An Unbiased CO Survey Toward the Northern Region of the Small Magellanic Cloud with the Atacama Compact Array. II. CO Cloud Catalog

Interstellar molecular clouds generally have hierarchical, complex structures composed of diffuse gas, dense filaments, and cores (e.g., Lada & Adams 1992). The complexity in nature makes it difficult for us to determine clear boundaries of each subcomponent; nevertheless, some decomposition analyses, which have been developed in the last decades (e.g., Williams et al. 1994; Rosolowsky & Leroy 2006; Rosolowsky et al. 2008), are still powerful tools for characterizing cloud properties and their statistical nature, such as the size–linewidth relation and mass function. As described in Paper I, the CO molecular clouds in the SMC are spatially more compact than those in the MW, and the outer boundaries are relatively easy to define. On the other hand, larger clouds in the observed field have multiple local peaks inside, requesting a hierarchical characterization of the structure with different intensity levels. Bolatto et al. (2013) suggested that the properties of the outer and inner regions of molecular clouds are somewhat different in low-metallicity environments, such as the SMC. Therefore, it is useful to treat the large outer and small inner structures separately. The dendrogram algorithm astrodendro (Rosolowsky et al. 2008; Shetty et al. 2012; Colombo et al. 2015) is one of the best options to meet our requirements (see also the comparison of different cloud-decomposition methods by Li et al. 2020). Several studies (Wong et al. 2017; Naslim et al. 2018; Nayak et al. 2018; Wong et al. 2019) applied the same scheme to ALMA CO data of molecular clouds in the Large Magellanic Cloud (LMC) at an angular resolution of ∼1 pc. The CPROPS method of Rosolowsky & Leroy (2006) is also promising, but there are limitations in decomposing physically reasonable objects in highly crowded and low-contrast environments (Colombo et al. 2014). A patchwork-like separation using CLUMPFIND (Williams et al. 1994) enables us to estimate the total flux of discrete objects, but large and small structures cannot be treated separately.

As input data, we used postprocessed CO cube, moment-masked data (see Dame 2011a) whose emission-free pixels were set at zero value judging from a smoothed data cube whose signal-to-noise ratio is higher than that of the raw data (see also the detailed description in Section 2 in Paper I). The astrodendro algorithm has three input parameters, min_value, min_npix, and min_delta. The first argument is the minimum-intensity value to consider in the cube data. Because most of the noise-component pixels have already been eliminated by the masking analysis, we decided to consider emissions that were as weak as possible by setting min_value to 0 K. This zero-level setting minimizes the truncation effect of weak emission and does not account for unreliable weak peaks. The combination with the other two parameters described below resulted in a significant cloud identification with a lowest peak intensity of 0.35 K (≳5σ) among all entities. The second parameter, min_pix, is the minimum number of voxels that have significant emission in the three-dimensional (x,y,v) axis needed to be connected as a single component. We set this value of 38 equal to the voxel number of at least a single-beam element in XY space and three pixels in the velocity direction. These two parameters are well defined by the setting of the observation, and thus, we treat them as fixed values, while the last parameter, min_delta, can be chosen arbitrarily. The value is a threshold for entities in close proximity to be considered as independent components. Our fiducial value of min_delta is 0.18 K, corresponding to a noise level of ∼3σ for the data set. The number of identified structures and statistical results does not change significantly even if this value is changed by a factor of several from the fiducial value. Although we decomposed the cloud and discussed the data using the fixed fiducial value, the parameter dependence is further discussed in the Appendix.

We performed the astrodendro analysis and identified 426 structures, called trunks, which are the largest continuous structures. Of these, 361 trunks do not contain internal structures and are categorized as single CO trunks, which are spatially/velocity-independent entities of the surroundings. In addition, 65 trunks contain internal structures (referred to as CO leaves) for a total of 257 internal leaves. We refer to the 426 trunks and 257 internal leaves as CO trunks and CO leaves, respectively. Figure 1 illustrates the boundary of individual sources of the two categories on the CO map. Figure 2 shows two examples of zoomed-in views toward the N66 and N78 regions to demonstrate how the identified structures are distributed in the two large systems. The CO trunk boundaries are determined by an isosurface close to the minimum-intensity contour level in the data cube, providing a fairly robust identification against the input parameter dependence. The 2D projected map sometimes shows overlapping boundaries, but they are independent entities in velocity space. The dependence of min_delta is somewhat more sensitive in the CO leaves than in the trunks. Nevertheless, the CO leaf boundary seems to reasonably trace local peaks on the CO map (see Figure 2).

