The Molecular Clouds in a Section of the Third Galactic Quadrant: Cloud Catalog

The third Galactic quadrant (195° < l < 220°, ∣b∣ < 5°) is part of the Milky Way Imaging Scroll Painting (MWISP) project, which is a multiline Galactic plane survey in CO and its isotopic transitions. Since the MWISP survey has been described in Su et al. (2021), we will briefly introduce it here.

The J = 1 − 0 transition lines of ¹²CO, ¹³CO, and C¹⁸O were obtained with the PMO 13.7 m millimeter telescope at Delingha. The telescope was mapped using a 3 × 3 pixel Superconducting Spectroscopic Array Receiver (SSAR) that works in sideband separation mode and employs the fast Fourier transform spectrometer (FFTS; Yang et al. 2008; Shan et al. 2012). The angular resolution of the 13.7 m telescope is about 49'' for ¹²CO and 51'' for ¹³CO and C¹⁸O. Each unit area of 30' × 30' was mapped using the on-the-fly (OTF) observation mode. The OTF raw data were regridded into regular data cubes with 30'' × 30'' pixels. Finally, the datacube units were mosaicked into a large datacube. Figure 1 shows the spectral noise distribution of ¹²CO, ¹³CO, and C¹⁸O in the total 250 deg² region. The mean noise σ is ∼0.45 K for ¹²CO and ∼0.25 K for ¹³CO and C¹⁸O. The spatial distribution of spectral noise (Figure 2) indicates that the noise level of the overall data does not change significantly throughout the region. The velocity resolution is about 0.16 km s⁻¹ for ¹²CO and 0.17 km s⁻¹ for ¹³CO and C¹⁸O.

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Figure 3 presents integrated intensity maps of ¹²CO, ¹³CO, and C¹⁸O within the velocity range of [−20, 70] km s⁻¹. We searched for the ¹²CO signal within [−200, 200] km s⁻¹ and found it only in the range of [−20, 70] km s⁻¹. The data covered a total area of 250 deg², which contains some interesting and well-known MCs, star clusters, and nebulae, such as Mon OB1 (Lim et al. 2022), NGC 2264 (Herbig 1954), the Rosette Nebula (Schneider et al. 1998; Di Francesco et al. 2010), Maddalena (Maddalena & Thaddeus 1985), and Sh 2–287 (Sharpless 1959). Li et al. (2018) found evidence for a cloud−cloud collision in the Rosette Molecular Cloud, and the abundance ratios of ¹³CO to C¹⁸O in the cloud have a mean value of 13.7, which is 2.5 times larger than the solar system value (Wilson & Matteucci 1992). Su et al. (2017) present CO observations toward three large supernova remnants (SNRs; Green 2014), G205.5+0.5 (Monoceros Nebula; Xiao & Zhu 2012), G206.9+2.3 (PKS 0646+06; Gao et al. 2011), and G213.0+0.6 (Reich et al. 2003), in this region. Su et al. (2017) confirm that the two SNRs are physically associated with their ambient MCs, and they also find that the shock of SNRs is interacting with the molecular gas. Yan et al. (2019) calculated distances of 11 MCs using CO observations and the Gaia DR2 parallax and G-band extinction measurements in this region.

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The ¹²CO emission shows the overall structure of the MC (Figure 3). It is noted that there is a large empty hole of no CO emission with an area of 8.4 deg² (l = 2175, b = 37' we named it the MWISP Hole) in the upper left corner. It is interesting that the MWISP Hole located in the Galactic disk with such low latitude and large size is quite rare. It also exists in the CO surveys of Dame et al. (1987). The strongest part of the ¹²CO emission is associated with NGC 2264. The ¹²CO intensity is mainly concentrated in the clouds Mon OB1, Rosette Nebula, and Maddalena, which are also the largest in the region.

Although the ¹³CO abundance is lower than that of the ¹²CO, this region still shows quite strong ¹³CO radiation. Its spatial distribution is similar to that of ¹²CO, and especially the clouds Mon OB1 and Rosette Nebula show a large area of spatial continuous structure. However, the emission of C¹⁸O is weak and it tends to be concentrated in a small dense core, so its radiation is not obvious on the large-scale spatial distribution map. We can see that the strongest C¹⁸O emission is in the cloud Mon OB1, but the radiation of other MCs is too weak and the spatial distribution scale is too small to be obvious.

Figure 4 presents the longitude–velocity map, which shows the velocity distribution of ¹²CO in this area. The figure clearly depicts the spiral arm structure in the third quadrant near the antigalactic center. The central velocities of ¹²CO emission in different spiral arms are systematically increased with the galactic longitude. The structure of spiral arms in the region will be discussed in detail in the future. A bright stripe exists at the velocity of 34.2 km s⁻¹, which is caused by bad channels in the ¹²CO spectra. However, the bad channels do not exist in the ¹³CO and C¹⁸O spectra. The bad channel may affect identification and statistics of MCs, so we address this issue in Section 3.1.

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Yan et al. (2020) investigated the decomposition of the ¹²CO spectral cube in the first Galactic quadrant using DBSCAN (Ester et al. 1996) and SCIMES (Colombo et al. 2015) algorithms, and they found that DBSCAN is more appropriate for identifying consecutive structures in position–position–velocity (PPV) space. In this paper, we follow Yan et al. (2020) to use the DBSCAN algorithm to build MC samples.

The algorithm has two parameters, eps and Minpts. In DBSCAN, eps means the maximum distances required to be considered as neighbors for two points, and Minpts defines core points. For core points, the minimum number of neighbors is no less than Minpts. Here we used connectivity 1 (eps = 1) and MinPts 4. The cutoff on the PPV data cubes is 2σ (∼1 K).

