | 4.7 | MWISP G106.122+00.579-002.93
MWISP G105.022+01.990-020.39 | 105.022 | 1.990 | 347 | 156 | -164 | -20.39 | 1.90 | 1.73 | 2.29 | 9.5 | 0.4 | 1.8e+21 | 723.6 | 43.9 | 209 | 13.2 | MWISP G104.985+02.011-020.40
MWISP G105.031+00.105-049.45 | 105.031 | 0.105 | 177 | 48 | 168 | -49.44 | 0.55 | 4.63 | 2.40 | 9.6 | 0.2 | 2.0e+20 | 564.0 | 31.2 | 142 | 1.5 | MWISP G105.389+00.275-052.19
MWISP G105.088+03.180-010.45 | 105.088 | 3.180 | 161 | 84 | 173 | -10.45 | 0.74 | … | … | … | … | … | … | … | … | … | …
MWISP G105.102+01.089-046.99 | 105.102 | 1.089 | 202 | 178 | 50 | -46.99 | 1.19 | 4.27 | 4.60 | 11.7 | 0.6 | 3.2e+21 | 7846.6 | 118.1 | 280 | 1.0 | MWISP G105.094+01.123-047.81
MWISP G105.237+00.781-052.64 | 105.237 | 0.781 | 183 | 60 | -172 | -52.64 | 0.84 | 4.71 | 2.78 | 7.8 | 0.3 | 2.4e+20 | 699.0 | 28.7 | 112 | 3.2 | MWISP G105.230+00.787-052.97
MWISP G105.269+05.089-008.95 | 105.269 | 5.089 | 200 | 65 | -137 | -8.95 | 0.95 | 0.87 | 0.56 | 14.8 | 0.3 | 6.1e+20 | 60.7 | 62.2 | 1219 | 9.6 | MWISP G106.529+04.081-007.04
MWISP G105.471-01.101-007.97 | 105.471 | -1.101 | 206 | 67 | 123 | -7.97 | 0.57 | 0.26 | 0.17 | 12.2 | 0.3 | 4.1e+20 | 3.8 | 40.1 | 2520 | 17.5 | MWISP G105.691-01.341-008.22
MWISP G105.504+01.705-020.42 | 105.504 | 1.705 | 126 | 54 | -178 | -20.42 | 0.83 | 1.73 | 0.79 | 8.5 | 0.3 | 1.3e+20 | 51.1 | 26.0 | 359 | 12.4 | MWISP G106.064+01.491-023.45
MWISP G105.505-01.254-008.59 | 105.505 | -1.254 | 174 | 37 | 100 | -8.59 | 0.90 | 0.26 | 0.12 | 10.8 | 0.2 | 1.2e+20 | 1.1 | 25.6 | 2393 | 99.4 | MWISP G105.691-01.341-008.22
MWISP G105.630+03.365-008.76 | 105.630 | 3.365 | 524 | 148 | 168 | -8.76 | 1.67 | 0.87 | 1.38 | 20.5 | 0.6 | 1.1e+22 | 1076.0 | 180.4 | 1429 | 4.2 | MWISP G106.529+04.081-007.04
MWISP G105.632+00.341-052.38 | 105.632 | 0.341 | 649 | 210 | 145 | -52.38 | 1.38 | 4.63 | 9.76 | 25.7 | 0.4 | 1.9e+22 | 54287.3 | 181.3 | 202 | 0.4 | MWISP G105.389+00.275-052.19
MWISP G105.665+04.784-008.20 | 105.665 | 4.784 | 221 | 106 | 66 | -8.20 | 0.48 | 0.87 | 0.75 | 17.7 | 0.5 | 1.8e+21 | 185.0 | 104.5 | 1520 | 1.1 | MWISP G106.529+04.081-007.04
MWISP G105.751+00.778-003.26 | 105.751 | 0.778 | 986 | 515 | 61 | -3.26 | 0.70 | 0.41 | 1.67 | 10.8 | 0.8 | 2.0e+22 | 451.3 | 51.7 | 338 | 2.1 | MWISP G106.122+00.579-002.93
MWISP G105.774+02.876-004.31 | 105.774 | 2.876 | 265 | 132 | 87 | -4.31 | 0.91 | 0.87 | 0.92 | 9.7 | 0.6 | 1.4e+21 | 144.9 | 54.5 | 647 | 6.1 | MWISP G106.529+04.081-007.04
MWISP G105.792+01.622-023.18 | 105.792 | 1.622 | 390 | 174 | -141 | -23.18 | 0.93 | 1.73 | 2.57 | 11.2 | 0.7 | 4.3e+21 | 1719.0 | 83.0 | 353 | 1.5 | MWISP G106.064+01.491-023.45
MWISP G105.793-00.577-037.50 | 105.793 | -0.577 | 132 | 49 | 102 | -37.50 | 1.01 | 3.27 | 1.46 | 11.9 | 0.4 | 5.7e+20 | 807.9 | 120.3 | 898 | 2.1 | MWISP G105.798-00.603-036.76
MWISP G105.821-00.098-054.00 | 105.821 | -0.098 | 182 | 32 | -178 | -53.99 | 0.40 | 4.63 | 1.94 | 11.7 | 0.3 | 2.1e+20 | 598.0 | 50.5 | 284 | 0.6 | MWISP G105.389+00.275-052.19
MWISP G105.837+00.260-051.09 | 105.837 | 0.260 | 182 | 69 | 82 | -51.09 | 0.83 | 4.63 | 2.92 | 17.4 | 0.3 | 9.3e+20 | 2655.8 | 99.0 | 370 | 0.9 | MWISP G105.389+00.275-052.19
MWISP G105.855+04.123-008.87 | 105.855 | 4.123 | 897 | 702 | 67 | -8.87 | 1.47 | 0.87 | 3.92 | 31.4 | 0.4 | 9.0e+22 | 8987.6 | 185.8 | 517 | 1.1 | MWISP G106.529+04.081-007.04
MWISP G106.116+03.034-007.74 | 106.116 | 3.034 | 158 | 71 | 54 | -7.74 | 0.50 | 0.87 | 0.52 | 9.4 | 0.3 | 2.0e+20 | 20.2 | 24.3 | 514 | 7.4 | MWISP G106.529+04.081-007.04
MWISP G106.196+01.399-022.05 | 106.196 | 1.399 | 219 | 199 | 72 | -22.06 | 1.01 | 1.73 | 2.05 | 9.4 | 0.5 | 1.0e+21 | 397.9 | 30.2 | 160 | 6.1 | MWISP G106.064+01.491-023.45
MWISP G106.267+00.046-056.07 | 106.267 | 0.046 | 310 | 162 | 46 | -56.07 | 1.03 | 4.87 | 6.20 | 14.8 | 0.3 | 1.7e+21 | 5260.1 | 43.5 | 76 | 1.5 | MWISP G106.342-00.084-055.73
MWISP G106.325+01.239-028.09 | 106.325 | 1.239 | 126 | 53 | 59 | -28.09 | 0.65 | 1.73 | 0.78 | 8.8 | 0.3 | 1.1e+20 | 44.8 | 23.2 | 323 | 8.5 | MWISP G106.064+01.491-023.45
MWISP G106.339+03.276-006.58 | 106.339 | 3.276 | 582 | 309 | 56 | -6.58 | 0.96 | 0.87 | 2.10 | 12.6 | 0.3 | 3.4e+21 | 344.2 | 24.9 | 129 | 6.6 | MWISP G106.529+04.081-007.04
MWISP G106.460+00.896-053.92 | 106.460 | 0.896 | 217 | 103 | 135 | -53.92 | 0.72 | 4.70 | 3.98 | 12.7 | 0.5 | 1.7e+21 | 5034.3 | 101.0 | 277 | 0.5 | MWISP G106.475+00.931-053.87
MWISP G106.481+03.112-011.21 | 106.481 | 3.112 | 201 | 110 | 147 | -11.21 | 0.67 | 0.87 | 0.73 | 17.2 | 0.8 | 5.4e+21 | 545.0 | 325.6 | 4873 | 0.7 | MWISP G106.529+04.081-007.04
MWISP G106.523+00.507-056.03 | 106.523 | 0.507 | 157 | 72 | 170 | -56.03 | 0.55 | 4.87 | 2.92 | 8.9 | 0.4 | 3.8e+20 | 1207.1 | 45.1 | 168 | 0.8 | MWISP G106.440+00.388-055.76
MWISP G106.534+01.262-026.82 | 106.534 | 1.262 | 192 | 88 | 175 | -26.82 | 0.69 | 1.73 | 1.27 | 9.2 | 0.5 | 7.6e+20 | 302.1 | 59.8 | 515 | 2.3 | MWISP G106.064+01.491-023.45
MWISP G106.554+00.932-012.42 | 106.554 | 0.932 | 350 | 275 | 81 | -12.42 | 0.78 | 0.65 | 1.15 | 15.0 | 0.7 | 1.4e+22 | 781.1 | 188.1 | 1787 | 1.0 | MWISP G106.663+01.012-011.66
MWISP G106.562+01.048-061.18 | 106.562 | 1.048 | 310 | 196 | 157 | -61.18 | 0.87 | 5.34 | 7.50 | 19.4 | 0.3 | 4.2e+21 | 16173.9 | 91.5 | 133 | 0.4 | MWISP G106.492+01.037-061.09
MWISP G106.693+03.364-007.26 | 106.693 | 3.364 | 304 | 204 | 106 | -7.26 | 0.53 | 0.87 | 1.23 | 8.6 | 0.5 | 8.1e+20 | 81.4 | 17.2 | 152 | 4.8 | MWISP G106.529+04.081-007.04

