Molecular Clouds in the Second Quadrant of the Milky Way Midplane from l = 104.°75 to l = 119.°75 and b = −5.°25 to b = 5.°25

Yuehui Ma; Hongchi Wang; Chong Li; Lianghao Lin; Yan Sun; Ji Yang

doi:10.3847/1538-4365/abe85c

1. Introduction

Molecular clouds are the birthplaces of stars. They constitute the coldest and densest part of the turbulent and multiphased interstellar medium (ISM). Since its discovery by Wilson et al. (1970), the CO molecule has become the most widely-used tracer of molecular clouds, both in the Milky Way and other galaxies. Due to 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 can therefore be used to effectively trace the regions of molecular clouds at higher densities. Our knowledge of the distribution and physical properties of molecular clouds in the Milky Way comes primarily from large-scale surveys of the rotational transitional emission of 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 mass of molecular clouds ranges from a few tens of solar masses to about 10⁶ M_⊙, while the size varies from ∼10 to 150 pc. The typical velocity dispersion of molecular clouds, as revealed by the surveys, is ∼1 km s⁻¹. The most massive molecular entities (>10⁴ M_⊙) are known as giant molecular clouds (GMCs); these have complex and hierarchical structures that can be further subdivided into clouds, clumps, and cores (Blitz & Williams 1999). The cloud mass function (CMF) is found to follow a power-law distribution of exponents, in a range from ∼−1.4 to ∼−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). A power-law correlation also exists 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, 2010b).

The hierarchical structure, the power-law behavior of the CMF, and the σ_v–r relation of molecular clouds are found, based on various numerical simulations, to be the outcome of large-scale turbulence, ignoring self-gravitation (Vázquez-Semadeni & García 2001; Padoan 2002; Federrath et al. 2009). However, gravity is found to play an important role in the dynamics of molecular clouds on a smaller scale (<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 worthwhile to investigate the statistical properties and equilibrium states of molecular structures, via molecular cloud surveys which combine high sensitivity, good spatial resolution, and wide sky coverage. This type of survey is 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 type of survey allows 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 with good opportunity to study the statistical properties of molecular clouds. For this investigation, we first need to decompose the molecular line emission into individual clouds. For this purpose, we employed the DENDROGRAM⁴ (Rosolowsky et al. 2008) and SCIMES⁵ (Colombo et al. 2015) algorithms. Colombo et al. (2015) have conducted a detailed performance comparison between the DENDROGRAM+SCIMES algorithm, and other algorithms, such as CPROPS (Rosolowsky & Leroy 2006), and ClumpFind (Williams et al. 1994), which are 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 gases. Other traditional algorithms, such as GAUSSCLUMPS (Stutzki & Guesten 1990) and FELLWALKER (Berry 2015), are more suitable for the identification of clumps or cores.

The probability distribution function of the H₂ column density (N-PDF) of molecular clouds is a useful statistical tool with which to investigate the underlying physics influencing the structure of molecular clouds. Log-normal behavior in terms of N-PDF has been predicted in theoretical studies (Vazquez-Semadeni 1994; Padoan et al. 1997; Klessen 2000), and is attributed to supersonic turbulence in molecular clouds. Previous observations have confirmed the existence of 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, have been observed in the N-PDFs of active star-forming regions, together 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 completeness, i.e., the last closed contour, has a significant influence on the shape of N-PDFs, concluding 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 N-PDFs and the underlying physics of molecular clouds, as log-normal N-PDFs are observed in their modeled clouds in the absence of supersonic turbulence.

In this work, we use the DENDROGRAM+SCIMES algorithms to extract molecular clouds in the second quadrant of the Milky Way midplane, from l = 104 fdg 75 to l = 119 fdg 75, and b = −5 fdg 25 to b = 5 fdg 25, using ¹²CO and ¹³CO data sets from the MWISP project, and to 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 summarise our conclusions 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° × 10°, from l = 104 fdg 75 to l = 119 fdg 75, and b = −5 fdg 25 to b = 5 fdg 25. This 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. Detailed observational information, together with the data processing procedure for the MWISP project, have been comprehensively covered by 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 between 2012 March and 2018 October, using the Purple Mountain Observatory (PMO) 13.7 m millimeter-wavelength telescope located at Delingha, China. The half-power beamwidth (HPBW) of the telescope is around 52'' and 50'' at 110 GHz and 115 GHz, respectively, and the pointing of the telescope has an accuracy of about 5'' for all 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 mixer functions 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 the ¹³CO J = 1 − 0 and C¹⁸O J = 1 − 0 lines are covered by the lower sideband. The backend of the receiver is a fast Fourier transform spectrometer with a total bandwidth of 1 GHz, and 16,384 frequency channels, providing a spectral resolution of 61 kHz per channel, corresponding to a velocity resolution of 0.17 km s⁻¹ at 110 GHz. The antenna temperature is calibrated according to ${T}_{{\rm{mb}}}={T}_{{A}}^{* }/{\eta }_{{\rm{mb}}}$ during observation, where η_mb is the main beam efficiency; its value can be found in the annual status report⁶ of the PMO-13.7 m millimeter telescope.

In the MWISP project, the survey area is divided into individual cells measuring $30^{\prime} \,\times$ 30'. For each cell, the observations were made in the position-switch on-the-fly mode, along the directions of Galactic longitude and Galactic latitude. The scanning rate is 50'' per second, and the dump time is 0.3 s. The data products of the MWISP survey are automatically pre-processed after observation. This pre-processing includes the rejection of prominent bad channels, the subtraction of a first-order baseline from every spectrum, and the combination of spectra obtained at different times for the same sky position. The final data are regrided into 30'' × 30'' pixels in the directions of Galactic longitude and latitude. The required standard for the median RMS noise level in the MWISP project is below ∼0.5 K per channel at the ¹²CO J = 1–0 line wavelength, and below ∼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 the ¹²CO J = 1 − 0 line has three main velocity components, centered at ∼−52, ∼−35, and ∼−10 km s⁻¹, respectively, whereas there are only two velocity components, −52 and −10 km s⁻¹, in the ¹³CO J = 1 − 0 line. Some ¹²CO emission is also present in the velocity range from −115 to −75 km s⁻¹, but is not visible in the total spectrum, as it is confined in small regions. For clarity, in Figure 1 we have inserted the average spectrum of the ¹²CO line at the positions where the ¹²CO emission is detected, in a velocity range from −115 to −75 km s⁻¹. The ¹²CO, ¹³CO, and C¹⁸O line emission is considered as having been detected at a given position only when its spectrum shows at least five, four, and three contiguous channels, respectively, with intensities above 2σ_RMS. The C¹⁸O emission in the region is too weak to be identified in the average spectrum. However, it clearly emerges in the average spectra of those positions where the C¹⁸O J = 1 − 0 emission is above the detection criterion (see the inset in Figure 1). The spikes at ∼34 and ∼45 km s⁻¹ in the ¹²CO spectrum, and at ∼−75 and ∼10 km s⁻¹ in the ¹³CO spectrum, are residual bad channels not properly removed from the automatic reduction pipeline, as are the spikes at ∼−127, ∼−110, ∼−23, and ∼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.

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 by red, green, and blue colors, respectively. In the observed portion of the outer Galaxy, a more negative local standard of rest velocity corresponds to greater distance. The nearby molecular gas, shown in red, spreads over the entire observed Galactic latitude range. The most distant gas, shown in blue, only distributes at positive Galactic latitudes, which may be a result of a warp in 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. A detailed analysis of the physical properties of Cas GMC was presented in our previous work, Ma et al. (2019).