These parameters allow us to detect more weak signals, but they also inevitably introduce noise. To remove noise clusters, we followed Yan et al. (2020) using four criteria: (1) the voxel number is not less than 16, (2) the peak brightness temperature is greater than 5σ, (3) the channel number in the velocity axis is at least 3, and (4) the spatial projection area contains a compact region ($2^{\prime} \times 2^{\prime}$).

Finally, 7762 clouds have been decomposed based on DBSCAN algorithms. Due to the bad channel of ¹²CO data at 34.2 km s⁻¹, it will contaminate ¹²CO spectra, which cause some false clouds to be identified. To make sure the signal is authentic and the data are not contaminated, we eliminated 693 MCs with central velocities between [33.5, 34.5] km s⁻¹. We do not rule out the possibility of real signals in 693 clouds, but only 7069 MC samples were studied for statistical reliability. Figure 5 shows the spatial distribution of 7069 clouds. It is interesting that these clouds are densely spaced all over the region except for the MWISP Hole. The clouds, which are large in spatial projection, are more concentrated within ±3° of the Galactic latitude.

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Table 1 shows the basic parameters of ¹²CO for 7069 clouds. The cloud names are listed in Column (1), and the Galactic coordinates and velocity V_LSR of peak ¹²CO intensity are listed in Columns (2)–(4). Columns (5)–(8) present the projected angular area of clouds, velocity dispersion of average spectrum δ_v , peak intensity, and flux of ¹²CO line emission flux, respectively. The velocity dispersion of average spectrum and flux can be calculated according to the following formula (Rosolowsky & Leroy 2006):

$$\begin{eqnarray}&&\bar{v}=\displaystyle \frac{{\sum }_{i}^{\mathrm{cloud}}{T}_{i}{v}_{i}}{{\sum }_{i}^{\mathrm{cloud}}{T}_{i}}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{\delta }_{v}=\sqrt{\displaystyle \frac{{\sum }_{i}^{\mathrm{cloud}}{T}_{i}{\left[{v}_{i}-\bar{v}\right]}^{2}}{{\sum }_{i}^{\mathrm{cloud}}{T}_{i}}}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&\mathrm{Flux}={\sum }_{i}^{\mathrm{cloud}}{T}_{i}{\rm{\Delta }}{v}_{i}{\rm{\Delta }}{l}_{i}{\rm{\Delta }}{b}_{i}.\end{eqnarray} \tag{ 3 }$$

Here T_i is the main-beam brightness temperature of ¹²CO, and $\bar{v}$ is mean velocity. The sums run over all emission in the cloud. The definitions of velocity dispersion and flux also apply to ¹³CO and C¹⁸O.

Even though thousands of MCs are identified by DBSCAN, the portion of clouds that contain ¹³CO and C¹⁸O emission is unknown. Stacking multiple spectra is often used in the study of extragalactic galaxies, and it is good at finding weak signals. In this study, we develop two algorithms for identifying ¹³CO and C¹⁸O signals based on spectral stacking, named stacking bump and stacking intensity, respectively. We also tried to use the DBSCAN algorithm to search for ¹³CO and C¹⁸O signals. Through the comparison of these three algorithms (Section 5), we find that the stacking bump at 2σ algorithm is more suitable for searching for ¹³CO and C¹⁸O signals in our datacube. This section mainly introduces the stacking bump at 2σ algorithm, and the results of the other two algorithms are shown in Section 5.

Since ¹³CO and C¹⁸O are less abundant than ¹²CO, the intensities of ¹³CO and C¹⁸O are significantly lower than ¹²CO emission. The weak parts of ¹³CO and C¹⁸O emissions are more likely present in the spectrum as bump features owing to spectral noise. The basic principle of the stacking bump algorithm is to search for the bump in the original spectrum of ¹³CO and C¹⁸O according to a specific signal-to-noise ratio (S/N) within the ¹²CO boundary in PPV space, then average the spectrum containing bump components, and finally identify the emission of ¹³CO and C¹⁸O based on the S/N of the average spectrum.

The basic steps of the stacking bump at 2σ algorithm mainly include four steps. The first step is to determine the cloud boundary in PPV space. In this paper, we determine the cloud boundary based on the DBSCAN algorithm from the ¹²CO datacube as shown in Section 3.1. The second step is to search for the bump in the original spectrum of ¹³CO and C¹⁸O within the ¹²CO boundary in PPV space. The bump is defined based on the criterion that three contiguous channels were larger than a certain value threshold (such as 1.5σ or 2σ; different thresholds result in different signal number and flux; see Section 5). The third step is to average this bump-feature spectrum and calculate the noise of the average spectrum σ_a (σ_a = $\sigma \sqrt{{N}_{\mathrm{spectrum}}}$, where N_spectrum is the spectrum number involved in averaging). The average spectrum for ¹³CO and C¹⁸O will be identified as a signal based on the criterion that it should contain at least three consecutive channels with intensities above 3σ _a . The last step is to check the spectrum and remove the false detection caused by the wavelike baseline through visual inspection by comparing the average spectral lines of ¹³CO and C¹⁸O of these identified signals with the spectra of ¹²CO. All the steps are based on the S/N values to identify the signals, except in the last step, which is to manually check for wavelike baseline interference.