Note. — Same as Table 2 but for 13CO clouds. Columns 2$-$6 give the centroid
positions, the intensity-weighted major and minor axes, and the position
angles of the clouds. The centroid velocity, the velocity dispersion, and the
distance of the clouds are presented in columns 7$-$9\. Columns 10$-$17 list
the derived parameters of the clouds, i.e., effective radius, excitation
temperature, the optical depth of 13CO emission, average column density, mass,
surface density, number density, and the virial parameters of the clouds,
respectively. The last column gives the name of the 12CO cloud that matches
the 13CO cloud in column 1.

This table is available in its entirety in machine$-$readable form in the
online material.

####  3.4.2 Size and Mass of the Clouds

The histograms of the effective radius of the 12CO and 13CO clouds are given
in Figures 11 and 12, respectively. More than half of the 12CO and 13CO clouds
have sub-pc sizes. In the conventional classification scheme of molecular gas
structures, these molecular entities should be classified as molecular clumps,
but, for simplicity, we still refer to them as “clouds” in this work. The
median radius of the 12CO molecular clouds in the Local and Perseus arms are
$\sim$0.5 and $\sim$3.0 pc, respectively, while the values are $\sim$0.7 and
$\sim$2.8 pc for the 13CO molecular clouds. The distributions of the mass of
the 12CO and 13CO clouds are presented in Figures 11 and 12. The median mass
of 12CO molecular clouds in the Local, Perseus, and Outer$+$OSC arms is
$\sim$20 M⊙, $1\times 10^{3}$ M⊙, and $2\times 10^{3}$ M⊙, respectively. The
median mass of the 13CO clouds in the Local and Perseus arms is 70 and
$2\times 10^{3}$ M⊙, respectively, which is moderately larger than that of the
12CO clouds. Generally, the molecular clouds in the Perseus and Outer$+$OSC
arms are much larger and more massive than the molecular clouds in the Local
arm. The possible reasons for the systematic difference between the median
radii and masses in the Local and Perseus arms are as follows.

First, the distance selection effect, i.e., only the molecular clouds that are
larger and more massive than the sensitivity limit can be detected, regardless
of their distance. The output molecular clouds of the SCIMES algorithm have
similar minimum angular sizes, $\sim$50 ″, and similar minimum total
integrated-intensities, $\sim$66 K km s-1, at different distances, as shown in
Figures 10 and 10. The minimum angular size and integrated-intensity
correspond to the minimum effective radius and mass that increase with
distance, therefore causes the non-detection of the smaller and less massive
clouds at the higher distances. Figures 10 and 10 shows the variation of the
effective radius and the mass of the 12CO clouds as a function of the cloud
distance. The minimum effective radius at 1 and 7.5 kpc, taken as the
reference upper limit distances of the Local and Perseus arms, is $\sim$0.25
and $\sim$1.9 pc, respectively, as shown in Figure 10, while the minimum mass
at these distances is $\sim$6 and $\sim$349 M☉, respectively. The finite
spatial resolution of our observations introduces an additional bias due to
the fact that the minimum projected angular distance on the sky between two
clouds that allows us to identify them as separate structures increases with
their distance. For this reason, clouds close to each other are seen as one
larger cloud at higher distances. Second, different methods are used in the
distance estimation for the clouds in the two arms. We find that the distance
estimated with the dust extinction map is usually smaller than the kinematic
distance. In addition, the distances of the molecular clouds in the Perseus
arm are also overestimated because of the kinematic abnormality of the Perseus
arm. Third, same settings and criteria are used with the SCIMES algorithm to
identify clouds in different spiral arms. It can be seen from Figures 10 and
10 that the clouds identified by the SCIMES algorithm have similar angular
sizes and total integrated intensities in the Local and Perseus arms,
therefore, the molecular clouds are inevitably less massive in the Local arm
than in the Perseus arm.

Figure 10: Variation versus distance of (a) the angular size, which is defined
as the geometric mean of the intensity weighted second-moment of the spatial
scale along the major and minor axes, (b) the effective radius, (c) the total
integrated intensity, and (d) the mass of the 12CO clouds. The red dashed
lines in panels (a) and (c) represent the minimum angular size and minimum
total integrated-intensity that detected from nearby to a distance of 7.5 kpc.
The red dashed lines in panels (b) and (d) are the minimum effective radius
and minimum mass corresponding to the minimum angular size and total
integrated-intensity at different distances.

Figure 11: Distributions of (a) effective radii, (b) masses from the XCO
method, (c) mass surface densities, (d) number densities, and (e) velocity
dispersions, of the identified 12CO clouds. The red and the blue dashed lines
in panels (a) and (b) give the power-law fitting of the distribution of the
radius and the mass of the clouds respectively, with the blue dashed lines for
the clouds in the Local arm and the red dashed lines for the clouds in the
Perseus arm. The blue and red dotted vertical lines in panel (a) and (b)
indicate the minimum values of the radius and mass at the distances of the
clouds in the Local and the Perseus arms, respectively. The green vertical
line in panel (c) marks the surface density corresponding to the star
formation threshold of column density, i.e., $6.3\times 10^{21}$ cm-2
(Johnstone et al., 2004; Lada et al., 2010; Kainulainen et al., 2014).

Figure 12: Same as Figure 11, but for 13CO clouds. The mass of the 13CO clouds
is calculated using the LTE method.

In the concept that molecular clouds are overdense sub-structures of the
turbulent, multi-phase fractal ISM (Scalo, 1988), the distributions both of
the size and the mass of the clouds possess power-law forms, $dN/dR\propto
R^{\alpha_{R}}$ $dN/dM\propto M^{\alpha_{M}}$, where $dN$ is the number of
clouds in the interval of $dR$ or $dM$. Instead of fitting $dN$ in equally
separated radius bins, we fitted the linear relationship between $\lg dN$ and
$\lg R$ (and $\lg M$) taking account of statistic errors, where $dN$, in this
case, is the number in each logarithmic bin. The resulting exponent in the
relation $dN/d(lgR)\propto R^{\beta}$ is related to $\alpha_{R}$ through
$\beta=1+\alpha_{R}$, and the same for the mass. The minimum effective radii
(or mass) of the 12CO clouds at the reference position of the Local and Pesrus
arms are near the peaks of their $\lg R$ (or $\lg M$) distributions.
Therefore, we consider them as a reasonable estimate of the completeness limit
of the radius (or mass) distribution, and fitted the distribution from the
center of the bin with the peak values of $dN$ to the center of the bin of the
largest $\lg R$ (or $\lg M$).