**Figure 2.** Color-coded intensity maps of ¹²CO emission in different velocity ranges. Red, green, and blue colors correspond to the ¹²CO integrated intensities in 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, σ is the RMS noise per velocity channel, and δ v is the width of the velocity channel. The orange ellipses show the extent of 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 by blue and magenta circles, respectively. The corresponding names of the H ii regions in the Sharpless catalog (Sharpless 1959) are denoted by yellow letters, while the names of the supernova remnants are shown in red. Some active star-forming regions, such as NGC 7822, are indicated by black letters.
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Figure 3 shows the position–velocity distribution of the ¹²CO emission along the directions of Galactic longitude and latitude. Within the span of Galactic longitude covered in this work, the spiral arms of the Galaxy are identified as continuous curves in the l–v diagram. The red dashed lines in Figure 3(a) show the projected l–v positions of the Local, Perseus, and Outer Arms, 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), as 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 identified kinematic anomaly, 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 displayed in Figure 3(a) by a separation between the red and black dashed "Perseus" lines. A velocity shear exists between the east and west parts of the Perseus Arm, divided by the shell-like structure located at l = 111°, v = −45 km s⁻¹, corresponding 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 occurs 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 also be clearly seen in the b–v diagram given in Figure 3(b). 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 blueshifted along the south-to-north direction, as is evident in Figure 3(b). Sun et al. (2015), and Du et al. (2016) identified hundreds of molecular clouds in the "New" arm, i.e., the extension of the Scutum–Centaurus Arm in the outer Galaxy (OSC Arm), and the Outer Arm, using MWISP data. The locations of those clouds falling within the region observed in this work are indicated by green circles and red squares, respectively. Some of the identified clouds are indiscernible in our position–velocity diagrams, owing to 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 ¹²CO, ¹³CO, and C¹⁸O emissions, respectively. Mask 1 is defined by regions where ¹²CO emission is detected. Mask 2 relates to regions where both ¹²CO and ¹³CO emission are detected, while Mask 3 is the region where emissions from all three kinds of isotopologues are detected. According to this definition, the Mask 1 regions contain Mask 2 and 3 regions, while Mask 2 regions contain Mask 3 regions. Here, ¹²CO, ¹³CO, and C¹⁸O line emissions are considered as having been detected at a given position only when their spectra show at least five, four, and three contiguous channels, respectively, with intensities above 2σ_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, whereas C¹⁸O emission is only detected in very few pixels of the first two layers, corresponding to the densest part of active star-forming regions, such as the Cep GMC and NGC 7538 complexes. The total numbers and percentages for 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; 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. In addition, we calculated physical properties such as the excitation temperature, the optical depth of the ¹³CO and C¹⁸O emission lines, and the column density of the three isotopologues of the molecular gas for each pixel in Masks 1–3 in both the Local and Perseus Arms. Given that the pixel numbers whose detection is rated as 'good' within the mask 2 and 3 regions in the Outer+OSC Arms are too few, their physical properties are not calculated. The column density of ¹²CO molecules is directly converted from the H₂ column density, via the abundance ratio [H₂/¹²CO] = 1.1 × 10⁴ (Frerking et al. 1982), while the H₂ column density is obtained by multiplying the integrated intensity of ¹²CO emission, using the conversion factor X_CO = 2.0 × 10²⁰ 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 for that Mask, using Equation (1) from Li et al. (2018). The optical depth of ¹³CO and C¹⁸O in Masks 2 and 3 is derived using the peak intensities of the ¹³CO and C¹⁸O emission in the corresponding Masks and velocity ranges, using Equations (2) and (3) from Li et al. (2018), respectively. The column densities of ¹³CO and C¹⁸O for the Local, Perseus, and Outer+OSC Arms are calculated based on the ¹³CO and C¹⁸O integrated intensities in the corresponding velocity ranges, using Equations (5) and (6) from Li et al. (2018). The statistics relating to physical properties such as the excitation temperature, optical depth, and column density of Masks 1–3 are summarized in Figure 5 and Table 1.

**Figure 4.** Spatial distributions of molecular gas in different masks in the three velocity layers. Blue, green, and red colors correspond to 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.
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**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.
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Table 1. Statistical Properties of Molecular Gas in the Four Arms of the Galaxy

Arms	Mask	Pixel	Area	T_ex	${\tau }_{{}^{13}{\rm{CO}}}$	${\tau }_{{{\rm{C}}}^{18}{\rm{O}}}$	$\mathrm{lg}({N}_{{}^{12}\mathrm{CO}})$	$\mathrm{lg}({N}_{{}^{13}\mathrm{CO}})$	$\mathrm{lg}({N}_{{{\rm{C}}}^{18}{\rm{O}}})$
Name	Name	Num (Per)	(deg²)	(K)			(cm⁻²)	(cm⁻²)	(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. Column 1: name of the arm. Column 2: mask used—the definition of the masks is as given in Section 3.2. Column 3: number of pixels with "good" detection, based on the criteria explained in Section 3.1; the percentage of the good pixels with respect to the total observed pixels is given in parenthesis. Column 4: total angular size of pixels with "good" detection. Column 5: range and median value (in parenthesis) of the excitation temperature. Columns 6–7: ranges and median values (in parenthesis) of the optical depths of ¹³CO and C¹⁸O emission, respectively. Columns 8–10: ranges and median values (in parenthesis) of the column density of ¹²CO, ¹³CO, and C¹⁸O, respectively.

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The evidence from Table 1 shows 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; these 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 to 47 K, indicating that large differences in the physical conditions and gas excitation are present within the molecular clouds at the spatial scales resolved by the MWISP survey. The densest regions, i.e., Mask 3, corresponding to active star-forming regions such as the Cep GMC, NGC 7822, L1188, and NGC 7538 complexes in the Local and Perseus Arms, have much higher excitation temperatures, with median values from 15 to 19 K. This is to be expected in regions where star formation is active, as the newborn stars warm up their envelopes. Moreover, the radiation emitted by stars which have already formed, particularly if those stars are massive, can warm up their surroundings. The optical depth of ¹³CO emission, τ_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 can be as high as 1.5 in some pixels, which may refer to small regions, such as clumps or cores. The density in these regions can be much higher than that in the more diffuse areas of the molecular clouds; 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 N_12CO has a shape similar to that of N_13CO. However, the median column densities of ¹²CO molecules is reduced by a factor of ∼3 in the Outer+OSC Arm, as compared with those found in the Local and Perseus Arms. This indicates that there is less material in the Outer+OSC Arms of the Milky Way, i.e., the most external arms, than in the two more internal arms. The column density of C¹⁸O molecules in the Perseus Arm is greater than that found in the Local Arm by a factor of ∼1.5.

