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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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