As shown in Figure 11, the measured exponent, $\alpha_{R}$, in the Local arm
is $-1.75$, while in the Perseus arm is $-2.42$. The exponents for the radius
distribution of the 13CO clouds are slightly smaller than the above values,
which are $-1.78$ and $-2.54$ for the Local and Perseus arms, respectively.
The best-fit of the power-law distribution $dN/dM\propto M^{\alpha}_{M}$ is
$\alpha_{M}=-1.40$ for the Local arm and $\alpha_{M}=-1.59$ for the Perseus
arm. The radius distributions derived in this work are shallower than those of
the OGS and GRS survey, $\alpha_{R}=-$3.2 in the OGS survey (Heyer et al.,
2001) and $\alpha_{R}=-$3.9 in the GRS survey (Roman-Duval et al., 2010), and
also shallower than the result $\alpha_{R}\sim-3.3$ from Elmegreen & Falgarone
(1996) by compiling size measurements of clumps and clouds. The mass
distribution is also shallower than those obtained by Rice et al. (2016) from
molecular clouds in the outer Galaxy, $\alpha_{M}$ = $-$2.2. A possible
explanation for the difference between our results and the above previous
results is that different methods of cloud identification are used in these
studies. For example, the CLUMPFIND algorithm used by Roman-Duval et al.
(2010) tends to separate molecular clouds into several small-scale structures
(Li et al., 2020). On the contrary, in this work, we aim at identifying large
structures that contain at least 50 voxels in p-p-v space. Besides, the SCIMES
algorithm uses a clustering process to merge the connecting “leaves” into a
cloud, tending to connect small structures into a large one.

####  3.4.3 Surface Density and Number Density

Figures 11 and 11 present the distributions of $\Sigma$ and $n_{H_{2}}$ of the
12CO molecular clouds, and the corresponding distributions of the 13CO
molecular clouds are given in Figure 12 and 12. The median mass surface
densities of the 12CO clouds in the Local, Perseus, and Outer$+$OSC arms are
$\sim$33, $\sim$45, and $\sim$26 $\rm{M_{\sun}\ pc^{-2}}$, respectively, and
the corresponding values of the 13CO clouds in the Local and the Perseus arms
are $\sim$44 and $\sim$89 $\rm{M_{\sun}\ pc^{-2}}$. In the Local arm, about
63% of the total mass of the 12CO clouds is contained in the clouds with
surface densities above the threshold for star formation, $\rm{\sim 140\
M_{\sun}\ pc^{-2}}$ (corresponds to N$\rm{}_{H2}{\sim 6.3\times 10^{21}}$
cm-2) (Johnstone et al., 2004; Lada et al., 2010; Kainulainen et al., 2014),
and the percentage is 88% in the Perseus arm.

The maximum surface densities of the 12CO and 13CO molecular clouds are 431
and 1703 $\rm{M_{\sun}\ pc^{-2}}$, which correspond to H2 column densities of
1.9$\times\ 10^{22}$ and 7.7$\times\ 10^{22}$ cm-2, respectively. The maximum
densities are located in the NGC 7538 GMC. Urquhart et al. (2013) suggested a
lower limit of mass surface density of 0.05 g cm-2 for massive star formation,
which corresponds to H2 column density $\sim$1.1$\rm{\times 10^{22}\
cm^{-2}}$. The mass surface density of the NGC 7538 GMC is much higher than
this limit, which is consistent with the observed concentration of CH3OH
masers within it (Moscadelli & Goddi, 2014), testifying the presence of high-
mass star formation activity in this region. We also checked the positions of
other five 12CO molecular clouds with mass surface densities above 0.05 g cm-2
and found that these molecular clouds are all located in the Perseus arm and
that they are associated with H II regions or H II region candidates (Anderson
et al., 2014).

The distributions of the number density of the 12CO and 13CO molecular clouds
in different spiral arms are shown in Figures 11 and 12, respectively. The
median values of $n_{H_{2}}$ of 12CO molecular clouds in the Local, Perseus,
and Outer$+$OSC arms are 648, 157, and 61 cm-3, respectively, while the
corresponding values of 13CO molecular clouds in the Local and Perseus arms
are 786 and 326 cm-3. The measured number densities of molecular clouds in the
Local arm is systematically higher than that in the Perseus and the
Outer$+$OSC arms with both 12CO and 13CO as the tracer, which may indicate a
bias and/or a systematic effect in the estimation of this parameter. This
consideration is also supported by the fact that the median number density of
the distant (d$>$2 kpc) molecular clouds is much below the critical density of
the 12CO and 13CO $J=1-0$ transition, $\sim$700 cm-3. One possible reason is
that the number density is a distance-dependent parameter. Therefore the same
caveats listed in the previus subsection for mass and distance are valid also
for the number density. In particular, it scales with $R_{eff}$ as $n\sim
R_{eff}^{p}$, where $p$ is in the range from $\sim-$0.6 to $\sim-$0.8 in this
work (see the scaling relations in Section 3.5). The dependence means that
when the distance, so is the $R_{eff}$, is overestimated by a factor of two,
which is the case for the massive star-forming region W3(OH) in the Perseus
arm (Xu et al., 2006), the number density could be underestimated for
$\sim$34% to $\sim$43%. However, even if this effect is corrected, the number
density in the Perseus arm is still much less than the 12CO critical density.
Another possible factor to cause underestimation is that the volume filling
factor of the 12CO and 13CO emission for the molecular clouds in the Perseus
arm is low. In other words, there are fine internal structures in the
molecular clouds that can not be resolved by the beam of the PMO-13.7m
telescope at the distance of the Perseus arm. Metaphorically speaking, there
could be “holes” in the molecular clouds that cause dilution of the molecular
line emission in the beam of the telescope.

####  3.4.4 Velocity Dispersion

The derived total velocity dispersion within the boundary of a given cloud
includes the contributions from the internal thermal motion and non-thermal
turbulence. As shown in Figure 11, the median velocity dispersions of 12CO
molecular clouds in the two spiral arms are similar, $\sim 1.1\ \rm{km\
s^{-1}}$. However the proportion of the molecular clouds with velocity
dispersions greater than 1.5 km s-1 is larger in the Perseus arm than that in
the Local arm. Most of the molecular clouds in the Perseus arm with
$\sigma_{v}>4\ \rm{km\ s^{-1}}$ are associated with or located in the vicinity
of H II regions like S 163, S 157, and NGC 7538, indicating complex dynamics
in these regions. The median values of $\sigma_{v}$ of the 13CO molecular
clouds in the Local and Perseus arms are 0.8 and 1.1 km s-1, respectively,
similar to that of the 12CO molecular clouds. The distribution and median
values of $\sigma_{v}$ from this work is consistent with that of the molecular
clouds in the solar circle (Roman-Duval et al., 2010), and the results from
the OGS survey (Heyer et al., 2001). Miville-Deschênes et al. (2017) used a
multi-Gaussian decomposition method to re-analysis the dataset from Dame et
al. (2001), and their results are nearly $\sim$2.1 times as large as our
results. This difference may be caused by the coarse velocity resolution (1.3
km s-1) of the CfA survey.

####  3.4.5 Surface Density Variation Across the Galactocentric Distance

Figure 13: Variation of the surface densities of molecular clouds as a
function of the galactocentric distances. The radii of the circles correspond
to the sizes of the clouds and the color shades correspond to the masses of
the clouds. The red diamonds are the average surface densities calculated
through dividing the total mass with the total area of all the clouds in each
interval of galactocentric distance of 0.5 kpc. The black pluses show the
medium surface density in each interval. The scatter of the medium surface
density in each interval is indicated in the figure, which is defined as the
square root of the mass-weighted mean squared deviation from the medium
surface density in each interval. The lower-ends of the error bars of the
first six median values are negative and are not displayed.