3.3. Catalogs of ¹²CO and ¹³CO Molecular Clouds

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

Using the ¹²CO and ¹³CO line emission data, we identify distinct ¹²CO and ¹³CO clouds in the surveyed region using the DENDROGRAM and 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 data cubes with median noise levels of 0.31 and 0.17 K, respectively. Prior to implementation of the DENDROGRAM algorithm, only those voxels within at least two consecutive velocity channels, and with intensities higher than 2σ 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 data cubes. The minimum difference between two separate "leaves" in a dendrogram tree is set to 3σ, and the bottom threshold for detection is 2σ. The minimum voxel number of an individual "leaf" is set to 50, corresponding to 3.7 consecutive pixels along each of the l–b–v axes. The above settings correspond to a molecular cloud measuring 0.5 × 0.5, and 1.6 × 1.6 pc², for distances of 1.0 and 3.0 kpc, respectively, and a 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 containing physical information regarding 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 result in false identification of molecular clouds. Therefore, following cloud identification, we performed a manual check for each identified cloud, to further ensure that the identified molecular clouds are real structures, rather than artifacts 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 are extracted from the ¹²CO J = 1 − 0 data, while 301 molecular clouds are extracted from the ¹³CO J = 1 − 0 data. Those molecular clouds with centroid velocities in 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, respectively. The ¹³CO cloud in the Outer+OSC Arm is found to be artificial, which is caused by bad velocity channels, and is therefore removed from the final catalog. Based on 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 illustrations 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, from 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) shows the integrated intensity of ¹²CO in a velocity range from −27 to 20 km s⁻¹, while that shown in panel (b) is the l–v diagram integrated along the Galactic latitude from b = −525 to b = 525.
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fdg — **Figure 6.** Demonstration of the outlines, from 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) shows the integrated intensity of ¹²CO in a velocity range from −27 to 20 km s⁻¹, while that shown in panel (b) is the l–v diagram integrated along the Galactic latitude from b = −525 to b = 525.
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**Figure 7.** As Figure 6, but for ¹³CO clouds.
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3.3.2. Distance Estimation

Distance is critical for any calculation of the physical parameters of molecular clouds. For those ¹²CO clouds with centroid velocities below −27 km s⁻¹, lying 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 R₀ = 8.34 kpc, and a rotational velocity of Θ₀ = 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 distances based on the kinematic method. Therefore, for these clouds, we use an alternative method to estimate 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 parallaxes from the Gaia DR2 catalog, and stellar photometry taken from Pan-STARRS 1 and 2MASS.

The public Python package, "dustmaps", is used to query the reddening map of Green et al. (2019). We query a region of the "median" dust reddening cube of the same pixel size and spatial extent as our CO datacube, which contains dust reddening along each line of sight, for a distance modulus ranging 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 a different distance modulus, as shown in Figure 8(a). 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 used to determine the distance modulus corresponding to the minimum of the second derivative of the reddening versus the distance modulus, as indicated by the blue dashed line in Figure 8(b). The second method is to derive the modulus at which the cross-correlation between the integrated intensity map and the reddening density map reaches its maximum, as indicated by the red dashed line in Figure 8(c). For molecular clouds with large angular sizes, such as the Cep GMC, as shown in Figure 8, the distances estimated by the two methods are consistent to within a 0.25 mag distance modulus. In this case, an averaged value across 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 where 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, 267 of the 440 nearby ¹²CO molecular clouds have their distance assigned using the extinction method.

**Figure 8.** Example of distance estimate of molecular clouds using the 3D dust maps given in Green et al. (2019). (a) Average reddening vs. distance modulus of the Cepheus GMC. The blue dashed line shows the distance of the Cepheus GMC. (b) Dust reddening density, ΔE(B − V)/Δd, vs. distance modulus. The blue dashed line marks the distance modulus corresponding to the maximum of the ΔE(B − V)/Δd 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 corresponding to the maximum of the cross-correlation. (d) ¹²CO intensity map of Cepheus GMC integrated within the PPV mask, derived 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.
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In summary, we estimated the distances of the molecular clouds of the Local Arm using the 3D-extinction method, while for clouds in the Perseus and Outer+OSC Arms, we used the kinematic method. The distances of the ¹³CO clouds are taken to be those of their counterpart ¹²CO clouds. For the ¹³CO clouds without counterpart ¹²CO clouds, distances are not assigned. The relationship of cloud distance, with centroid velocities 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: ∼250 and ∼750 pc, with small dispersions, while the distances of the molecular clouds in the Perseus Arm are distributed in a wider range, from ∼2 to ∼6 kpc, with a peak at ∼3.7 kpc. This differing 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 ∼6 to ∼9 kpc, without any concentration. Very few molecular clouds are located in the interarm regions.

**Figure 9.** Relationship between the centroid velocities and the distances of the ¹²CO clouds. The upper and right panels show the statistics relating to the centroid velocity and distance, respectively. We adopt extinction distances for clouds with velocities v > − 27 km s⁻¹, and kinematic distances for clouds with velocities v < − 27 km s⁻¹.
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3.4. Physical Properties of the Identified Molecular Clouds

The statistical properties of molecular clouds in our Galaxy can provide insight into 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 directly by the DENDROGRAM+SCIMES algorithms, 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, then deconvoluted with the HPBW of the PMO-13.7 m telescope,

$\begin{eqnarray}&&{R}_{\mathrm{eff}}=\displaystyle \frac{1}{2}d{({\theta }_{a}{\theta }_{b}-{\theta }_{\mathrm{beam}}^{2})}^{1/2}\end{eqnarray} \tag{ 1 }$

where θ_a, θ_b, are the fitted FWHM along the major and minor axes of the cloud, θ_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 exact area of each cloud, in units of square arcseconds, 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:

$\begin{eqnarray}&&{N}_{0}({H}_{2})={N}_{\mathrm{tot}}/{{num}}_{p}.\end{eqnarray} \tag{ 2 }$

where N_tot is the total column density of molecular hydrogen, and num_p is the total pixel number of a cloud, obtained by 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 is derived in the same way as described in Section 3.2, using the formula

$\begin{eqnarray}&&{N}_{\mathrm{tot}}={X}_{\mathrm{CO}}{I}_{\mathrm{CO}},\end{eqnarray} \tag{ 3 }$

where I_CO is the ¹²CO intensity integrated over the total area of the cloud, and X_CO = 2.0 × 10²⁰ 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, taking into account the estimate of the gas excitation temperature, the ¹³CO optical depth, and variations in the ¹²C/¹³C abundance ratio with galactocentric distance. In particular, assuming that the ¹³CO molecules exist under local thermodynamic equilibrium (LTE) conditions, the total H₂ column density of the ¹³CO clouds can be calculated based on the following:

$\begin{eqnarray}\begin{array}{rcl}{N}_{\mathrm{tot}} & = & A\times 2.42\times {10}^{14}\displaystyle \frac{\tau {(}^{13}\mathrm{CO})}{1-{e}^{-\tau {(}^{13}\mathrm{CO})}}\\ & & \times \displaystyle \frac{1+0.88/{T}_{{\rm{ex}}}}{1-{e}^{-5.29/{T}_{{\rm{ex}}}}}{I}_{{}^{13}\mathrm{CO}},\end{array}\end{eqnarray} \tag{ 4 }$

where A is a constant related to the abundance ratio to convert the ¹³CO column density to the H₂ column density, T_ex is the excitation temperature, τ(¹³CO) is the optical depth at the peak intensity of the ¹³CO emission within the boundary of a ¹³CO cloud, and ${I}_{{}^{13}\mathrm{CO}}$ is the total ¹³CO integrated intensity. The constant, A, is the product of the abundance ratio [¹²C/¹³C]=6.21d_GC + 18.71 (Milam et al. 2005), and H₂/¹²CO = 1.1 × 10⁴ (Frerking et al. 1982), where d_GC is the cloud's distance from the Galactic center. The excitation temperature is calculated in accordance with Equation (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 calculated based on Equation (3) in Li et al. (2018).