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The astrodendro analysis outputs the basic properties of the identified structures, their centroid coordinates in three-dimensional axes ($\overline{x}$, $\overline{y}$, $\overline{v}$), the rms size of the major/minor axes (σ_maj and ${\sigma }_{\min }$), the rms linewidth σ_v , and the position angle of the major axis (P.A.). Within the isosurface contours of all identified structures, we additionally derived several parameters. The brightness temperature T_peak is simply the peak value of the identified voxels. We integrated the flux to obtain the CO (J = 2–1) luminosity L_CO(2–1), adopting a distance of 62 kpc (Graczyk et al. 2020). The effective rms size, ${\sigma }_{r}=\sqrt{{\sigma }_{\mathrm{maj}}{\sigma }_{\min }}$, is multiplied by 1.91, as suggested by Solomon et al. (1987), to derive the observed spherical radius R_obs, and then we applied the beam-deconvolution scheme, ${R}_{\mathrm{deconv}}=\sqrt{{R}_{\mathrm{obs}}^{2}-{\theta }_{\mathrm{beam}}^{2}}$, where θ_beam is the beam size of the present study. We used an approach to estimate the uncertainties of the cloud properties following the bootstrap method (Rosolowsky & Leroy 2006). We generated 100 realizations to sample the derived parameters. Tables 1 and 2 summarize the properties of some of the identified CO trunks and leaves, respectively, and the full catalogs are available as online material.

Table 1. Physical Properties of the CO Trunks

id	R.A. (J2000.0)	Decl. (J2000.0)	$\overline{v}$	σv	δ σv	σmaj	${\sigma }_{\min }$	P.A.	Tpeak	LCO(2–1)	δ LCO(2–1)
	(hms)	(dms)	(km s−1)	(km s−1)	(km s−1)	(arcsec)	(arcsec)	(deg)	(K)	(K km s−1 pc2)	(K km s−1 pc2)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
0	0h57m468	$-72^\circ 19^{\prime} 04\buildrel{\prime\prime}\over{.} 8$	116.1	0.52	0.13	5.5	3.4	94.5	2.5	41.7	0.6
1	0h59m523	$-72^\circ 14^{\prime} 24\buildrel{\prime\prime}\over{.} 0$	117.0	0.37	0.18	4.3	2.7	110.4	2.8	21.3	1.1
2	0h59m334	$-72^\circ 20^{\prime} 34\buildrel{\prime\prime}\over{.} 8$	121.2	0.34	0.27	2.5	1.7	−156.6	1.1	3.9	1.4
3	0h59m370	$-72^\circ 20^{\prime} 42\buildrel{\prime\prime}\over{.} 0$	122.1	0.70	0.15	3.4	2.6	71.0	2.9	31.9	0.8
4	0h59m583	$-72^\circ 15^{\prime} 57\buildrel{\prime\prime}\over{.} 6$	121.7	0.38	0.28	2.1	1.9	−142.1	0.4	1.9	0.8
5	1h00m377	$-72^\circ 14^{\prime} 56\buildrel{\prime\prime}\over{.} 4$	128.1	0.43	0.22	2.4	2.2	114.9	1.4	6.7	0.9
6	0h59m041	$-72^\circ 11^{\prime} 02\buildrel{\prime\prime}\over{.} 4$	144.3	2.02	0.06	14.4	3.5	−175.8	4.4	343.0	0.3
7	0h58m226	$-72^\circ 12^{\prime} 46\buildrel{\prime\prime}\over{.} 8$	144.6	0.55	0.21	2.7	2.4	76.2	2.0	13.5	0.9
8	0h58m526	$-72^\circ 10^{\prime} 40\buildrel{\prime\prime}\over{.} 8$	145.1	1.55	0.06	5.8	3.6	48.4	1.9	72.9	0.3
9	0h58m046	$-72^\circ 20^{\prime} 31\buildrel{\prime\prime}\over{.} 2$	145.2	0.39	0.24	2.3	1.9	138.1	0.8	3.5	1.1
id	Rdeconv	δ Rdeconv	Mvir	δ Mvir	${N}_{{{\rm{H}}}_{2}}$	MCO	${n}_{{{\rm{H}}}_{2}}$	IR source
	(pc)	(pc)	(M⊙)	(M⊙)	(1021 cm−2)	(M⊙)	(102 cm−3)
(13)	(14)	(15)	(16)	(17)	(18)	(19)	(20)	(21)
0	2.26	0.08	634	310	3.0	751	6	B
1	1.66	0.11	235	239	1.9	385	8	A
2	0.63	0.24	74	144	0.9	69	27	B
3	1.38	0.10	696	301	4.3	574	21	A
4	0.51	0.23	78	147	0.5	34	24	B
5	0.88	0.18	167	192	1.3	120	17	B
6	3.98	0.04	16871	924	12.1	6183	9	A
7	1.05	0.13	332	258	2.4	243	20	A
8	2.41	0.06	6000	467	4.3	1315	9	A
9	0.65	0.20	101	148	0.8	62	21	B