Heyer & Dame (2015) have made from the literature a compilation of the cloud
surface density $\Sigma$ across the Galactocentric distance and found that the
surface densities of the molecular clouds in the inner Galaxy are
significantly higher than those in the outer Galaxy. Observations have shown
that $\Sigma$ in the outer Galaxy decreases exponentially as a function of the
Galactocentric distance (Wouterloot et al., 1990). This kind of radial
distribution of $\Sigma$ toward the outer Galaxy is confirmed by the re-
decomposition of the CO data from the CfA survey (Miville-Deschênes et al.,
2017). The surface densities of the 12CO clouds toward the observed region are
shown as a function of the galactocentric distance in Figure 13. The median
surface density of the clouds in each 0.5 kpc bin first increases from
$\sim$30 to $\sim$50 $\rm{M_{\sun}\ pc^{-2}}$ from d${}_{GC}=$8.5 to 9 kpc,
remains at around $\sim$45 $\rm{M_{\sun}\ pc^{-2}}$ from 9 to 11 kpc, and then
slightly decreases to $\sim$30 $\rm{M_{\sun}\ pc^{-2}}$ at 12.5 kpc. The
scatter of $\Sigma$ in each dGC bin is significant. The median $\Sigma$
obtained in this work is comparable to the compiled results in Heyer & Dame
(2015) and substantially lower than the surface density in the inner galaxy,
$\sim$170 $\rm{M_{\sun}\ pc^{-2}}$ (Roman-Duval et al., 2010; Heyer & Dame,
2015). The average surface density in galactocentric distance interval of 0.5
kpc is calculated as the total mass of the clouds divided by the total area of
the clouds. We can see that the average surface density is higher than the
median $\Sigma$ in the range of d${}_{GC}<11.5$ kpc, especially at the
distance of the Perseus arm ($d_{GC}\sim 9.5-10.5\ kpc$). This difference is
reasonable as we can see in Figure 13 that the large and massive molecular
clouds at these distances also have higher surface densities than the smaller
and less massive ones.

###  3.5 Scaling Relations and Equilibrium States of the molecular clouds

In this section, we present the scaling relations between the measured
physical parameters of molecular clouds.

Figure 14: (a) M$-$R relation of the 12CO clouds, (b) line-width$-$size
relation, (c) distribution of the virial parameters, (d) the relationship
between the virial parameters and the masses, and (e) the relationship between
$\sigma_{v}^{2}/R$ and surface density of the 12CO clouds. The orange shaded
area in panel (a) is the region defined by the M-R relations, found by
Bressert et al. (2012), for the molecular clouds capable of forming massive
proto clusters. The grey shaded area in panel (a) is the region where the
clouds cannot form high-mass stars according to the relation $M(R)\leqslant
870M_{\sun}(r/pc)^{1.33}$ of Kauffmann et al. (2010b). The grey dashed lines
in this panel indicate the empirical upper and lower bounds of the cloud
surface density of 1 g cm-2 and 0.05 g cm-2 for massive star formation
(Urquhart et al., 2013). The grey shaded area in panel (c) indicates
$\alpha_{\rm vir}<2$. The fraction of the clouds with $\alpha_{\rm vir}$ less
than 2 are shown in the top$-$right corner in panel (c). The fitted M$-$R,
$\sigma_{v}-$R, and M$-\alpha$ relations of the clouds in the Local and the
Perseus arms are shown in blue and in red in panels (a), (b), and (d),
respectively.

Figure 15: Same as Figure 14, but for 13CO clouds.

####  3.5.1 Mass-radius relation

Larson’s third law (Larson, 1981) states that molecular clouds have a constant
surface density which means that molecular clouds have a scaling relationship
between their masses and radii of the form of $M\propto R^{2}$. However, the
power-law exponent in the M-R relation is found to be a probe of the internal
density distribution of molecular fragments on the sub-pc to pc scales
(Kauffmann et al., 2010a, b). Observations of molecular clouds have shown that
the stellar cluster forming clumps are more massive than those clumps devoid
of stellar clusters although they have the same size (Rathborne et al., 2006;
Portegies Zwart et al., 2010; Walsh et al., 2011; Bressert et al., 2012).
Kauffmann et al. (2010b) obtained the empirical relationship $M(R)\geqslant
870M_{\sun}(R/pc)^{1.33}$ for molecular clouds capable to form massive stars.

The M-R relations of the 12CO clouds in the Local and Perseus arms are
presented in Figure 14. They can be well fitted with power-law functions of
exponents $\sim$2.2 in a broad range of radius from $\sim 0.06$ to $\sim 40$
pc. None of the 12CO molecular clouds are distributed in the region of the M-R
parameter space capable of hosting massive proto clusters following the
prescription of Bressert et al. (2012). However, five molecular clouds have
surface mass densities above the lower limit of massive star formation given
by Urquhart et al. (2013) and they are all associated with H II regions. The
M-R relations for the 13CO clouds are presented in Figure 15 and the fitted
power-law exponents of the 13CO clouds in the Local and Perseus arms are $\sim
2.4$, suggesting non-uniform inner densities. Most of the 13CO molecular
clouds located above both the grey shaded area and the 0.05 g cm-2 limit for
possible massive star formation (Urquhart et al., 2013) in Figure 15
correspond to active star-forming regions in the Local arm, such as Cep OB3
and L1188 GMCs, and the molecular clouds in the Perseus arm that are
associated with H II regions. Notably, the four molecular clouds that fall in
the region for massive proto-cluster candidates are all associated with H II
regions, namely NGC 7538, S157, and S152. These GMCs are candidate regions for
massive cluster formation.

####  3.5.2 Velocity Dispersion-Size relation

The resemblance of the exponent in the scaling relation $\sigma_{v}\propto
R^{0.38}$, found by Larson (1981), to that in the velocity structure-function
of incompressible turbulence (Kolmogorov, 1941) reminds us of the important
role of turbulence in molecular clouds. Observationally, Solomon et al. (1987)
found that the scaling relationship between $\sigma_{v}$ and $R$ is better
confined with a steeper power-law with an exponent of 0.5. This exponent has
been further confirmed by Heyer et al. (2009) using the GRS data with improved
spatial and spectral resolution. The interpretation of this relationship is
attributed to the simple virial equilibrium state of the molecular cloud.

The $\sigma_{v}-R$ relationship of the 12CO and 13CO clouds are presented in
Figures 14 and 15, respectively. The power-law exponents of the 12CO and 13CO
clouds in the Local arm are 0.27 and 0.29, respectively. The exponents of the
clouds in the Perseus arm are larger, 0.44 and 0.43 for 12CO and 13CO clouds,
respectively. The Pearson correlation coefficients of the fitted
$\sigma_{v}-R$ relations for the two arms lie in the range from 0.42 to 0.55.
The Larson’s relation with the exponent of 0.38 is also drawn in Figures 14
and 15 with grey dotted lines for comparison. The difference between the
scaling exponents of the molecular clouds in the Local and Perseus arms
possibly indicates different importance of turbulence in molecular clouds at
different Galactocentric distances. Traficante et al. (2018) and Benedettini
et al. (2020) suggested the presence of two different regimes in the
$\sigma_{v}-R$ relationship, with a quite flat power law for the smaller
clouds with radius below $\sim$2 pc and a steeper power law for the larger
clouds with radius above $\sim$2 pc. The exponents obtained in this work are
consistent with their suggestions in that the Local arm (smaller) clouds
exhibit a smaller exponent (0.27) than the Perseus arm (larger) clouds (0.44).