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

$\begin{eqnarray}&&M={N}_{\mathrm{tot}}{d}^{2}{\rm{\Omega }}\mu {m}_{{\rm{H}}},\end{eqnarray} \tag{ 5 }$

where d is the cloud distance, Ω is the solid angle of each pixel, and μ = 2.8 is the atomic weight per molecular hydrogen.

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

$\begin{eqnarray}&&{\rm{\Sigma }}=M/(\pi {R}_{\mathrm{eff}}^{2})\end{eqnarray} \tag{ 6 }$

$\begin{eqnarray}&&n({{\rm{H}}}_{2})=3M/(4\pi {R}_{\mathrm{eff}}^{3}\mu {m}_{{\rm{H}}}).\end{eqnarray} \tag{ 7 }$

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

$\begin{eqnarray}&&{\alpha }_{\mathrm{vir}}=\displaystyle \frac{5{\sigma }_{v}^{2}{R}_{\mathrm{eff}}}{{GM}},\end{eqnarray} \tag{ 8 }$

where G is the gravitational constant, and σ_v is the velocity dispersion. Theoretically, the critical value of α_vir for a nonmagnetized 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, where other physical mechanisms beside its self-gravity and internal pressure are not considered. We have derived the virial parameters for each ¹²CO and ¹³CO cloud.

All of the physical parameters of ¹²CO and ¹³CO clouds derived above are tabulated in Tables 2 and 3, respectively. In Tables 2 and 3, we have listed a total of 857 ¹²CO molecular clouds, and 300 ¹³CO molecular clouds, respectively. However, physical parameters, such as effective radius, mass, surface density, number density, and the 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; we also used the distance-assigned clouds as samples with which to study the scaling relations in Section 3.5.

Table 2. Properties of ¹²CO Clouds

Name	l	b	θ_a	θ_b	PA	v_lsr	σ_v	d	R_eff	N₀(H₂)	Mass	Σ	n	α_vir
	(deg)	(deg)	('')	('')	(deg)	(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", followed by the spatial coordinates of the molecular clouds, accurate to three decimal places, and their centroid velocities, accurate to two decimal places. The accuracy is set based on the pointing accuracy and velocity resolution of the PMO-13.7 m 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, velocity dispersion, and 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 virial parameters of the clouds, respectively.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Table 3. Properties of ¹³CO Clouds

Name	l	b	θ_a	θ_b	PA	v_lsr	σ_v	d	R_eff	T_ex	${\tau }_{{}^{13}{CO}}$	N₀(H₂)	Mass	Σ	n	α_vir	Name of matching ¹²CO cloud
	(deg)	(deg)	('')	('')	(deg)	(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. 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, velocity dispersion, and 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, 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 matching the ¹³CO cloud in column 1.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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3.4.2. Size and Mass of the Clouds

Histograms of the effective radius of the ¹²CO and ¹³CO clouds are given in Figures 11(b) and 12(b), respectively. More than half of the ¹²CO and ¹³CO clouds have sub-pc sizes. In the conventional classification scheme for molecular gas structures, these molecular entities should be classified as molecular clumps; however, 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 ∼0.5 and ∼3.0 pc, respectively, whereas these measurements are ∼0.7 and ∼2.8 pc for the ¹³CO molecular clouds. The mass distributions of the ¹²CO and ¹³CO clouds are presented in Figures 11(c) and 12(c). The median mass of ¹²CO molecular clouds in the Local, Perseus, and Outer+OSC Arms is ∼20 M_⊙, 1 × 10³ M_⊙, and 2 × 10³ M_⊙, respectively. The median mass of the ¹³CO clouds in the Local and Perseus Arms is 70 and 2 × 10³ 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 given below.

Firstly, the distance selection effect, i.e., only those 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, ∼50'', and similar minimum total integrated intensities, ∼66 K km s⁻¹, at different distances, as shown in Figures 10(a) and (c). The minimum angular size and integrated intensity correspond to the minimum effective radius and mass, which increase with distance, thereby resulting in the nondetection of smaller and less massive clouds at greater distances. Figures 10(b) and (d) show the variation in the effective radius and the mass of the ¹²CO clouds as a function of 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 ∼0.25 and ∼1.9 pc, respectively, as shown in Figure 10(b), while the minimum mass at these distances is ∼6 and ∼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, which allows us to identify them as separate structures, increases with their distance. For this reason, clouds lying close to one another are seen as one larger cloud at higher distances. Secondly, different methods are used for distance estimation of the clouds in the two arms. We find that the distance estimated via 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, owing to the kinematic abnormality of the Perseus Arm. Thirdly, the same settings and criteria are used in the SCIMES algorithm to identify clouds in different spiral arms. It can be seen from Figures 10(a) and (c) 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 vs. distance of (a) the angular size, 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 detected from nearby to a distance of 7.5 kpc. The red dashed lines in panels (b) and (d) show the minimum effective radius and minimum mass corresponding to the minimum angular size and total integrated intensity at different distances.
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Integral to the concept that molecular clouds are overdense substructures of the turbulent, multiphase fractal ISM (Scalo 1988), is the idea that 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. Rather than fitting dN in equally separated radius bins, we fitted the linear relationship between $\mathrm{lg}{dN}$ and lgR (and lgM), taking account of statistical 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 α_R through β = 1 + α_R, and the same goes for the mass. The minimum effective radii (or mass) of the ¹²CO clouds at the reference position of the Local and Perseus Arms are near the peaks of their lgR (or lgM) distributions. We therefore consider them to be a reasonable estimate of the completeness limit of the radius (or mass) distribution, and fit the distribution from the center of the bin with the peak values of dN to the center of the bin of the largest lgR (or lgM).

As shown in Figure 11(b), the measured exponent, α_R, in the Local Arm is −1.75, while in the Perseus Arm it 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, ${dN}/{dM}\propto {M}_{M}^{\alpha }$ , is α_M = − 1.40 for the Local Arm, and α_M = −1.59 for the Perseus Arm. The radius distributions derived in this work are shallower than those of the OGS or GRS surveys; α_R = −3.2 in the OGS survey (Heyer et al. 2001), and α_R = −3.9 in the GRS survey (Roman-Duval et al. 2010); it is also shallower than the α_R ∼ −3.3 result given in Elmegreen & Falgarone (1996), based on compiling the size measurements of clumps and clouds. The mass distribution is also shallower than those obtained by Rice et al. (2016) for molecular clouds in the outer Galaxy, α_M = −2.2. A possible explanation for the difference between our results and the above previous results is that different methods of cloud identification were utilized 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). In contrast, in this work, we aim to identify large structures, containing at least 50 voxels in PPV space. Moreover, the SCIMES algorithm uses a clustering process to merge the connecting "leaves" into a cloud, tending to connect small structures into a larger one.

3.4.3. Surface Density and Number Density

Figures 11(d) and (e) represent the distributions of Σ and ${n}_{{{\rm{H}}}_{2}}$ for the ¹²CO molecular clouds, with the corresponding distributions of the ¹³CO molecular clouds given in Figures 12(a) and (e). The median mass–surface densities of the ¹²CO clouds in the Local, Perseus, and Outer+OSC Arms are ∼33, ∼45, and ∼26 M_⊙ pc⁻², respectively, and the corresponding values of the ¹³CO clouds in the Local and the Perseus Arms are ∼44 and ∼89 M_⊙ pc⁻², respectively. In the Local Arm, about 63% of the total mass of the ¹²CO clouds is contained in clouds with surface densities above the threshold for star formation, i.e., ∼140 M_⊙ pc⁻² (corresponding to N_H2 ∼ 6.3 × 10²¹ cm⁻²) (Johnstone et al. 2004; Lada et al. 2010; Kainulainen et al. 2014), and the percentage is 88% for the Perseus Arm.