Based on the above principles and basic steps, we summarize four criteria for the identification of the ¹³CO signal. (1) Three contiguous channels in the ¹³CO spectrum were larger than 2σ (∼0.38 K). (2) At least one of its eight adjacent pixels satisfies condition 1. (3) Each cloud must have at least two pixels. (4) The average spectrum based on these pixels has three consecutive channels above 3σ_a . Based on these criteria and manual examination of the ¹²CO and ¹³CO average spectrum, a total of 1197 clouds with ¹³CO signals have been identified.

The basic parameters of ¹³CO for 1197 clouds are listed in Table 2, including names, the position and velocity of maximum of ¹³CO, projected angular area, velocity dispersion of average spectrum, peak intensity, and ¹³CO flux. These parameters are defined in the same way as in Table 1.

Table 2. A Catalog of Molecular Clouds Identified with ¹³CO Emission

Name	${l}_{\mathrm{peak}}^{13}$	${b}_{\mathrm{peak}}^{13}$	${V}_{\mathrm{LSR}}^{13}$	Area13	${\delta }_{v}^{13}$	${T}_{\mathrm{peak}}^{13}$	Flux13
	(deg)	(deg)	(km s−1)	(arcmin2)	(km s−1)	(K)	(K km s−1 arcmin2)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
G195.000−03.458+005.87	195.000	−03.475	+5.65	1.75	0.47	1.3	1.3
G195.000−01.575+013.33	195.000	−01.567	+13.45	44.25	1.17	4.3	123.8
G195.000+01.725+007.94	195.000	+01.725	+7.80	6.75	0.42	2.7	7.5
G195.067−01.025+017.78	195.058	−01.025	+18.43	5.25	0.69	1.6	5.6
G195.100−00.442+003.65	195.100	−00.450	+3.65	68.50	0.77	2.1	68.1
G195.100+04.108−010.16	195.108	+04.117	−10.29	0.75	0.28	1.0	0.4
G195.133−03.058+002.70	195.133	−03.058	+2.99	1.25	0.35	1.0	0.8
G195.133+01.792+004.44	195.133	+01.792	+4.32	0.50	0.24	0.7	0.2
G195.175+00.400−006.83	195.183	+00.358	−6.64	3.75	0.45	1.3	2.7
G195.233−03.300+003.81	195.267	−03.317	+3.65	1.25	0.50	1.0	1.0
G195.367−02.875+011.91	195.283	−02.775	+10.96	3.50	0.57	1.1	2.5
G195.292−02.242+018.73	195.292	−02.250	+18.93	3.50	0.44	1.8	3.9
G195.008+00.467+008.10	195.325	+00.583	+4.82	7.50	1.39	1.2	5.8
G195.350+04.350−013.65	195.342	+04.350	−13.62	1.25	0.59	1.3	0.6
G195.358+01.325+006.83	195.358	+01.333	+6.48	1.00	0.38	1.1	0.8
G195.408−02.708+012.06	195.417	−02.700	+12.45	1.00	0.83	0.9	1.1
G195.442+01.050+009.84	195.433	+01.050	+9.96	7.50	0.42	2.5	7.8
G195.400+04.258+010.79	195.442	+04.267	+11.46	0.75	0.30	0.8	0.4
G195.458−00.133+020.64	195.475	+00.000	+19.76	176.50	0.67	3.6	286.6
G195.475−00.500+020.79	195.508	−00.508	+19.92	25.50	0.65	2.9	41.3
G195.542−01.992+015.56	195.533	−02.000	+15.44	134.50	1.01	3.3	202.8
G195.550+00.467+031.91	195.533	+00.483	+32.38	25.00	0.75	3.4	42.4
G195.575−00.200+015.72	195.542	−00.092	+14.45	5.00	0.60	1.8	4.0
G195.625+00.525+032.07	195.642	+00.517	+31.71	2.75	0.44	1.3	2.2
G195.650−00.067+032.07	195.650	−00.067	+32.21	116.75	1.51	5.8	332.6
G195.658+00.350−006.67	195.650	+00.358	−6.14	1.50	0.37	1.2	0.8
G195.667−02.633+011.75	195.658	−02.650	+11.46	11.50	0.52	1.6	10.1
G195.667−04.150+024.92	195.667	−04.142	+24.91	0.75	0.30	0.9	0.3
G195.692−00.567+033.18	195.683	−00.567	+33.04	2.50	0.33	1.6	1.9
G195.692−02.800+013.97	195.692	−02.800	+13.78	0.50	0.43	0.8	0.3
G195.717−02.708+010.00	195.717	−02.708	+9.80	4.25	0.91	1.2	3.6
G195.717−01.383+013.02	195.717	−01.383	+13.12	1.75	0.75	1.1	1.7
G195.675−02.342+004.60	195.742	−02.300	+4.32	203.50	0.59	7.7	508.1
G195.767+01.917-009.37	195.758	+01.892	−8.63	0.50	0.39	0.7	0.4
G195.775−01.933+018.25	195.775	−01.933	+18.60	1.00	0.28	1.0	0.7
G195.783−02.050+014.29	195.783	−02.058	+15.28	0.50	0.55	0.8	0.4
G195.800−03.575+013.33	195.800	−03.592	+13.62	9.75	0.47	1.7	9.0
G196.050−02.583+006.83	195.808	−02.400	+10.13	11.75	1.23	1.5	7.8
G195.833−00.358+035.72	195.833	−00.358	+35.86	0.75	0.47	1.1	0.6
G195.883−00.692+017.30	195.883	−00.683	+17.43	3.00	0.81	1.5	3.0

Note. Columns are cloud names, the position and velocity of maximum of ¹³CO channels in Galactic coordinates, projected angular area of clouds, line width of average spectrum, peak intensity, and flux of ¹³CO. The entire table (1197 clouds) is available from the online journal.