####  3.5.3 Equilibrium State of the Molecular Clouds

Figures 14 and 15 display the distribution of the virial parameters of the
12CO and 13CO clouds, respectively, and also show the portion of the
gravitationally bound ($\alpha_{\rm vir}\leq 2$) molecular clouds in each arm.
A subcritical ($\alpha_{\rm vir}>2$) cloud will dissipate unless an external
pressure from the environment can help to confine the cloud, while a
supercritical ($\alpha_{\rm vir}\ll 2$) cloud will collapse within a few free
fall time scales unless some other physical processes like the magnetic field
are included in supporting the cloud against gravity. The virial parameters of
the 12CO clouds in the Local arm span a broad range from $\sim$1 to
$\sim$1000, while those of the 12CO clouds in the Perseus arm lie in the range
from $\sim$0.3 to $\sim$60\. However, the virial parameters of the 13CO clouds
are much smaller, from $\sim$0.4 to $\sim$99 with an average of $\sim$7.5 for
the clouds in the Local arm and $\sim$0.1 to $\sim$25 with an average of
$\sim$1.6 for the clouds in the Perseus arm. The virial parameters of the 12CO
clouds in the Outer$+$OSC arm distributed within the range of $\alpha_{\rm
vir}$ from $\sim$1 to $\sim$10\. The majority, $\sim$98.1%, of the 12CO clouds
in the Local arm are gravitationally unbound, whereas in the Local and Perseus
arms, 19.1% and 58.2% of the 13CO clouds are gravitationally bound,
respectively. The systematic difference of the virial parameter between the
clouds in the Local and the Perseus arms may indicate different dynamical
states of molecular clouds in the two arms. However, the percentage of the
gravitationally bound clouds is distance-dependent, since the detection of
small and less massive molecular clouds is not complete in the Perseus arm.
Besides, based on the scaling relation we have obtained in Figures 14 and 15,
the virial parameters of the molecular clouds in the Perseus arm are
proportional to $R_{eff}^{-0.3\sim-0.6}$. If the distances of the molecular
clouds in the Perseus arm are overestimated by a factor of two, the virial
parameters would be underestimated by a factor of $\sim 19\%$ to $\sim 34\%$.
This means the true fraction of the gravitationally bound molecular clouds in
the Perseus arm could be lower than the values shown in Figures 14 and 15.
Nevertheless, even considering the possible underestimation of $\alpha_{\rm
vir}$, the percentage of the gravitationally bound clouds in the Perseus arm
is still higher than that in the Local arm. The overall difference of the
masses of the molecular clouds in the two spiral arms is another potential
cause for the difference in virial parameters. As discussed in the next
paragraph, there is an anti-correlation between the masses of the clouds and
their virial parameter. The molecular clouds in the Perseus arm usually have
larger masses, therefore, tending to have smaller virial parameters.

Bertoldi & McKee (1992) have presented a theoretical argument that when self-
gravity is unimportant, the virial parameter is expected to be correlated with
$M^{-2/3}$ for the pressure-confined clumps. Kauffmann et al. (2013) have
reevaluated virial parameters for dense cores and clouds using data compiled
from the literature. The power-law behavior $\alpha_{\rm vir}\propto
M^{h_{\alpha}}$ is confirmed for all the different samples of dense cores and
clouds, and the exponents are tabulated in their table 2. We also find the
$\alpha_{\rm vir}\propto M^{h_{\alpha}}$ behaviour both for the 12CO and 13CO
clouds in our survey (Figures 14 and 15). The power-law exponents of the
$\alpha_{\rm vir}-M$ relation of 12CO clouds in the Local and the Perseus arms
are $-0.41$ and $-0.53$, respectively, within the mass range from $\sim$0.1 M⊙
to $\sim 10^{4}$ M⊙. The exponents in $\alpha_{\rm vir}-M$ relation for 13CO
clouds in the Local and the Perseus arms are $-0.41$ and $-0.37$,
respectively. The results obtained in this work resemble those derived by
Kauffmann et al. (2013) for the GRS survey (Heyer et al., 2009; Roman-Duval et
al., 2010).

Subcritical molecular clouds need other confining sources to keep the
equilibrium state. The virial theorem for a uniform, isothermal, non-
magnetized, spherical cloud immersed in the interstellar environment with
pressure $P_{e}$ can be written as (Spitzer, 1978; Field et al., 2011),

$\frac{\sigma^{2}}{R}=\frac{1}{3}(\frac{3\pi
G\Sigma}{5}+\frac{4P_{e}}{\Sigma})$ (9)

The solution for the pressure-confined virial equilibrium state (PVE) is the
V-shaped lines in Figures 14 and 15 for different external pressures. The
relation between $\sigma^{2}/R$ and $\Sigma$ under the simple virial
equilibrium condition (SVE) (when the internal pressure balances with the
self-gravity) with $\alpha_{\rm vir}=1$ and $\alpha_{\rm vir}=2$ are also
shown in Figures 14 and 15. In Figure 14, the subcritical 12CO molecular
clouds in the Local and the Perseus arms show poor correlation of
$\sigma^{2}/R$ with $\Sigma$ and they are clustered in the regime of external
pressures from $P_{e}/k\sim\ 10^{4}$ K cm-3 to $P_{e}/k\sim 10^{6}$ K cm-3,
with a trend that the 12CO clouds in the Local arm have higher $P_{e}$ than
the clouds in the Perseus arm. Some of the Perseus arm clouds are located
below the $\alpha_{\rm vir}\sim 2$ SVE line, indicating the important role of
self-gravity in these clouds. The 13CO molecular clouds in the Local arm also
show concentration in the $\sigma^{2}/R$ versus $\Sigma$ diagram (Figure 15).
The external pressure needed to confine the 13CO molecular clouds in the Local
arm is comparable to that of the 12CO clouds.

##  4 Discussion

###  4.1 Probability Distribution Functions of H2 Column Density of Large
molecular clouds

In this section, we investigate the N-PDFs of molecular clouds in the surveyed
region. Since the abundance of 12CO is much higher than 13CO in molecular
clouds and the 12CO emission is more extended than that of 13CO , a 12CO cloud
usually corresponds to several 13CO clouds that can be considered as the
denser parts of the same and more extend structure traced by the 12CO
emission. Therefore, the boundary extracted from the 12CO emission is more
representative of the edge of a molecular cloud in the N-PDF analysis. To have
sufficient pixels to derive a robust N-PDF for a cloud, we selected molecular
clouds of relatively large projected area. According to the exact projected-
area in the 12CO catalog, forty clouds with area greater than 0.35 arcdeg2,
i.e., 5000 pixels, are selected, among which 29 clouds belong to the Local arm
and 11 clouds to the Perseus arm. Since the 13CO emission has a lower optical
depth than the 12CO emission, we used the 13CO emission within a 12CO cloud
boundary to estimate the H2 column density. The H2 column density is
calculated as described in Section 3.4.1 at pixels where the peak brightness
of the 13CO spectrum is at least above 4$\sigma_{RMS}$. An N-PDF is simply the
histogram of the logarithm of the normalized column density,
$s=\ln(N_{H_{2}}/<N_{H_{2}}>)$. If the column density is log-normally
distributed, the PDF of $s$ follows the formula

$p(s)=\frac{1}{\sqrt{2\pi}\sigma}\exp[{-\frac{(s-\mu)^{2}}{2\sigma^{2}}}],$
(10)

where $\mu$ and $\sigma$ are the mean and dispersion of the normal
distribution of s. If the column density is power-law-distributed, which means
$p(s)\propto N_{H_{2}}^{\alpha}$, the PDF of $s$ follows

$\ln p(s)=\alpha s+c,$ (11)

where $\alpha$ is the power-law index and c is a constant related to the
probability of the starting location of the fitting. In the log-log space, the
N-PDFs that have log-normal shapes show as parabolas, while those that have
power-law shapes show as straight lines.