**Figure 12.** As Figure 11, but for ¹³CO clouds. The mass of the ¹³CO clouds is calculated using the LTE method.
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The maximum surface densities of the ¹²CO and ¹³CO molecular clouds are 431 and 1703 M_⊙ pc⁻², respectively, corresponding to H₂ column densities of 1.9 × 10²² and 7.7 × 10²² 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 an H₂ column density of ∼1.1 × 10²² cm⁻². The mass–surface density of NGC 7538 GMC is much higher than this limit, which is consistent with the observed concentration of CH₃OH masers within it (Moscadelli & Goddi 2014), and testifies to the presence of high-mass star-formation activity in this region. We also checked the positions of another five ¹²CO molecular clouds with mass–surface densities above 0.05 g cm⁻², finding that these molecular clouds are all located in the Perseus Arm, and 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(e) and 12(e), respectively. The median values of ${n}_{{{\rm{H}}}_{2}}$ 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 those in the Perseus and the Outer+OSC Arms with both ¹²CO and ¹³CO as tracers, 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 well below the critical density of the ¹²CO and ¹³CO J = 1 − 0 transition, i.e., ∼700 cm⁻³. One possible reason for this is that number density is a distance-dependent parameter. As such, the same caveats listed in the previous subsection for mass and distance are also valid with respect to number density. In particular, it scales with R_eff as $n\sim {R}_{\mathrm{eff}}^{p}$ , where p is in the range from ∼−0.6 to ∼−0.8 in this work (see the scaling relations in Section 3.5). This dependence means that when the distance is overestimated by a factor of two, so is the R_eff, as is the case for the massive star-forming region W3(OH) in the Perseus Arm (Xu et al. 2006), such that the number density could be underestimated for ∼34% to ∼43%. However, even if this effect is corrected, the number density in the Perseus Arm is still much lower than the ¹²CO critical density. Another possible factor in terms of underestimation is that the volume-filling factor of the ¹²CO and ¹³CO emission for 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-13.7 m 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 contributions from internal thermal motion and nonthermal turbulence. As shown in Figure 11(a), the median velocity dispersions of ¹²CO molecular clouds in the two spiral arms are similar, at ∼1.1 km s⁻¹. However the proportion of 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 σ_v > 4 km s⁻¹ are associated with, or located in the vicinity of, H ii regions such as S 163, S 157 and NGC 7538, indicating complex dynamics in these regions. The median values of σ_v of the ¹³CO molecular clouds in the Local and Perseus Arms are 0.8 and 1.1 km s⁻¹, respectively, similar to those of the ¹²CO molecular clouds. The distribution and median values of σ_v from this work are consistent with those of the molecular clouds in the solar circle (Roman-Duval et al. 2010), and the results of the OGS survey (Heyer et al. 2001). Miville-Deschênes et al. (2017) used a multi-Gaussian decomposition method to reanalyze the dataset of Dame et al. (2001), and their results are a factor of ∼2.1 larger than 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

Heyer & Dame 2015 made a compilation of the cloud surface density Σ across the Galactocentric distance, based on the literature, finding that the surface densities of the molecular clouds in the inner Galaxy are significantly higher than for those in the outer Galaxy. Observations have shown that Σ in the outer Galaxy decreases exponentially as a function of Galactocentric distance (Wouterloot et al. 1990). This kind of radial distribution of Σ 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 galactocentric distance in Figure 13. The median surface density of the clouds in each 0.5 kpc bin first increases from ∼30 to ∼50 M_⊙ pc⁻²at d_GC = 8.5 to 9 kpc, remains at around ∼45 M_⊙ pc⁻² from 9 to 11 kpc, then slightly decreases to ∼30 M_⊙ pc⁻² at 12.5 kpc. The scatter of Σ in each d_GC bin is significant. The median Σ obtained in this work is comparable to the compiled results of Heyer & Dame (2015), and is substantially lower than the surface density in the inner galaxy, which is ∼170 M_⊙ pc⁻² (Roman-Duval et al. 2010; Heyer & Dame 2015). The average surface density in galactocentric distance intervals of 0.5 kpc is calculated based on the total mass of the clouds, divided by the total area of the clouds. We note that the average surface density is higher than the median Σ in the range of d_GC < 11.5 kpc, particularly at the distance of the Perseus Arm (d_GC ∼ 9.5–10.5 kpc). This difference is reasonable, as Figure 13 clearly shows that the large and massive molecular clouds at these distances also have higher surface densities than the smaller and less massive ones.

**Figure 13.** Variation in the surface densities of molecular clouds as a function of galactocentric distance. The radii of the circles correspond to the sizes of the clouds, and the color shades correspond to the respective masses of the clouds. The red diamonds denote the average surface densities, calculated by dividing the total mass with the total area of all the clouds for each interval of galactocentric distance of 0.5 kpc. The black pluses show the medium surface density for each interval. The scatter of the medium surface density for each interval is indicated in the figure, and 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.
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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.

3.5.1. Mass–Radius Relation

Larson's third law (Larson 1981) states that molecular clouds have a constant surface density, meaning that molecular clouds have a scaling relationship between their masses and radii of the form M ∝ R². 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, 2010b). Observations of molecular clouds have shown that stellar cluster-forming clumps are more massive than those clumps devoid of stellar clusters, although they are 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 $M{(R)\geqslant 870{M}_{\odot }(R/\mathrm{pc})}^{1.33}$ for molecular clouds capable of forming massive stars.

The M–R relations of the ¹²CO clouds in the Local and Perseus Arms are presented in Figure 14(a). They can be well fitted with power-law functions of exponents of ∼2.2 in a broad range of radii, from ∼0.06 to ∼40 pc. None of the ¹²CO molecular clouds are distributed in the region of the M–R parameter space capable of hosting massive protoclusters, 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 all are associated with H ii regions. The M–R relations for the ¹³CO clouds are presented in Figure 15(a), where the fitted power-law exponents of the ¹³CO clouds in the Local and Perseus Arms are ∼2.4, suggesting nonuniform inner densities. Most of the ¹³CO molecular clouds located above both the gray shaded area and the 0.05 g cm⁻² limit for possible massive star formation (Urquhart et al. 2013) in Figure 15(a) correspond to active star-forming regions in the Local Arm, such as Cep OB3 and L1188 GMCs, as well as those molecular clouds in the Perseus Arm that are associated with H ii regions. Notably, the four molecular clouds lying in the region for massive protocluster candidates are all associated with H ii regions, i.e., NGC 7538, S157, and S152. These GMCs are candidate regions for massive cluster formation.