Note. δ denotes the errors, and they are derived using the bootstrap method (see the text in Section 3.1). Column density (${N}_{{{\rm{H}}}_{2}}$), CO luminosity masses (M_CO), and H₂ volume density (${n}_{{{\rm{H}}}_{2}}$) assuming X_CO = 7.5 × 10²⁰ cm⁻²(K km s⁻¹)⁻¹ and a CO (2–1)/(1–0) ratio of 0.9. A and B represent the Spitzer + Herschel YSO candidate and other Spitzer catalog sources, respectively (see the text in Section 3.3). The full catalog is available as online material.

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 2. Physical Properties of the CO Leaves

id	R.A. (J2000.0)	Decl. (J2000.0)	$\overline{v}$	σv	δ σv	σmaj	${\sigma }_{\min }$	P.A.	Tpeak	LCO(2–1)	δ LCO(2–1)
	(hms)	(dms)	(km s−1)	(km s−1)	(km s−1)	(arcsec)	(arcsec)	(deg)	(K)	(K km s−1 pc2)	(K km s−1 pc2)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
0	0h58m569	$-72^\circ 10^{\prime} 55\buildrel{\prime\prime}\over{.} 2$	140.5	1.30	0.22	2.6	2.0	−140.9	0.9	9.6	0.3
1	0h59m010	$-72^\circ 11^{\prime} 02\buildrel{\prime\prime}\over{.} 4$	142.8	0.75	0.25	2.8	1.5	−173.0	2.4	21.1	0.3
2	0h59m055	$-72^\circ 11^{\prime} 02\buildrel{\prime\prime}\over{.} 4$	145.3	1.08	0.11	6.5	2.2	176.3	4.4	142.3	0.3
3	0h59m146	$-72^\circ 11^{\prime} 06\buildrel{\prime\prime}\over{.} 0$	146.4	1.45	0.13	3.3	2.5	155.2	1.9	38.6	0.4
4	0h58m533	$-72^\circ 10^{\prime} 44\buildrel{\prime\prime}\over{.} 4$	144.0	0.47	0.33	3.5	1.7	46.1	1.9	11.9	0.4
5	0h58m571	$-72^\circ 11^{\prime} 02\buildrel{\prime\prime}\over{.} 4$	144.3	0.44	0.29	2.2	1.7	−139.0	1.1	5.1	0.7
6	0h57m547	$-72^\circ 01^{\prime} 40\buildrel{\prime\prime}\over{.} 8$	146.7	0.99	0.09	5.0	3.0	171.0	3.2	71.4	0.4
7	0h58m521	$-72^\circ 10^{\prime} 37\buildrel{\prime\prime}\over{.} 2$	146.2	0.62	0.30	3.6	1.5	79.8	1.3	10.0	0.2
8	0h58m535	$-72^\circ 09^{\prime} 46\buildrel{\prime\prime}\over{.} 8$	147.4	0.87	0.17	4.0	1.6	105.1	1.2	9.1	0.3
9	0h59m185	$-72^\circ 11^{\prime} 09\buildrel{\prime\prime}\over{.} 6$	147.2	0.50	0.31	4.9	1.4	−137.3	1.7	10.3	0.3
id	Rdeconv	δ Rdeconv	Mvir	δ Mvir	${N}_{{{\rm{H}}}_{2}}$	MCO	${n}_{{{\rm{H}}}_{2}}$
	(pc)	(pc)	(M⊙)	(M⊙)	(1021 cm−2)	(M⊙)	(102 cm−3)
(13)	(14)	(15)	(16)	(17)	(18)	(19)	(20)
0	0.80	0.15	1406	514	1.9	173	32
1	0.59	0.14	346	256	4.5	381	180
2	1.93	0.07	2367	472	10.0	2565	34
3	1.31	0.10	2870	533	5.1	696	30
4	0.94	0.16	216	314	1.8	214	25
5	0.41	0.24	82	155	1.2	93	132
6	1.97	0.10	2026	399	5.7	1286	16
7	0.88	0.19	355	364	2.0	180	26
8	1.07	0.16	847	368	1.6	165	13
9	1.11	0.17	292	374	1.9	186	13