The derived N-PDFs for the selected clouds in the Local and the Perseus arms
are presented in Figures 16 and 17, respectively, in the order of the angular
sizes of the 12CO boundaries. Because the names of the molecular clouds under
the MWISP standard, like those in Table 2, are too long to conveniently legend
in Figures 16 and 17, we use in this section the shortened names, which start
with a letter “G” and followed by the spatial coordinates accurate to two
decimal places. Except for Section 4.1, the identified molecular clouds are
all named according to the MWISP standard. The N-PDF of each cloud is fitted
with a log-normal function or a power-law, depending on the shape. For the
N-PDFs that both a log-normal function and a power-law function can be fit, we
use the reduced chi-squared of the fittings as the criterion to choose the
better form of the fitting, with the fitting form of smaller reduced chi-
squared being chosen. We fixed the upper limit of the fitting in the higher
bin with at least ten counts. The lower limit for the power-law fitting is
fixed at the peak of the distribution. For the log-normal fitting, ideally,
the detection completeness limit should be used as the lower limit in the
fitting. However, an accurate value of the detection completeness limit for H2
column density is hard to determine. In this work, we calculated the median
uncertainty of H2 column density within the 13CO cloud and take three times
the median uncertainty, which we refer to as reference detection completeness
limit, as the lower limit in the log-normal fitting. By manual examination, we
found that the reference detection completeness limit defines a closed contour
that is nearly identical to the emission cutoff of the 13CO cloud (see, e.g.,
Figure 18). Therefore, we believe that the reference completeness limit is a
reasonable value for the lower limit in the log-normal fitting. The mean
column densities, statistical, and fitted parameters of the N-PDFs of the
selected molecular clouds are tabulated in Tables 4 and 5.

Figure 16: N-PDFs of the twenty-nine selected molecular clouds in the Local
arm. The column densities of the clouds are normalized by their mean, and the
upper axes give the corresponding values of N${}_{H_{2}}$. The vertical black
dash-dotted lines in each panel indicate the reference detection completeness
limit of the column density of each cloud. The horizontal dashed lines mark
the $p(s)$ at which the count in a bin is ten. The blue dashed curves are the
Gaussian fittings of the N-PDFs, while the magenta curves are the power-law
fittings. The corresponding fitting ranges are marked with purple (Gaussian
fittings) or blue (power-law fittings) dotted lines in the panels of the
fitted N-PDFs. The fitted parameters $\mu$ and $\sigma$ of the Gaussian
function are indicated in blue, and the fitted exponents of the power-law
function $p(s)\propto N_{H_{2}}^{\alpha}$ are indicated in magenta. The red
bars mark the statistical errors in each bin of s. Figure 17: Same as Figure
16, but for the eleven selected clouds in the Perseus arm. Table 4: Properties
of the N-PDFs of the Clouds in the Local Arm

Name | d | MLTE | $<N_{H_{2}}>$ | $\mu_{data}$ | $\sigma_{data}$ | $\mu_{fit}$ | $\sigma_{fit}$ | $\alpha$ | Shape
---|---|---|---|---|---|---|---|---|---
| kpc | (M⊙) | (cm-2) |  |  |  |  |  | (LN/LN∗/PL)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
G117.70+4.33 | 0.67 | 8.48$\times 10^{3}$ | 1.15$\times 10^{21}$ |  $-$0.24 | 0.68 |  $-$0.30 | 0.73 | … | LN
G110.69+1.82 | 0.77 | 2.79$\times 10^{4}$ | 2.86$\times 10^{21}$ |  $-$0.46 | 0.91 |  $-$0.60 | 1.03 | … | LN∗
G106.53+4.08 | 0.87 | 1.31$\times 10^{4}$ | 2.41$\times 10^{21}$ |  $-$0.48 | 0.92 |  $-$0.97 | 1.23 | … | LN∗
G115.58$-$2.72 | 0.33 | 6.83$\times 10^{2}$ | 9.46$\times 10^{20}$ |  $-$0.19 | 0.61 |  $-$0.26 | 0.67 | … | LN
G112.22$-$2.38 | 0.27 | 8.99$\times 10^{1}$ | 5.43$\times 10^{20}$ |  $-$0.12 | 0.48 |  $-$0.29 | 0.59 | … | LN
G115.50+1.84 | 0.77 | 5.54$\times 10^{3}$ | 1.34$\times 10^{21}$ |  $-$0.23 | 0.67 |  $-$0.27 | 0.72 | … | LN
G115.33+4.08 | 1.16 | 7.34$\times 10^{3}$ | 1.39$\times 10^{21}$ |  $-$0.17 | 0.59 |  $-$0.16 | 0.60 | … | LN
G118.05+3.15 | 1.09 | 1.30$\times 10^{4}$ | 2.18$\times 10^{21}$ |  $-$0.31 | 0.73 |  $-$0.43 | 0.80 | … | LN∗
G106.12+0.58 | 0.41 | 6.36$\times 10^{2}$ | 9.80$\times 10^{20}$ |  $-$0.18 | 0.61 | … | … | … | …
G109.71+1.82 | 0.24 | 6.87$\times 10^{1}$ | 6.48$\times 10^{20}$ |  $-$0.12 | 0.50 |  $-$0.12 | 0.50 | … | LN
G112.72+2.71 | 1.16 | 8.62$\times 10^{3}$ | 1.91$\times 10^{21}$ |  $-$0.24 | 0.71 |  $-$0.23 | 0.73 | … | LN
G114.71+1.09 | 0.77 | 1.63$\times 10^{3}$ | 9.66$\times 10^{20}$ |  $-$0.19 | 0.61 |  $-$0.22 | 0.65 | … | LN
G107.64+1.35 | 0.25 | 5.71$\times 10^{1}$ | 7.35$\times 10^{20}$ |  $-$0.11 | 0.46 |  $-$0.15 | 0.49 | … | LN
G119.18+1.55 | 0.65 | 1.03$\times 10^{3}$ | 1.25$\times 10^{21}$ |  $-$0.22 | 0.65 |  $-$0.31 | 0.76 | … | LN
G115.70+3.71 | 0.31 | 1.27$\times 10^{2}$ | 7.20$\times 10^{20}$ |  $-$0.13 | 0.52 |  $-$0.12 | 0.52 | … | LN
G110.26+3.55 | 0.27 | 2.82$\times 10^{1}$ | 5.40$\times 10^{20}$ |  $-$0.14 | 0.52 |  $-$0.19 | 0.57 | … | LN
G117.41+2.50 | 0.32 | 4.43$\times 10^{1}$ | 8.62$\times 10^{20}$ |  $-$0.16 | 0.55 | … | … |  $-$1.29 | PL
G107.87+1.90 | 0.61 | 1.44$\times 10^{2}$ | 8.30$\times 10^{20}$ |  $-$0.13 | 0.49 | … | … |  $-$1.82 | PL
G113.59+4.62 | 0.65 | 2.13$\times 10^{2}$ | 8.54$\times 10^{20}$ |  $-$0.13 | 0.51 |  $-$0.14 | 0.55 | … | LN
G115.90$-$0.56 | 0.31 | 4.89$\times 10^{0}$ | 4.21$\times 10^{20}$ |  $-$0.06 | 0.33 |  $-$0.03 | 0.30 | … | LN
G110.78+3.86 | 0.19 | 2.32$\times 10^{1}$ | 9.42$\times 10^{20}$ |  $-$0.15 | 0.57 |  $-$0.10 | 0.60 | … | LN
G113.31$-$1.22 | 0.26 | 1.34$\times 10^{0}$ | 3.64$\times 10^{20}$ |  $-$0.05 | 0.32 | … | … | … | …
G106.66+1.01 | 0.65 | 7.47$\times 10^{2}$ | 1.89$\times 10^{21}$ |  $-$0.31 | 0.80 |  $-$0.40 | 0.97 | … | LN∗
G108.75+2.69 | 0.75 | 3.72$\times 10^{3}$ | 4.18$\times 10^{21}$ |  $-$0.63 | 1.10 |  $-$0.93 | 1.42 | … | LN∗
G111.11$-$3.73 | 0.20 | 1.65$\times 10^{0}$ | 3.68$\times 10^{20}$ |  $-$0.05 | 0.33 |  $-$0.04 | 0.38 | … | LN
G114.78+0.82 | 0.55 | 1.71$\times 10^{2}$ | 8.07$\times 10^{20}$ |  $-$0.13 | 0.51 | … | … |  $-$1.75 | PL
G106.06+1.49 | 1.73 | 2.22$\times 10^{3}$ | 1.11$\times 10^{21}$ |  $-$0.20 | 0.59 | … | … |  $-$1.46 | PL
G117.54$-$0.57 | 0.26 | 1.72$\times 10^{1}$ | 7.61$\times 10^{20}$ |  $-$0.16 | 0.53 | … | … |  $-$1.20 | PL
G119.18+4.38 | 0.31 | 3.47$\times 10^{1}$ | 5.57$\times 10^{20}$ |  $-$0.16 | 0.56 |  $-$0.18 | 0.60 | … | LN