**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 virial parameters and mass, and (e) the relationship between the ${\sigma }_{v}^{2}/R$ and surface density of the ¹²CO clouds. The orange shaded area in panel (a) is the region defined by the M–R relations, as given in Bressert et al. (2012), for molecular clouds capable of forming massive protoclusters. The gray shaded area in panel (a) is the region where the clouds cannot form high-mass stars, based on the relation $M{(R)\leqslant 870{M}_{\odot }(r/\mathrm{pc})}^{1.33}$ given in Kauffmann et al. (2010b). The gray 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 gray shaded area in panel (c) indicates α_vir < 2. The fraction of clouds with α_vir less than 2 are shown in the top−right corner in panel (c). The fitted M–R, σ_v–R, and M–α 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.
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**Figure 15.** As Figure 14, but for ¹³CO clouds.
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3.5.2. Velocity Dispersion–Size Relation

The resemblance of the exponent in the scaling relation σ_v ∝ 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 σ_v and R is better confined using a steeper power law with an exponent of 0.5. This exponent has been further confirmed by Heyer et al. (2009), based on 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 σ_v–R relationship of the ¹²CO and ¹³CO clouds is presented in Figures 14(b) and 15(b), 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, being 0.44 and 0.43 for ¹²CO and ¹³CO clouds, respectively. The Pearson correlation coefficients of the fitted σ_v–R relations for the two arms lie in a range from 0.42 to 0.55. The Larson's relation, with an exponent of 0.38, is also drawn in Figures 14(b) and 15(b), with gray dotted lines for comparison. The difference between the scaling exponents of the molecular clouds in the Local and Perseus Arms possibly indicates the differing significance 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 σ_v–R relationship, with a quite flat power law for smaller clouds with radii below ∼2 pc, and a steeper power law for larger clouds with radii above ∼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(c) and 15(c) display the distribution of the virial parameters of the ¹²CO and ¹³CO clouds, respectively, and also show the portion of the gravitationally-bound (α_vir ≤ 2) molecular clouds in each arm. A subcritical (α_vir > 2) cloud will dissipate unless external pressure from the environment can help to confine the cloud, while a supercritical (α_vir ≪ 2) cloud will collapse within a few freefall timescales unless some other physical processes, such as 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 ∼1 to ∼1000, while those of the ¹²CO clouds in the Perseus Arm lie in the range from ∼0.3 to ∼60. However, the virial parameters of the ¹³CO clouds are much smaller, from ∼0.4 to ∼99, with an average of ∼7.5 for clouds in the Local Arm and ∼0.1 to ∼25, with an average of ∼1.6, for clouds in the Perseus Arm. The virial parameters of the ¹²CO clouds in the Outer+OSC Arm are distributed within a range of α_vir from ∼1 to ∼10. The majority, i.e., ∼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 in the virial parameter between the clouds in the Local and the Perseus Arms may be indicative of different dynamical states of molecular clouds in the two arms. However, the percentage of gravitationally-bound clouds is distance-dependent, since the detection of small and less massive molecular clouds is not complete in the Perseus Arm. Moreover, 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 ${R}_{\mathrm{eff}}^{-0.3\sim -0.6}$ . 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 between ∼19% and ∼34%. This means that the true fraction of the gravitationally-bound molecular clouds in the Perseus Arm could be lower than the values shown in Figures 14(c) and 15(c). Nevertheless, even considering the possible underestimation of α_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 paragraph below, there is an anti-correlation between the masses of the clouds and their virial parameters. The molecular clouds in the Perseus Arm usually have larger masses, and therefore tend to have smaller virial parameters.

Bertoldi & McKee (1992) have presented a theoretical argument that where self-gravity is unimportant, the virial parameter is expected to be correlated with M^−2/3 with respect to pressure-confined clumps. Kauffmann et al. (2013) have reevaluated the virial parameters for dense cores and clouds, using data compiled from the literature. The power-law behavior ${\alpha }_{\mathrm{vir}}\propto {M}^{{h}_{\alpha }}$ is confirmed for all the different samples of dense cores and clouds, and the exponents are tabulated in their table 2. We also find ${\alpha }_{\mathrm{vir}}\propto {M}^{{h}_{\alpha }}$ behavior, in relation to both ¹²CO and ¹³CO clouds in our survey (see Figures 14(d) and 15(d)). The power-law exponents of the α_vir–M relation of ¹²CO clouds in the Local and the Perseus Arms are −0.41 and −0.53, respectively, within a mass range of ∼0.1 M_⊙ to ∼10⁴ M_⊙. The exponents in the α_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 maintain an equilibrium state. The virial theorem for a uniform, isothermal, nonmagnetized, spherical cloud immersed in an interstellar environment with pressure P_e can be written as follows (Spitzer 1978; Field et al. 2011):

$\begin{eqnarray}&&\displaystyle \frac{{\sigma }^{2}}{R}=\displaystyle \frac{1}{3}\left(\displaystyle \frac{3\pi G{\rm{\Sigma }}}{5}+\displaystyle \frac{4{P}_{e}}{{\rm{\Sigma }}}\right)\end{eqnarray} \tag{ 9 }$

The solution for the pressure-confined virial equilibrium state (PVE) is given by the V-shaped lines in Figures 14(e) and 15(e) for different external pressures. The relation between σ²/R and Σ under the simple virial equilibrium condition (SVE) (i.e., where the internal pressure balances with the self-gravity) with α_vir = 1 and α_vir = 2 are also shown in Figures 14(e) and 15(e). In Figure 14(e), the subcritical ¹²CO molecular clouds in the Local and the Perseus Arms show poor correlation of σ²/R with Σ, and are clustered in the regime of external pressures from P_e/k ∼ 10⁴ K cm⁻³ to P_e/k ∼ 10⁶ K cm⁻³, with a trend such that the ¹²CO clouds in the Local Arm have higher P_e than those in the Perseus Arm. Some of the Perseus Arm clouds are located below the α_vir ∼ 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 σ²/R versus Σ diagram (Figure 15(e)). 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, which can be considered as denser parts of the same and more extended structures traced by the ¹²CO emission. Therefore, the boundary extracted from ¹²CO emissions is more representative of the edge of a molecular cloud in the N-PDF analysis. To find sufficient pixels to derive a robust N-PDF for a cloud, we selected molecular clouds over a relatively large projected area. According to the exact projected area in the ¹²CO catalog, forty clouds with an area greater than 0.35 arcdeg², i.e., 5000 pixels, are selected, of which 29 clouds belong to the Local Arm, and 11 clouds to the Perseus Arm. Since ¹³CO emission has a lower optical depth than 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, for pixels where the peak brightness of the ¹³CO spectrum is at least above 4σ_RMS. An N-PDF is simply a histogram of the logarithm of the normalized column density, $s=\mathrm{ln}({N}_{{{\rm{H}}}_{2}}/\langle {N}_{{{\rm{H}}}_{2}}\rangle )$ . If the column density is log-normally distributed, the PDF of s follows the formula

$\begin{eqnarray}&&p(s)=\displaystyle \frac{1}{\sqrt{2\pi }\sigma }\exp \left[-\displaystyle \frac{{\left(s-\mu \right)}^{2}}{2{\sigma }^{2}}\right],\end{eqnarray} \tag{ 10 }$

where μ and σ are the mean and dispersion of the normal distribution of s, respectively. If the column density is power-law-distributed, i.e., $p(s)\propto {N}_{{{\rm{H}}}_{2}}^{\alpha }$ , the PDF of s follows

$\begin{eqnarray}&&\mathrm{ln}\,p(s)=\alpha s+c,\end{eqnarray} \tag{ 11 }$

where α 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, N-PDFs with log-normal shapes show as parabolas, while those with 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, in this section we use the shortened names, which start with a letter "G" and are followed by the spatial coordinates, accurate to two decimal places. Except in 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 N-PDFs for which both a log-normal function and a power-law function can be fitted, we use the reduced chi-squared of the fittings as the criterion with which to select the better form for 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 calculate the median uncertainty of H₂ column density within the ¹³CO cloud, and take three times the median uncertainty, which we refer to as the reference detection completeness limit, as the lower limit in the log-normal fitting. By a process of 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 density, statistical, and fitted parameters of the N-PDFs for the selected molecular clouds are tabulated in Tables 4 and 5.