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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The emission of C¹⁸O is significantly weaker than ¹²CO and ¹³CO, so the extraction of the C¹⁸O signal should be very cautious. As discussed in Section 5, the stacking bump at 2σ algorithm is suitable not only for searching for ¹³CO signals but also for searching for C¹⁸O signals. In this section, we only introduce and show the results of the stacking bump at 2σ algorithm in searching for C¹⁸O signals, and the comparison with other algorithms will be mainly shown in Section 5.

The basic principle and steps of the stacking bump at 2σ algorithm are shown in Section 3.2. The steps and criteria of searching for ¹³CO and C¹⁸O signals are basically the same.

According to the above discussion on the difference between searching for ¹³CO and C¹⁸O signals, we summarize the following four criteria for searching for C¹⁸O signals: (1) Three contiguous channels in the C¹⁸O spectrum were larger than 2σ (∼0.5 K). (2) At least one of its eight adjacent pixels identically satisfies condition 1. (3) Each cloud must have at least two pixels. (4) The average spectrum based on these pixels has three consecutive channels above the 3σ_a threshold. These four conditions are basically the same as those for selecting ¹³CO signals. Finally, by checking the average spectra of the three molecular lines ¹²CO, ¹³CO, and C¹⁸O, 32 MCs were confirmed to contain C¹⁸O emission.

Figures 6(a)–(b) show the average spectra of ¹²CO, ¹³CO, and C¹⁸O for 32 clouds detected in C¹⁸O. Different algorithms can lead to differences in the measurement of C¹⁸O flux, and we will discuss this effect in detail in Section 5.

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Table 3 lists the basic parameters of C¹⁸O emission for 32 clouds. The columns are the same as in Tables 1 and 2, but they are calculated from C¹⁸O data.

Table 3. A Catalog of Molecular Clouds Identified with C¹⁸O Emission

Name	${l}_{\mathrm{peak}}^{18}$	${b}_{\mathrm{peak}}^{18}$	${V}_{\mathrm{LSR}}^{18}$	Area18	${\delta }_{v}^{18}$	${T}_{\mathrm{peak}}^{18}$	Flux18
	(deg)	(deg)	(km s−1)	(arcmin2)	(km s−1)	(K)	(K km s−1 arcmin2)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
G195.458−00.133+020.64	195.450	−00.125	+18.86	1.25	0.78	1.2	1.4
G195.675−02.342+004.60	195.717	−02.308	+4.36	14.25	0.85	1.9	17.6
G195.650−00.067+032.07	195.817	−00.208	+30.03	1.75	1.53	1.5	2.8
G195.992−02.758+005.40	195.992	−02.733	+3.86	0.75	0.87	0.9	0.4
G196.158−01.258+013.02	196.158	−01.250	+12.19	0.50	1.82	0.9	0.7
G196.458−01.683+017.78	196.408	−01.708	+17.03	4.75	1.46	1.2	6.4
G196.917+00.633+021.59	196.967	+00.583	+19.36	1.75	1.37	1.1	1.6
G197.583−03.067+003.49	197.658	−03.083	+3.19	1.50	0.29	1.5	1.0
G198.842−02.150+018.89	198.850	−02.158	+18.03	2.25	1.73	1.2	2.5
G200.167+01.550+020.79	199.900	+01.225	+21.03	3.75	0.75	1.3	4.0
G201.358+01.625+022.54	201.375	+01.600	+22.53	1.00	1.27	0.9	1.1
G203.017−03.750+019.52	203.017	−03.733	+19.19	1.25	0.26	1.2	0.5
G202.942+02.075+010.48	203.217	+02.075	+5.03	1028.00	2.12	3.5	1363.0
G206.000−00.267+019.52	205.892	+00.167	+20.03	0.50	0.27	1.1	0.2
G206.008−00.417+022.86	206.025	−00.417	+21.86	2.00	1.28	1.5	3.2
G206.017−00.575+011.43	206.267	−00.700	+10.03	1.00	0.63	1.0	0.3
G206.592−04.358+006.83	206.875	−04.375	+9.19	1.50	1.31	1.1	1.5
G207.017−01.825+015.40	207.108	−01.833	+10.69	362.50	2.61	2.6	462.5
G208.800+02.342+009.84	208.533	+02.375	+9.03	17.75	0.64	1.2	8.4
G208.642−02.900+025.08	208.625	−02.892	+25.03	5.75	1.37	1.6	7.2
G211.592+01.058+044.61	211.517	+00.975	+44.36	2.75	1.57	1.2	2.2
G212.058−03.650+017.78	212.058	−03.633	+17.69	2.25	0.59	1.5	2.0
G212.292−03.308+015.40	212.317	−03.333	+16.03	1.75	0.91	1.0	1.5
G212.958+01.292+042.70	212.950	+01.300	+42.53	3.25	1.35	1.1	3.1
G215.192+00.808+047.62	214.700	+00.708	+47.53	6.25	1.37	1.2	6.0
G214.492−01.808+026.67	215.075	−01.758	+27.03	11.25	1.70	1.4	9.7
G215.483+00.275+049.05	215.492	+00.250	+48.69	0.50	0.81	0.9	0.3
G217.942−02.083+034.45	216.775	−02.650	+23.69	18.25	2.33	1.3	13.8
G217.275−00.317+016.98	217.242	−00.242	+16.03	3.75	0.59	1.5	3.7
G217.333−01.367+052.38	217.333	−01.367	+50.36	0.50	1.45	1.2	0.8
G217.517−02.750+011.59	217.500	−02.758	+10.86	1.00	0.64	1.0	0.9
G217.383−00.083+026.19	218.175	−00.675	+25.19	60.00	1.45	2.1	81.2

Note. Columns are cloud names, the position and velocity of maximum of C¹⁸O channels in Galactic coordinates, projected angular area of clouds, line width of average spectrum, peak intensity, and flux of C¹⁸O. The entire table (32 clouds) is available from the online journal.