Note. Same as Table 1, but for CO leaves. Information of infrared source associations to the CO leaves is included in the final column (see Section 3.3). The full catalog is available as online material.

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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Figure 3 shows histograms of the R_deconv, σ_v , L_CO(2−1), and T_peak of the CO trunks and leaves. The total number of luminous large structures is not very large with respect to the full population. The most CO luminous source (L_CO(2−1) ∼2500 K km s⁻¹ pc²) is the northern filamentary complex in N66 (see also Neelamkodan et al. 2021), as shown at the upper left side of Figure 2(a). For the smaller structure, the CO trunks and leaves seem to exhibit relatively similar properties as a whole.

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The physical quantities described above are purely determined from the observational data. Although additional assumptions are needed, we calculated the following properties to further characterize the identified CO sources. We derived the virial mass, ${M}_{\mathrm{vir}}=1040{\sigma }_{v}^{2}{R}_{\mathrm{deconv}}$ (Solomon et al. 1987) assuming the density profile of ρ ∝ r⁻¹, ignoring the effect of external pressure and magnetic field. The peak-integrated intensity was used to calculate the H₂ column density (${N}_{{{\rm{H}}}_{2}}$) with the assumptions of a CO-to-H₂ conversion factor, X_CO = 7.5 × 10²⁰ cm⁻²(K km s⁻¹)⁻¹ (Muraoka et al. 2017) in the SMC and an intensity ratio of CO (J = 2–1)/CO (J = 1–0), R_2−1/1−0 of 0.9 (Bolatto et al. 2003; Paper I). Note that the X_CO factor in the low-metallicity SMC environment is not as tightly constrained as the Galactic value. Based on the recent measurement in the literature, the mass determination accuracy is presumably a factor of two or three at best (see also the discussion and our independent estimation using the current CO data set in Section B). M_CO is the total gas mass integrated over the regions inside the lowest contour level of the identified structure. We estimated the average H₂ number density using the following equation: ${n}_{{{\rm{H}}}_{2}}=3{M}_{\mathrm{CO}}/4\pi \mu {{\rm{m}}}_{{\rm{H}}}{R}_{\mathrm{doconv}}^{3}$, where μ is the mean molecular weight per hydrogen (2.7), and m_H is the H atom mass.

We further explain the relation among the cloud properties, such as the size–linewidth relation, and the cloud mass function in Sections 3.2, 4.1 and 4.2. We also perform cross-matching analyses with the CO trunks and infrared young stellar sources in Section 3.3.

Large-scale molecular cloud surveys found the famous scaling relation between the molecular cloud radius R in pc units and the velocity dispersion σ_v : that is, σ_v ≈ 0.72R^0.5 km s⁻¹ (e.g., Larson 1981; Solomon et al. 1987; Heyer et al. 2001). This relation is established over a wide spatial range from ∼1 pc to several hundred pc. The sizes (radii) of our CO cloud sample identified as trunks range from ∼1 pc to a few dozen pc, which allows us to test whether a similar relation to the MW is also valid in the SMC over an order of magnitude. Figure 4 shows the σ_v − R_deconv plot of the CO trunks and leaves: σ_v becomes larger as R_deconv increases.