Note. — Columns 1$-$4 give the name, distance, mass, and the mean $H_{2}$
column density. The mass and the column density are derived using the 13CO
emission. The statistical mean and dispersion of $s=\ln N_{H_{2}}/<N_{H_{2}}>$
of the clouds are presented in columns 5-6, while columns 7-8 give the
corresponding fitted parameters. Column 9 presents the exponents, $\alpha$, of
the fitted power-law distributions. Column ten is the description of the shape
of the fitted N-PDFs, where LN means log-normal, LN∗ means log-normal
distribution with slight excesses at the high-density end, and PL means power-
law.

Table 5: Properties of the N-PDFs of the Clouds in the Perseus Arm

Name | d | MLTE | $<N_{H_{2}}>$ | $\mu_{data}$ | $\sigma_{data}$ | $\mu_{fit}$ | $\sigma_{fit}$ | $\alpha$ | Shape
---|---|---|---|---|---|---|---|---|---
| kpc | (M⊙) | (cm-2) |  |  |  |  |  | (LN/LN∗/PL)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
G111.53$-$2.56 | 3.13 | 2.06$\times 10^{5}$ | 2.38$\times 10^{21}$ |  $-$0.24 | 0.71 |  $-$0.26 | 0.71 | … | LN
G109.97$-$0.21 | 4.05 | 5.35$\times 10^{5}$ | 4.02$\times 10^{21}$ |  $-$0.49 | 0.98 |  $-$0.58 | 1.07 | … | LN
G111.47+0.79 | 4.32 | 7.38$\times 10^{5}$ | 7.96$\times 10^{21}$ |  $-$0.74 | 1.20 |  $-$1.05 | 1.49 | … | LN∗
G113.29$-$0.73 | 3.01 | 1.21$\times 10^{4}$ | 1.55$\times 10^{21}$ |  $-$0.37 | 0.76 | … | … |  $-$1.25 | PL
G105.39+0.28 | 4.63 | 4.87$\times 10^{4}$ | 1.85$\times 10^{21}$ |  $-$0.30 | 0.71 |  $-$0.41 | 0.73 | … | LN∗
G116.80$-$3.12 | 2.72 | 5.92$\times 10^{3}$ | 9.79$\times 10^{20}$ |  $-$0.15 | 0.54 |  $-$0.19 | 0.58 | … | LN∗
G115.67$-$1.61 | 3.09 | 3.28$\times 10^{4}$ | 2.90$\times 10^{21}$ |  $-$0.39 | 0.84 |  $-$0.58 | 1.00 | … | LN
G108.61$-$1.01 | 4.33 | 1.44$\times 10^{5}$ | 5.32$\times 10^{21}$ |  $-$0.72 | 1.12 |  $-$1.19 | 1.41 | … | LN∗
G111.47+2.42 | 4.19 | 1.52$\times 10^{4}$ | 1.51$\times 10^{21}$ |  $-$0.18 | 0.59 | … | … |  $-$2.14 | PL
G111.66+4.11 | 2.38 | 1.60$\times 10^{3}$ | 6.72$\times 10^{20}$ |  $-$0.07 | 0.38 |  $-$0.07 | 0.41 | … | LN
G109.69+1.89 | 4.78 | 1.19$\times 10^{4}$ | 1.36$\times 10^{21}$ |  $-$0.20 | 0.61 |  $-$0.29 | 0.69 | … | LN

Note. — Same as Table 4 but for the clouds in the Perseus arm.

Thirty-one (77.5%) of the forty selected clouds have log-normal N-PDFs above
the reference completeness limit of column density without significant
excesses at the high density end, while seven of the selected clouds have
power-law N-PDFs and the N-PDFs of two clouds can not be fitted with either
log-normal or power-law functions. Some molecular clouds have log-normal
N-PDFs with minor excesses at the high column density ends. Most of the
molecular clouds in our results have log-normal N-PDFs, which is different
from the results obtained by Alves et al. (2017). We note that the reference
detection completeness limit, which we used in the fitting of log-normal
N-PDF, is very close to the last closed N(H2) isocontour of the cloud in Alves
et al. (2017). Although the detailed shape of the N-PDF at the low column
density end may be affected by the selected different closed isocontours, the
existence of the turn-over in the N-PDF, which is the important signature of
log-normal N-PDF, can not be altered by the small difference between the
reference detection completeness limit in this work and the last closed
isocontour in Alves et al. (2017). The molecular clouds can be divided into
three categories according to the shapes of their N-PDFs, i.e., pure log-
normal (LN), log-normal with minor excess (LN*), and power-law (PL).

Kainulainen et al. (2009) derived the N-PDFs for 23 molecular clouds in the
solar neighborhood, d$\sim$ 250-700 pc, using the near-infrared dust
extinction as the tracer of H2 column density. Their results suggest that
molecular clouds that are active in star formation have log-normal forms of
N-PDFs at low column density ends, but show significant excesses above log-
normal distributions or power-law distributions at high column density ends.
Similar distributions have also been obtained in Herschel observations, such
as the results of Schneider et al. (2013), Schneider et al. (2015), and
Pokhrel et al. (2016). The $\sigma$ parameters obtained by Kainulainen et al.
(2009) from the fitting of the log-normal components of the N-PDFs lie between
$\sim$0.3$-$0.5. The fitted dispersions of $s$, $\sigma_{fit}$ (in order to
distinguish from $\sigma_{data}$ in the following text), in this work,
however, lie between $\sim 0.3$ and $\sim 1.5$ with a median value of
$\sim$0.7, which are approximately 1.7 times the widths of the N-PDFs of
Kainulainen et al. (2009). This is in part due to the different fitting ranges
used in the two studies. The log-normal fitting in Kainulainen et al. (2009)
is limited to s $=-$0.5$-$1\. Therefore, the high-density part of the N-PDF
will significantly exceed the log-normal distribution and the resulting
$\sigma$ is then narrow. The fitting ranges are much broader in this work,
which may result in broader log-normal N-PDFs. Nevertheless, the dispersion of
$s$ $(\sigma_{data})$ calculated directly from the data for the N-PDFs of
active star-forming regions in Kainulainen et al. (2009) are all greater than
1. The $\sigma_{data}$ parameters in this work are similar to those of
Kainulainen et al. (2009).

###  4.2 Relation Between the Shapes of the N-PDFs and the Star Forming
Activities in the molecular clouds

We compare the spatial distribution of the H2 column densities of the selected
clouds with the infrared, WISE 3/4 (12/22 $\mu m$) band images, to examine the
relation between the N-PDF forms and the star formation activities in these
molecular clouds. The WISE 3 and 4 bands are good indicator of star formation
since they contain the polycyclic aromatic hydrocarbon (PAH) emission and the
emission from the warm dust heated by star formation activities.

(a)

(b)

(c)

(d)

Figure 18: Column density distribution (left) and the WISE 3/4 band images
(right) for the selected molecular clouds in the Local arm. Panels (a)$-$(c)
are three examples of the clouds that have log-normal N-PDFs with slight
excesses at the high-density end. The black contours in the left panels and
the white contours in the right panels show the reference detection
completeness limit of the H2 column density of the clouds. The green contours
in the left panels and the red contours in the right panels in (a)-(c)
correspond to the column densities where the N-PDFs start to show excesses
above log-normal distributions. Panel (d) is an example of the molecular
clouds with power-law N-PDFs. The magenta contours in panel (d) show the
column density peak occurrence. The orange circles in these figures mark the
positions of the H II regions or H II region candidates in the WISE catalog.