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.

Download table as:  DataTypeset image

A total of 7069 clouds were identified based on the DBSCAN algorithm in the ¹²CO data. We identified 1197 clouds having ¹³CO emission and 32 clouds having C¹⁸O emission based on the stacking bump algorithm in the catalog of 7069 clouds, respectively. The detection rate of C¹⁸O, defined by the number of C¹⁸O-emitting clouds divided by the number of ¹²CO clouds, is 0.5%, much lower than the detection rate of ¹³CO (16.9%).

Figure 7 presents ¹³CO and C¹⁸O percentage rates of clouds against different parameters (peak intensity, projected area, and total flux). The rate is the percentage of clouds with ¹³CO (red triangles) and C¹⁸O (blue circles) emission. The percentage rate of ¹³CO increases rapidly with all three parameters and stays at 100% above a certain parameter region (${T}_{\mathrm{peak}}^{12}$ > 10 K, ¹²CO projected area >500 arcmin², ¹²CO flux >1000 K km s⁻¹ arcmin²). The percentage rate of C¹⁸O increases slowly with increasing parameters and reaches 100% after dropping or flattening.

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Figure 8 shows ¹³CO and C¹⁸O percentage rates pixel by pixel against different spectral parameters (peak intensity, integrated intensity). The percentage rate of ¹³CO increases rapidly with ¹²CO peak and intensity, with a peak of 9 K or intensity of 30 K km s⁻¹ giving a 100% percentage rate. The percentage rate of C¹⁸O increases slowly with increasing ¹²CO peak and intensity. Above the integrated intensity of 140 K km s⁻¹ of the ¹²CO emission, the percentage rate of C¹⁸O reaches 100%.

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Surprisingly, the percentage rate of C¹⁸O drops and stays between 50% and 80% when the ¹²CO peak value is greater than 24 K. Notably, the pixels with ¹²CO T_peak greater than 24 K come from six MCs (G202.942+02.075+010.48, G207.017−01.825+015.40, G196.458−01.683+017.78, G217.383−00.083+026.19, G196.825−03.108+025.56, and G211.250−00.375+021.27). In four of the six clouds, C¹⁸O emission was detected (G202.942+02.075+010.48, G207.017−01.825+015.40, G196.458−01.683+017.78, and G217.383−00.083+026.19), while the pixels with ${T}_{\mathrm{peak}}^{12}$ greater than 24 K but without C¹⁸O detection come from three clouds (G202.942+02.075+010.48, known as NGC 2264; G207.017−01.825+015.40, known as the Rosette Nebula; and G196.458−01.683+017.78). Among these three clouds, the pixels with ${T}_{\mathrm{peak}}^{12}$ greater than 24 K but without C¹⁸O detection are only distributed at the boundary of the dense regions and in an arc shape. There are strong radiation fields around these regions, suggesting that the depletion of C¹⁸O could come from the selective photodissociation of C¹⁸O by the radiation field. ¹²CO and ¹³CO are preserved owing to the self-shielding effect.

The peak velocity distributions of clouds that have ¹²CO, ¹³CO, and C¹⁸O emissions are shown in Figure 9. The V_peak distribution of clouds with ¹²CO emission has four components that peak at −10, 10, 23, and 42 km s⁻¹. The V_peak distribution of ¹³CO follows that of ¹²CO and also has four components. However, for C¹⁸O, the first component in the V_peak distribution of −10 km s⁻¹ is absent.

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Figure 10 shows the basic properties of the cloud, including peak intensity, projected angular area, line width of average spectrum, and flux. The ¹²CO peak intensity ${T}_{\mathrm{peak}}^{12}$ ranges from 1.4 to 37.5 K and follows a power-law distribution. We fit the power-law distributions of peak intensity, projected area, line width, and flux by the formula

$$\begin{eqnarray}&&{dN}/{dX}\propto {X}^{-(\alpha +1)},\end{eqnarray} \tag{ 4 }$$

where X is the derived parameter. The fitting index α of ${T}_{\mathrm{peak}}^{12}$ is 4.23. Although the maximum ${T}_{\mathrm{peak}}^{13}$ and ${T}_{\mathrm{peak}}^{18}$ are only 15 and 3.5 K, respectively, which are lower than ${T}_{\mathrm{peak}}^{12}$, they have indices similar to ${T}_{\mathrm{peak}}^{12}$, which are 3.61 and 3.58, respectively. It should be noted that the range and sample number of ${T}_{\mathrm{peak}}^{18}$ are not sufficient to obtain the fitting error. In comparison with the index of ${T}_{\mathrm{peak}}^{12}$ in the second quadrant (Yuan et al. 2021), which is 2.8, we find that the α here is quite different.

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The statistical results of ¹²CO projected angular area are distributed in [1, 3.6 × 10⁴] arcmin², which spans four orders of magnitude. The distribution range of ¹³CO is slightly narrower than ¹²CO with a maximum of 1.3 × 10⁴, while the range of C¹⁸O is much narrow than ¹²CO with a maximum of 1.5 × 10³. The fitting indices α of the distribution of the ¹²CO, ¹²CO, and C¹⁸O clouds are 0.96, 0.75, and 0.41, respectively. In comparison with index of ¹²CO projected angular area in the second quadrant (Yuan et al. 2021), which is 1.9, our projected angular area is flatter.