**Figure 16.** N-PDFs of the 29 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 ${N}_{{{\rm{H}}}_{2}}$ . The vertical black dashed–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 10. 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, μ and σ, of the Gaussian function are indicated in blue, and the fitted exponents of the power-law function, $p(s)\propto {N}_{{{\rm{H}}}_{2}}^{\alpha }$ , are indicated in magenta. The red bars mark the statistical errors in each bin of s.
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**Figure 16.** N-PDFs of the 29 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 ${N}_{{{\rm{H}}}_{2}}$ . The vertical black dashed–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 10. 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, μ and σ, of the Gaussian function are indicated in blue, and the fitted exponents of the power-law function, $p(s)\propto {N}_{{{\rm{H}}}_{2}}^{\alpha }$ , are indicated in magenta. The red bars mark the statistical errors in each bin of s.
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**Figure 17.** As Figure 16, but for the 11 selected clouds in the Perseus Arm.
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**Figure 18.** Column density distribution (left) and WISE 3/4 band images (right) for the selected molecular clouds in the Local Arm. Panels (a)−(c) show three examples of clouds with 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) shows an example of 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 H ii region or H ii region candidates in the WISE catalog.
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Table 4. Properties of the N-PDFs of Clouds in the Local Arm

Name	d	M_LTE	$\langle {N}_{{{\rm{H}}}_{2}}\rangle$	μ_data	σ_data	μ_fit	σ_fit	α	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 × 10³	1.15 × 10²¹	−0.24	0.68	−0.30	0.73	⋯	LN
G110.69+1.82	0.77	2.79 × 10⁴	2.86 × 10²¹	−0.46	0.91	−0.60	1.03	⋯	LN*
G106.53+4.08	0.87	1.31 × 10⁴	2.41 × 10²¹	−0.48	0.92	−0.97	1.23	⋯	LN*
G115.58−2.72	0.33	6.83 × 10²	9.46 × 10²⁰	−0.19	0.61	−0.26	0.67	⋯	LN
G112.22−2.38	0.27	8.99 × 10¹	5.43 × 10²⁰	−0.12	0.48	−0.29	0.59	⋯	LN
G115.50+1.84	0.77	5.54 × 10³	1.34 × 10²¹	−0.23	0.67	−0.27	0.72	⋯	LN
G115.33+4.08	1.16	7.34 × 10³	1.39 × 10²¹	−0.17	0.59	−0.16	0.60	⋯	LN
G118.05+3.15	1.09	1.30 × 10⁴	2.18 × 10²¹	−0.31	0.73	−0.43	0.80	⋯	LN*
G106.12+0.58	0.41	6.36 × 10²	9.80 × 10²⁰	−0.18	0.61	⋯	⋯	⋯	⋯
G109.71+1.82	0.24	6.87 × 10¹	6.48 × 10²⁰	−0.12	0.50	−0.12	0.50	⋯	LN
G112.72+2.71	1.16	8.62 × 10³	1.91 × 10²¹	−0.24	0.71	−0.23	0.73	⋯	LN
G114.71+1.09	0.77	1.63 × 10³	9.66 × 10²⁰	−0.19	0.61	−0.22	0.65	⋯	LN
G107.64+1.35	0.25	5.71 × 10¹	7.35 × 10²⁰	−0.11	0.46	−0.15	0.49	⋯	LN
G119.18+1.55	0.65	1.03 × 10³	1.25 × 10²¹	−0.22	0.65	−0.31	0.76	⋯	LN
G115.70+3.71	0.31	1.27 × 10²	7.20 × 10²⁰	−0.13	0.52	−0.12	0.52	⋯	LN
G110.26+3.55	0.27	2.82 × 10¹	5.40 × 10²⁰	−0.14	0.52	−0.19	0.57	⋯	LN
G117.41+2.50	0.32	4.43 × 10¹	8.62 × 10²⁰	−0.16	0.55	⋯	⋯	−1.29	PL
G107.87+1.90	0.61	1.44 × 10²	8.30 × 10²⁰	−0.13	0.49	⋯	⋯	−1.82	PL
G113.59+4.62	0.65	2.13 × 10²	8.54 × 10²⁰	−0.13	0.51	−0.14	0.55	⋯	LN
G115.90−0.56	0.31	4.89 × 10⁰	4.21 × 10²⁰	−0.06	0.33	−0.03	0.30	⋯	LN
G110.78+3.86	0.19	2.32 × 10¹	9.42 × 10²⁰	−0.15	0.57	−0.10	0.60	⋯	LN
G113.31−1.22	0.26	1.34 × 10⁰	3.64 × 10²⁰	−0.05	0.32	⋯	⋯	⋯	⋯
G106.66+1.01	0.65	7.47 × 10²	1.89 × 10²¹	−0.31	0.80	−0.40	0.97	⋯	LN*
G108.75+2.69	0.75	3.72 × 10³	4.18 × 10²¹	−0.63	1.10	−0.93	1.42	⋯	LN*
G111.11−3.73	0.20	1.65 × 10⁰	3.68 × 10²⁰	−0.05	0.33	−0.04	0.38	⋯	LN
G114.78+0.82	0.55	1.71 × 10²	8.07 × 10²⁰	−0.13	0.51	⋯	⋯	−1.75	PL
G106.06+1.49	1.73	2.22 × 10³	1.11 × 10²¹	−0.20	0.59	⋯	⋯	−1.46	PL
G117.54−0.57	0.26	1.72 × 10¹	7.61 × 10²⁰	−0.16	0.53	⋯	⋯	−1.20	PL
G119.18+4.38	0.31	3.47 × 10¹	5.57 × 10²⁰	−0.16	0.56	−0.18	0.60	⋯	LN

Note. Columns 1–4 give the name, distance, mass, and mean H₂ column density. The mass and the column density are derived using the ¹³CO emission. The statistical mean and dispersion of $s=\mathrm{ln}{N}_{{{\rm{H}}}_{2}}/\langle {N}_{{{\rm{H}}}_{2}}\rangle$ of the clouds are presented in columns 5–6, while columns 7–8 give the corresponding fitted parameters. Column nine presents the exponents, α, 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.