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We performed an orthogonal distance regression (ODR) fitting, taking into account the errors in both axes (scipy.odr; Virtanen et al. 2020), to determine the intercept and slope of σ_v = α₀ R^−β . As shown in Figure 4, the best-fit values are (α₀, β) = (0.46 ± 0.01, 0.56 ± 0.02) for the CO trunks and (α₀, β) = (0.49 ± 0.01, 0.46 ± 0.04) for the CO leaves. The fitted intercepts are ∼0.2 lower than that in the MW standard relation, while the power-law index is comparable to that of the MW. The recent CO (2–1) SMC survey at a 9 pc resolution also reproduced a similar trend (Saldaño et al. 2023). We discuss the implications of the size–linewidth relation in Section 4.1.

We investigated whether the CO trunks have known infrared sources with their categories of (1) Spitzer + Herschel young stellar object (YSO) candidates and (2) not necessarily categorized as YSO, but infrared point sources discovered by Spitzer. Based on a better infrared position accuracy than the beam size of the ACA, we regarded a CO trunk as an associated source if there was at least a single infrared source within its cloud boundary.

Gordon et al. (2011) obtained a comprehensive point-source catalog from the Spitzer Space Telescope Surveying the Agents of Galaxy Evolution in the Tidally Stripped, Low Metallicity Small Magellanic Cloud (SAGE–SMC) Legacy Program. The SAGE-SMC IRAC (InfraRed Array Camera) Single Frame + Mosaic Photometry Catalog has an angular resolution of ∼2'' at IRAC bands (3.5/4.5/5.8/8.0 μm) with a pointing accuracy of ∼03 (see the documentation by Gordon et al. 2014 ¹⁶ ), which is sufficiently high to be compared with the ACA CO map at ∼7'' resolution. The Spitzer/SAGE-SMC point-source catalog includes not only YSOs, but also many normal stars, evolved stars, and background galaxies (see, e.g., Boyer et al. 2011). Several studies identified and characterized the young population based on the color–magnitude diagram (CMD) spectral energy distribution (SED) modeling by combining data from other wavelengths. There is a list of 4927 objects in the SMC that has at least two or more band identifications as point sources in the IRAC(3.5/4.5/5.8/8.0 μm) or MIPS 24 μm detectors and that satisfy certain CMD criteria to exclude contamination from background galaxies and evolved stars (see Section 4.1 in Sewiło et al. 2013). Sewiło et al. (2013) identified 742 high-reliability YSO candidates across the SMC based on the CMD color–magnitude cuts, image inspection, SED fitting, and a CMD score (a measure of confidence that a source is not a non-YSO contaminant, based on its position in CMDs used for the initial source selection). Out of these, 452 candidates are well characterized by YSO SED models (Robitaille et al. 2006). Within the ACA observed field, the total number of the Spitzer-based YSO candidates is 254; they are plotted in Figure 5(a). Seale et al. (2014) extended the YSO search to longer wavelengths based on the HERschel Inventory of the Agents of Galaxy Evolution (HERITAGE) data (Meixner et al. 2013). Figure 5(b) shows the identified candidates, which are the high-reliability + possible YSOs in the Seale et al. (2014) catalog. In the ACA observed field, there are 25 YSO candidates that were not cataloged in the Spitzer mid-infrared studies above, indicating that they are likely younger. We call them (1) Spitzer + Herschel YSO candidate list and investigate whether they are contained within the lowest contours of the CO trunks.