Velocity dispersion δ_v of the average spectrum traced by different isotopologues is shown in Figure 10. The ranges of ¹²CO, ¹³CO, and C¹⁸O are [0.1, 4.3], [0.2, 5.2], and [0.5, 4.6] km s⁻¹, respectively. The fitting indices of δ_v are 4.4, 3.7, and 1.8 for ¹²CO, ¹³CO, and C¹⁸O, respectively. Ma et al. (2022) found a relation between the dispersion of normalized column density and the sonic Mach number of MCs based on the same data and catalog.

The fluxes of ¹²CO and ¹³CO are distributed in the ranges of [0.7, 4.6 × 10⁵] and [0.2, 6.8 × 10⁴] K km s⁻¹ arcmin², respectively. While the C¹⁸O flux only distributed in the range of [1.7 × 10⁻³, 1.7 × 10³], its maximum flux is lower than ¹²CO and ¹³CO by two and one orders of magnitude, respectively. The flux power-law indices are 0.73, 0.69, and 0.42 for ¹²CO, ¹³CO, and C¹⁸O, respectively. Details will be discussed in our next paper (Wang et al., in preparation).

Large-scale sample studies of MCs help us to understand the basic properties of MCs. But the creation of MC samples depends on algorithms. Clipping (Dame 2011), DBSCAN (Yan et al. 2020), and moment mask (Dame 2011) algorithms are commonly used. Yuan et al. (2022) used these three different methods to extract the ¹³CO gas structures within each ¹²CO cloud based on the counterpart data of the MWISP project in the second Galactic quadrant. They concluded that the clipping extracts plenty of noise spikes with values larger than the 4σ threshold while losing a significant part of faint emission having intensities less than 4σ. The moment mask leaves out a part of faint and tiny ¹³CO structures, due to the smooth procedure. The DBSCAN algorithm can not only avoid the noise spikes but also preserve the faint and tiny ¹³CO structures not identified by the moment mask. This indicates that the DBSCAN algorithm is better than the other two algorithms for searching for ¹³CO and C¹⁸O signals in our data. Therefore, in this paper we mainly compare the differences between DBSCAN and the new algorithms.

The cloud catalog of this paper is established from the ¹²CO datacube by the DBSCAN algorithm, which is more appropriate for identifying consecutive structures within the observed PPV space (Yan et al. 2020). Since ¹³CO and C¹⁸O are less abundant than ¹²CO, one can reasonably assume that the emission of these isotopic lines is within the extent defined by the ¹²CO boundary in PPV space. Therefore, we made measurements of ¹³CO and C¹⁸O emission within the envelope of each ¹²CO map. However, since ¹³CO and C¹⁸O are significantly weaker than ¹²CO, using the same parameters to search for their signals with the DBSCAN algorithm may be questionable because of the low‐S/N of the ¹³CO and C¹⁸O emission. Therefore, the choice of ¹³CO and C¹⁸O signal detection algorithms requires careful comparison. In this study we tried to search for ¹³CO and C¹⁸O signals with three different algorithms, DBSCAN, stacking intensity, and stacking bump.

The first is to directly apply the DBSCAN algorithm to ¹³CO and C¹⁸O. The criteria are shown in Section 3.1. A total of 709 identified clouds have ¹³CO signals, and 11 clouds have C¹⁸O signals.

The alternative algorithm is spectral stacking, which means that the spectra from the same cloud are aggregated to increase the intensity of the signal to meet the detection standard. Stacking multiple spectra based on different criteria may reduce the noise. However, an arbitrary increase of the number of spectra may also reduce the signal's strength. The result is sensitive to the selection of channel (velocity) range. We chose two methods to identify the possible signal range. One is based on the 3σ of the velocity-integrated intensity pixel (pixel is the position in the spatial map; we named it the stacking intensity algorithm), and the other is by looking for weak bumps in the original spectrum that might be weak signals (we named it stacking bump, as we presented in Sections 3.2 and 3.3).

The principle of the stacking intensity algorithm is to search for pixels identified as possible signals based on the S/N threshold in the intensity map of ¹³CO and C¹⁸O. Then, we average the spectrum of those pixels. Finally, we identify the emission of ¹³CO and C¹⁸O based on the S/N of the average spectrum. The principle of the stacking intensity algorithm is similar to the principle of the stacking bump algorithm, but there are differences in how to select the spectrum.

The basic steps of the stacking intensity algorithm mainly include four steps similar to the stacking bump algorithm. The first step is to determine the cloud boundary in PPV space as we do in Section 3.1. ¹³CO and C¹⁸O intensity is integrated within channel (velocity) range based on the envelope obtained by the DBSCAN algorithm in the ¹²CO datacube. The second step is to select pixels in the intensity map of ¹³CO and C¹⁸O. The selected criterion is that ¹³CO and C¹⁸O intensity is above the triple intensity noise threshold (σ_i = $\sigma \sqrt{{N}_{\mathrm{channels}}{\rm{\Delta }}{v}_{i}}$, where N_channels is the channel number in the spectrum). The third step is to average those pixels' spectra and calculate the noise of the average spectrum σ_a . The average spectrum will be identified as a signal based on the criterion of three consecutive channels above the 3σ_a threshold for ¹³CO, but the 2σ_a threshold for C¹⁸O. The last step is to check the spectrum and remove the false detection caused by the wavelike baseline through visual inspection by comparing the average spectral lines of ¹³CO and C¹⁸O of these identified signals with the spectra of ¹²CO. The last two steps of the stacking intensity algorithm are consistent with the stacking bump, and the signal is identified by the S/N values in the step, instead of being identified artificially.