(a)

(b)

(c)

(d)

Figure 19: Same as Figure 18 but for the clouds in the Perseus arm. The first
three panels are three examples of LN∗ clouds, and the last panel is an
example of PL clouds.

Figures 18 presents the H2 column density maps and the WISE 3/4 images of
three LN∗ molecular clouds and one PL clouds in the Local arm and Figure 19
presents the example clouds in the Perseus arm. The H2 column density maps and
WISE 3/4 images of other selected molecular clouds are given in Figures 23-31
in the Appendix. The green contours in the left panel and the red contours in
the right panel of Figure 18(a) correspond to N$\sim 3\times$1022 cm-2, at
which the cloud G110.69+1.82 (Cep GMC) has slight excesses above its log-
normal N-PDF. The contours coincide with three intensity peaks (Cep A, Cep B,
and Cep F) in the column density map, of sizes of $\leqslant$1 pc. The N-PDF
of the LN∗ cloud G118.05+3.15 show excess above log-normal distribution at two
column densities, N${}_{H_{2}}\sim 7\times 10^{21}$ cm-2 (within $<$5 pc) and
N${}_{H_{2}}\sim 2\times 10^{22}$ cm-2 (within $<$1 pc), shown as the two
green contours in Figure 18(b) and this region is associated with a WISE H II
region.

The N-PDF of LN∗ molecular cloud G108.75+2.69 exhibits slight excesses above
the log-normal distribution at the column density N${}_{H_{2}}\sim 1\times
10^{22}$ cm-2, shown as the green and red contours in Figure 18(c). These
contours coincide with a WISE H II region ($\sim$ 2pc). In the Local arm, the
column densities that correspondes to the excesses above the log-normal N-PDFs
are mainly concentrated in clumps of sizes of $\sim 1-5$ pc. Similar to the
case of the Local arm, the slight high-density excesses of the N-PDF of the
LN∗ molecular clouds in the Perseus arm are mainly concentrated in regions of
sizes of $\sim 5-10$ pc that are associated with H II regions (Figure 19).

The images for the cloud G106.06+1.49 which has the PL form of N-PDF are shown
in Figure 18(d). We can see that this cloud does not have signature of star
formation activity. The other five molecular clouds with PL N-PDFs in our
survey also do not exhibit star formation activity (see Figures 26, 26, 28,
29, and 31 in the Appendix). The power-law parts of the N-PDFs of the PL
molecular clouds are concentrated in clumps or filaments of size or width of
$\sim 0.2-1$ pc. For example, the PL cloud G114.78+0.82 is composed of several
filamentary structures of size $\sim$1 pc. The PL portion of the N-PDF of
cloud G113.29-0.73 corresponds to several filamentary structures around the H
II region S 163. The PL cloud G111.47+2.42 consists of a few filamentary
structures with lengths of $\sim$5 pc and widths of $\sim$1 pc, and its WISE
3/4 images do not show active star formation (see Figure 31).

##  5 Summary

We have conducted a comprehensive study of the properties of molecular clouds
in a 15°$\times$10.5$\arcdeg$ region in the second quadrant of the Milky Way
mid-plane using the 12CO , 13CO , and C18O data from the MWISP survey. The
distribution and basic statistics of the physical properties of the molecular
gas are presented. Using the DENDROGRAM based SCIMES algorithm, we used the
12CO and 13CO line emission to identify molecular clouds and studied the
statistical properties of these clouds. The scaling relations between the
physical parameters are investigated, and comparisons of the scaling relations
between different spiral arms are discussed. Forty clouds are selected as a
sub-sample to study the properties of the N-PDFs using the 13CO emission line
as the tracer of H2 column density. The main results are presented as follows.

  1. 1.

Under the influence of the distance selection effect, we have identified
molecular clouds in the Local arm above the size limit of $\sim$0.25 pc and
mass limit of $\sim$6 M☉, and large and massive molecular clouds in the
Perseus arm above the size limit of $\sim$1.9 pc and mass limit of $\sim$349
M☉. With this bias, the median mass of the identified 12CO and 13CO molecular
clouds in the Perseus arm is $\sim$50 and $\sim$30 times that of the Local
arm, respectively, and the molecular clouds in the Perseus arm are $\sim$6
times larger than those of the Local arm, as measured by 12CO emission, while
$\sim$4 times larger, as measured by 13CO emission. The surface density of
molecular clouds is significantly enhanced in the Perseus arm, up to $\sim$100
M⊙ pc-2.

  2. 2.

The exponent of the $\sigma_{v}-R$ relation is $\sim$0.29 for the molecular
clouds in the Local arm, while it is $\sim$0.44 for those in the Perseus arm,
showing that turbulence of molecular clouds may vary with Galactocentric
distance.

  3. 3.

The percentage of gravitationally bound molecular clouds in the Perseus arm
(58.2%) is much higher than that in the Local arm (19.1%) in our results,
partly due to the distance selection effect. An external pressure
Pe/k$\sim$10${}^{4}-10^{6}$ cm-3 is needed for the molecular clouds in the
Local arm to stay in equilibrium.

  4. 4.

The N-PDFs derived with the 13CO emission are dominated by log-normal
distributions with few or only minor excesses above the log-normal
distribution. The excesses at high-density correspond to star-forming regions
of scales $\sim 1-5$ pc for the Local arm and of scales $\sim 5-10$ pc for the
Perseus arm. The majority of the clouds that have power-law N-PDFs correspond
to molecular clumps of sizes of $\sim$1 pc or filaments of widths of $\sim$1
pc.

We thank the PMO-13.7 m telescope staffs for their supports during the
observation and the staffs of the MWISP scientific group for their valuable
suggestions. We thank the anonymous referee for his/her constructive
suggestions that help to improve this manuscript. Y. M. thanks Fujun Du for
his helpful discussion. This work is supported by the National Key R$\&$D
Program of China (NO. 2017YFA0402701) and Key Research Program of Frontier
Sciences of CAS under grant QYZDJ-SSW-SLH047. We acknowledge the support by
NSFC grant 11973091. Y.M. acknowledges financial supports by the Natural
Science Foundation of Jiangsu Province of China (Grant No. BK20181513) and by
the Natural Science Foundation of China (Grant No. 11973090). Y.S.
acknowledges supports by NSFC grant 11773077. This work makes use of the
SIMBAD database, operated at CDS, Strasbourg, France. This research made use
of SCIMES, a Python package to find relevant structures into dendrograms of
molecular gas emission using the spectral clustering approach. Figures 20-22
give the demonstration of the cloud identification using the DENDROGRAM+SCIMES
algorithms for different tracers and different spiral arms. Figures 23-31
present the column density maps and the WISE 3/4 band images of the selected
molecular clouds.

Figure 20: Demonstration of the outlines of the identified 12CO molecular
clouds in the Perseus arm in the (a) l-b space and the (b) l-v space.
Different colors correspond to different molecular clouds.

Figure 21: Same as Figure 20, but for the 12CO clouds in the Outer$+$OSC arm.

Figure 22: Same as Figure 20, but for 13CO clouds in the Perseus arm.

Figure 23: Same as Figure 18, but for clouds G117.70+4.33 etc.

Figure 24: Same as Figure 18, but for clouds G115.50+1.84 etc.

Figure 25: Same as Figure 18, but for clouds G112.72+2.71 etc.

Figure 26: Same as Figure 18, but for clouds G115.70+3.71 etc.

Figure 27: Same as Figure 18, but for clouds G113.59+4.62 etc.

Figure 28: Same as Figure 18, but for clouds G106.66+1.01 etc.

Figure 29: Same as Figure 18, but for clouds G117.54-0.57 etc.

Figure 30: Same as Figure 18, but for clouds G111.53-2.56 etc.

Figure 31: Same as Figure 18, but for clouds G108.61-1.01 etc.

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