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

Name	d	M_LTE	$\langle {N}_{{{\rm{H}}}_{2}}\rangle$	μ_data	σ_data	μ_fit	σ_fit	α	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 × 10⁵	2.38 × 10²¹	−0.24	0.71	−0.26	0.71	⋯	LN
G109.97−0.21	4.05	5.35 × 10⁵	4.02 × 10²¹	−0.49	0.98	−0.58	1.07	⋯	LN
G111.47+0.79	4.32	7.38 × 10⁵	7.96 × 10²¹	−0.74	1.20	−1.05	1.49	⋯	LN*
G113.29−0.73	3.01	1.21 × 10⁴	1.55 × 10²¹	−0.37	0.76	⋯	⋯	−1.25	PL
G105.39+0.28	4.63	4.87 × 10⁴	1.85 × 10²¹	−0.30	0.71	−0.41	0.73	⋯	LN*
G116.80−3.12	2.72	5.92 × 10³	9.79 × 10²⁰	−0.15	0.54	−0.19	0.58	⋯	LN*
G115.67−1.61	3.09	3.28 × 10⁴	2.90 × 10²¹	−0.39	0.84	−0.58	1.00	⋯	LN
G108.61−1.01	4.33	1.44 × 10⁵	5.32 × 10²¹	−0.72	1.12	−1.19	1.41	⋯	LN*
G111.47+2.42	4.19	1.52 × 10⁴	1.51 × 10²¹	−0.18	0.59	⋯	⋯	−2.14	PL
G111.66+4.11	2.38	1.60 × 10³	6.72 × 10²⁰	−0.07	0.38	−0.07	0.41	⋯	LN
G109.69+1.89	4.78	1.19 × 10⁴	1.36 × 10²¹	−0.20	0.61	−0.29	0.69	⋯	LN

Note. As Table 4, but for the clouds in the Perseus Arm.

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Thirty-one (77.5%) of the 40 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 cannot 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 differs 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-PDFs, 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 selection of different closed isocontours, the existence of the turnover 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 ∼ 250–700 pc, using 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 from the Herschel observations, e.g., the results of Schneider et al. (2013, 2015), and Pokhrel et al. (2016). The σ parameters obtained by Kainulainen et al. (2009) from the fitting of the log-normal components of the N-PDFs lie between ∼0.3−0.5. The fitted dispersions of s, σ_fit (in order to distinguish from σ_data in the following text), in this work, however, lie between ∼0.3 and ∼1.5, with a median value of ∼0.7, and are approximately 1.7 times the widths of the N-PDFs given in 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 σ 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(σ_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 σ_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

Here, we compare the spatial distribution of the H₂ column densities of the selected clouds with the infrared, WISE 3/4 (12/22 μm) band images, in order 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 emission as well as emissions of warm dust heated by star-formation activities.

Figure 18 presents the H₂ column density maps and WISE 3/4 images of three LN* molecular clouds and one PL cloud in the Local Arm, and Figure 19 presents 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 ∼ 3 × 10²² cm⁻², at which the cloud G110.69+1.82 (Cep GMC) shows 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 ≤1 pc. The N-PDF of the LN* cloud, G118.05+3.15, shows excess above log-normal distribution at two column densities, ${N}_{{{\rm{H}}}_{2}}\sim 7\times {10}^{21}$ cm⁻² (within <5 pc), and ${N}_{{{\rm{H}}}_{2}}\sim 2\times {10}^{22}$ cm⁻² (within <1 pc), as indicated by the two green contours in Figure 18(b); 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 ${N}_{{{\rm{H}}}_{2}}\sim 1\times {10}^{22}$ cm⁻², indicated by the green and red contours in Figure 18(c). These contours coincide with a WISE H ii region (∼2pc). In the Local Arm, the column densities corresponding to the excesses above the log-normal N-PDFs are mainly concentrated in clumps, with sizes of ∼1–5 pc. Similarly 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 with sizes of ∼5–10 pc, which 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 lacks the 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(c), (d), 28(d), 29(a), and 31(b) in the Appendix). The power-law components of the N-PDFs of the PL molecular clouds are concentrated in clumps or filaments with a size or width of ∼0.2–1 pc. For example, the PL cloud, G114.78+0.82, is composed of several filamentary structures measuring ∼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 ∼5 pc and widths of ∼1 pc, and its WISE 3/4 images do not show active star formation (see Figure 31(b)).

5. Summary

In this paper, we have conducted a comprehensive study of the properties of molecular clouds in a 15° × 10.5° region in the second quadrant of the Milky Way midplane, 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 emissions to identify molecular clouds, and studied the statistical properties of these clouds. The scaling relations between the physical parameters were investigated, and comparisons of the scaling relations between different spiral arms have been discussed. Forty clouds were selected as a sub-sample with which 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.
Under the influence of the distance selection effect, we have identified molecular clouds in the Local Arm above a size limit of ∼0.25 pc, and a mass limit of ∼6 M_⊙, and large and massive molecular clouds in the Perseus Arm above a size limit of ∼1.9 pc, and a mass limit of ∼349 M_⊙. With this bias, the median mass of the identified ¹²CO and ¹³CO molecular clouds in the Perseus Arm is ∼50 and ∼30 times that of the Local Arm, respectively, and the molecular clouds in the Perseus Arm are ∼6 times larger than those of the Local Arm, as measured by ¹²CO emission, while ∼4 times larger, as measured by ¹³CO emission. The surface density of molecular clouds is significantly enhanced in the Perseus Arm, being up to ∼100 M_⊙ pc⁻².
2.
The exponent of the σ_v–R relation is ∼0.29 for the molecular clouds in the Local Arm, while it is ∼0.44 for those in the Perseus Arm, showing that turbulence of molecular clouds may vary with Galactocentric distance.
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 of P_e/k ∼ 10⁴–10⁶ cm⁻³ is needed for the molecular clouds in the Local Arm to remain in equilibrium.
4.
The N-PDFs derived via 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 ∼1–5 pc for the Local Arm, and of scales ∼5–10 pc for the Perseus Arm. The majority of the clouds exhibiting power-law N-PDFs correspond to molecular clumps at sizes of ∼1 pc, or filaments with widths of ∼1 pc.

We thank the PMO-13.7 m telescope staff for their support during our observations, and the staff of the MWISP scientific group for their valuable suggestions. We thank the anonymous referee for his/her constructive suggestions, which have helped to improve this manuscript. Y.M. thanks Fujun Du for helpful discussions. This work is supported by the National Key R&D Program of China (NO. 2017YFA0402701), and the Key Research Program of Frontier Sciences of CAS, under grant QYZDJ-SSW-SLH047. We acknowledge the support of NSFC grant 11973091. Y.M. acknowledges financial support from the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20181513), and the Natural Science Foundation of China (Grant No. 11973090). Y.S. acknowledges support from 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 of dendrograms of molecular gas emission, using the spectral clustering approach.

Appendix

Figures 20–22 provide a demonstration of cloud identification using the DENDROGRAM+SCIMES algorithms for different tracers and different spiral arms. Figures 23–31 present column density maps and 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.
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**Figure 21.** As Figure 20, but for the ¹²CO clouds in the Outer+OSC Arm.
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**Figure 22.** As Figure 20, but for ¹³CO clouds in the Perseus Arm.
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**Figure 23.** As Figure 18, but for clouds G117.70+4.33 etc.
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**Figure 24.** As Figure 18, but for clouds G115.50+1.84 etc.
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**Figure 25.** As Figure 18, but for clouds G112.72+2.71 etc.
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**Figure 26.** As Figure 18, but for clouds G115.70+3.71 etc.
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**Figure 27.** As Figure 18, but for clouds G113.59+4.62 etc.
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**Figure 28.** As Figure 18, but for clouds G106.66+1.01 etc.
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**Figure 29.** As Figure 18, but for clouds G117.54-0.57 etc.
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**Figure 30.** As Figure 18, but for clouds G111.53-2.56 etc.
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**Figure 31.** As Figure 18, but for clouds G108.61-1.01 etc.
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Molecular Clouds in the Second Quadrant of the Milky Way Midplane from l = 10475 to l = 11975 and b = −525 to b = 525

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Abstract

1. Introduction

2. Observations

3. Results

3.1. Overall Distribution of Molecular Gas

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