According to the principles and basic steps of stacking intensity, we summarize four criteria for the identification of ¹³CO and C¹⁸O signals. (1) According to the envelope of MCs obtained by the DBSCAN algorithm in the ¹²CO datacube, ¹³CO and C¹⁸O intensity is integrated along velocity. ¹³CO and C¹⁸O integrated intensity is above the 3σ_i threshold. (2) At least one of its eight adjacent pixels satisfies condition 1. (3) Each cloud must have at least two pixels. (4) The average spectrum based on these pixels has three consecutive channels above the 3σ_a threshold for ¹³CO and C¹⁸O. Based on these criteria and manual examination of the average spectrum, a total of 1128 clouds had ¹³CO signals and 32 clouds had C¹⁸O signals (Table 4).

Another spectral stacking algorithm is stacking bump. It is to search the bump in the original spectrum of ¹³CO and C¹⁸O based on the criterion that three contiguous channels were larger than a certain value threshold (1.5σ or 2σ). These bumps are most likely to be weak signals of ¹³CO and C¹⁸O. Finally, the signal was identified by stacking these spectra containing the bump according to the S/N values. Since the stacking bump algorithm is sensitive to the criterion of the 1.5σ or 2σ threshold in spectrum, we test these two thresholds when using it to search for the bump. The first threshold is 2σ, shown in Sections 3.2 and 3.3, and named as stacking bump at 2σ. The second threshold is 1.5σ, named as stacking bump at 1.5σ. The only difference between these two algorithms is the threshold for the bump, and all steps and criteria of the stacking bump at 2σ algorithm are the same as the stacking bump at 1.5σ algorithm. Based on the stacking bump at 1.5σ algorithm, a total of 1197 clouds had ¹³CO signals and 33 clouds had C¹⁸O signals (Table 4).

In terms of quantity, the number of ¹³CO and C¹⁸O signals found by the DBSCAN algorithm is the least, while the other two algorithms are relatively close to each other. The DBSCAN is good at identifying consecutive structures in PPV space, which is highly dependent on the 2σ threshold. As a result, it may lose some clouds of weak signal.

The stacking algorithm searches for ¹³CO or C¹⁸O spectra with either "bumps" feature or the 3σ threshold of integrated intensity in a small range of velocity defined by the ¹²CO emission and then averaging those spectra, which may result in false detection caused by spurious noise spikes. Determining the authenticity of the ¹³CO or C¹⁸O emission requires a noise test for algorithms. We chose two kinds of noise to test the stacking algorithm with different parameters; one is Gaussian noise, and the other is real noise in the velocity range of the spectrum without ¹²CO emission in the data.

We replace the ¹³CO and C¹⁸O cube with a cube containing only Gaussian noise at the same level as the actual cube, and then we run the stacking algorithm with different parameters on the noise-only cube. Tables 5 and 6 show results of different stacking algorithms according to the 7069-cloud boundary on the noise-only cube. The test results show that, for Gaussian noise, the algorithm can only produce one false detection. However, the real noise of the data may not be Gaussian. It is also necessary to test in real data noise space.

Our observation data are 3D PPV data, and the boundary of these 7069 clouds is a three-dimensional structure distributed in the velocity range [−20, 70] km s⁻¹. In order to test the real data noise on the algorithm, we shifted the boundary of the cloud to the [−135, −45] and [105, 195] km s⁻¹ velocity intervals without signal emission in the velocity dimension space. According to the results of the Columbia CO survey (Dame et al. 2001), there is no CO emission in these two velocity intervals. We also searched for ¹²CO signals in these two intervals and confirmed that there is no ¹²CO signal in these two intervals. In addition, we checked data of the Leiden/Argentine/Bonn (LAB) Survey of Galactic H i (Kalberla et al. 2005), and there was also no H i signal in the two velocity intervals. The absence of CO emission indicates that these two intervals are suitable for verifying the algorithm.

We tested the results of the algorithm with different parameters in these two velocity intervals. We tested different rms thresholds in the stacking bump algorithm and the stacking intensity algorithm. The results (Tables 5 and 6) indicate that an rms threshold of 2σ can effectively avoid the possibility of false detections generated by noise. The number of false detections (1–3) generated by the 2σ threshold is very small, far less than the number of ¹³CO and C¹⁸O (1197 and 32) signals identified in [−20, 70] km s⁻¹, and it will not have a significant impact on the results. On the other hand, the stacking intensity algorithm produced more false detection than the stacking bump at 2σ algorithm. Therefore, from these noise tests, it can be determined that the possibility of false detection generated by the stacking bump at 2σ algorithm is very low. It should be noted that the pure noise cube yields so few spurious clouds compared with the number derived from the velocity edges of the real data with the same noise level. Based on the noise statistical distribution (Figure 1), the real noise distribution has Gaussian-like characteristics, but it is not perfect Gaussian noise. This difference between real noise and pure noise cube can lead to more spurious noise spikes in real data. Moreover, a slight difference in the spatial distribution of noise (Figure 2) may also affect the results of signal searching.

Figure 11 illustrates the spatial boundary of ¹³CO emission of cloud G207.017−01.825+015.40 (known as the Rosette Nebula; Li et al. 2018) based on different algorithms. The DBSCAN algorithm shows a smooth and coherent structure in the boundary of ¹³CO compared to other algorithms owing to its high threshold in pixel number, but it does not detect the ¹³CO emission in some regions with weak ¹²CO intensity. The other algorithms exhibit similar properties of fragmented spatial distribution in ¹³CO.

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Similar maps that show the spatial boundaries of the detected C¹⁸O emission within the Rosette Nebula are given in Figure 12. Compared with other algorithms, the results of the stacking bump at 2σ algorithm are more extended than the results of the DBSCAN algorithm and can also detect sporadic distribution in the region with weak ¹²CO intensity. Although the stacking bump at 1.5σ algorithm can detect the widest area of C¹⁸O emission, it may lead to false high-σ signals owing to its low 1.5σ threshold, as confirmed in Section 5.2.

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The spatial boundaries of ¹³CO and C¹⁸O emission of cloud G217.383−00.083+026.19 (known as Sh 2–287; Li et al. 2018) are presented in Figures 13 and 14, respectively. As with the results of the Rosette Nebula, the DBSCAN algorithm shows a smoother boundary of ¹³CO and C¹⁸O than the others. The stacking bump at 2σ algorithm is more complete in overall distribution than the DBSCAN algorithm, although the spatial coverage area in the stacking bump at 2σ algorithm is smaller than the result in the stacking bump at 1.5σ algorithm.

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By comparing the spatial distribution of ¹³CO and C¹⁸O emission identified by different algorithms, it is found that all the algorithms can find the main structure of ¹³CO and C¹⁸O emission, which means that there is no difference between these algorithms for detecting strong signals. The main difference among these algorithms is in the detection of weak signals. However, the stacking bump at 1.5σ algorithm shows the widest area of C¹⁸O emission. However, considering the false detections caused by spurious noise spikes (as discussed in Section 5.2), the weak signal identified by the stacking bump at 1.5σ algorithm partially comes from spurious noise spikes. Considering the accuracy and completeness of the algorithm, we prefer the stacking bump at 2σ algorithm.

Figure 15 shows a statistical comparison of the number of pixels and the flux of clouds identified with ¹³CO signals under different algorithms, respectively. This indicates that in terms of the overall distribution, there is no significant difference in the ¹³CO flux value obtained among the three algorithms. It is obvious that the ¹³CO flux of each cloud searched by DBSCAN is systematically lower than the value obtained by the stacking bump at 2σ algorithm. There is no significant systematic bias in the number of pixels between the two algorithms in the clouds with large flux (¹²CO Flux > 1 × 10² K km s⁻¹ arcmin²). This is due to the interception of data by DBSCAN based on the 2σ threshold when searching and calculating signals, which results in the loss of weak signals in each spectrum that are below the 2σ threshold. This effect is more significant in MCs with large pixel numbers.

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The pixel number and flux found by stacking intensity and stacking bump at 1.5σ are systematically higher than the results of the stacking bump at 2σ. As shown in the noise test results in Section 5.2, the systematic high results of the stacking intensity and stacking bump at 1.5σ algorithms may be caused by the noise injection after the threshold reduction. This indicates that blindly lowering the threshold may introduce too much noise into the statistics and lead to systematic bias in the results.

The comparison results of the C¹⁸O signals are similar to those of the ¹³CO signal (Figure 16). In the cross-sample between the DBSCAN algorithm and the stacking bump algorithm, the flux and pixel number obtained by the DBSCAN algorithm are systematically lower than those of the stacking bump algorithm, and the difference is stronger than that obtained by ¹³CO.

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As with the case of ¹³CO, the stacking bump algorithms are systematically biased in terms of flux and pixel number. As discussed above, this is caused by spurious noise spikes when lowering the threshold.

According to the above results, compared with the other two algorithms, the stacking bump at 2σ algorithm not only has a very low false signal detection rate in noise testing (Section 5.2) but also is better than DBSCAN in flux and spatial distribution. In a future study, we will focus on the results of the stacking bump algorithm.

The integral range of ¹²CO is determined by the DBSCAN algorithm. Since the abundance of ¹³CO is lower than ¹²CO, its velocity range is generally slightly smaller than the ¹²CO range. Therefore, the approximation that the emission range in the ¹³CO spectrum is the same as ¹²CO can be a convenient way to determine the integration interval for ¹³CO. Even though noise will increase as the square root of the number of spectral channels in the integral interval, the difference in the velocity range between ¹²CO and ¹³CO is too small to produce a difference by orders of magnitude. However, this method is not suitable for C¹⁸O. The abundance of C¹⁸O is much lower than that of ¹²CO and ¹³CO; its velocity range is much smaller than the ¹²CO range. Hence, using the velocity range of the ¹²CO spectrum to integrate C¹⁸O is not a good idea; we try to integrate the C¹⁸O spectrum using the emission range of the ¹³CO spectrum.

Figure 17 shows the intensity distribution of cloud MWISP G217.942−02.083+034.45 by integrating C¹⁸O signals according to the velocity range within ¹²CO and ¹³CO emission regions (great than 2σ in the spectrum), respectively. This clearly shows that integrating C¹⁸O over the velocity range of ¹²CO will produce a large scattering, and the noise intensity is even greater than the signal intensity. If the C¹⁸O is integrated with the signal range of ¹³CO, the noise of the C¹⁸O integration intensity will be greatly reduced, which makes the signal easier to detect. Considering the influence of noise comprehensively, the integration of C¹⁸O in this paper is carried out in a range greater than the 2σ threshold in the ¹³CO spectrum.

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