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The positions of the Spitzer + Herschel YSO candidates show a good spatial correlation with the CO cloud distributions, indicating that they are true YSOs enveloped in their natal molecular material. However, due to the CMD selection criteria, these highly reliable YSO samples are mostly biased toward high- and intermediate-mass objects (Sewiło et al. 2013). In addition, the angular resolution of the previous CO survey (e.g., ∼160''; Mizuno et al. 2001) was two orders of magnitude coarser than that of Spitzer, making it impossible to accurately investigate whether the IRAC point sources are spatially correlated with molecular clouds. Our analysis of the CO cloud association with the full IRAC/MIPS catalog potentially allows us to search for additional YSO candidate samples. We conducted a cross-matching between the SAGE-SMC catalog sources and our CO data and found that 336 CO trunks were associated, while the remaining 90 entities did not match the catalog. Additionally, we compared with the S³MC (Spitzer Survey of the Small Magellanic Cloud) catalog (Bolatto et al. 2007; Simon et al. 2007), which is based on a deeper survey than SAGE-SMC. The combined SAGE-SMC and S³MC source lists are collectively referred to as "other Spitzer catalog sources". We first checked whether the list (1) is in the CO clouds, and if it was not, (2) we investigated whether the other Spitzer source list was attached within them. For display purposes, we only plot the (2) sources with a CO detection within the lowest contours of the trunks (Figure 5(c)).

If there is no other Spitzer catalog source in the CO trunks, it is regarded as a starless cloud candidate, highlighted in blue contours in Figure 5(c). It should be noted that according to the current criteria for infrared catalog extraction, these candidates are still considered to be in a purely starless phase. Upon our visual inspection of the IRAC maps, some sources with extended emission also have local peaks that appear to be associated with CO clouds. Furthermore, even in sources that are completely dark in the Spitzer survey, high-resolution molecular gas studies have sometimes discovered molecular outflow as a strong indicator of protostar formation in infrared-quiescent regions in the MW (e.g., Tan et al. 2016) and the LMC (e.g., Tokuda et al. 2019, 2022). The James Webb Space Telescope (JWST) will enable us to detect these faint sources that are missed with Spitzer. However, because these sources are low-mass sources or are in an early stage of high-mass star formation, we believe that their feedback effect on the parental cloud itself is negligible on a large scale, and it is not deeply explored in this work.

Column (21) of Table 1 denotes the cross-matched results. The 426 CO trunks in total (see Section 3.1) can be divided into three categories: 94 Spitzer + Herschel YSO sources, 303 Spitzer catalog sources, and 29 starless cloud candidates. To facilitate the comparison among the categories, the following analysis excludes the CO trunks with CO leaves, i.e., complex, large structures. Table 3 summarizes the typical (median) properties of the single CO trunks of each category. The resulting numbers of Spitzer + Herschel sources, other Spitzer catalog sources, and starless cloud candidates are 57, 275, and 29, respectively. We performed a Kolmogorov-Smirnov (KS) test to determine whether the physical properties belonged to different populations. The p-values for the Spitzer + Herschel YSO, other Spitzer catalog, and starless candidate source properties are all below 0.05, except for ${n}_{{{\rm{H}}}_{2}}$. Nevertheless, we argue that all the samples belong to distinct populations.

Table 3. The Median Properties of the Three Categories of the Single CO Trunks in the SMC North

Category	Number	σv	±σv	LCO(2–1)	±LCO(2–1)	Rdeconv	±Rdeconv
		(km s−1)	(km s−1)	(K km s−1 pc2)	(K km s−1 pc2)	(pc)	(pc)
Spitzer + Herschel YSO candidate	57	0.66	0.25	31.9	47.3	1.57	0.80
other Spitzer catalog source	275	0.46	0.17	7.2	20.9	1.14	0.66
Starless cloud candidate	29	0.40	0.13	4.2	4.1	0.91	0.38
Category	${N}_{{{\rm{H}}}_{2}}$	$\pm {N}_{{{\rm{H}}}_{2}}$	MCO	±MCO	${n}_{{{\rm{H}}}_{2}}$	$\pm {n}_{{{\rm{H}}}_{2}}$	Total MCO
	(1021 cm−2)	(1021 cm−2)	(M⊙)	(M⊙)	(102 cm−3)	(102 cm−3)	[104 M⊙]
Spitzer + Herschel YSO candidate	3.9	2.5	574	853	14	23	4.8
other Spitzer catalog source	1.1	1.1	130	377	10	49	7.1
Starless cloud candidate	0.7	0.4	75	73	10	29	0.3

Note. ± denotes the standard deviation of each physical property. We adapted X_CO = 7.5 × 10²⁰ cm⁻²(K km s⁻¹)⁻¹ to obtain the column density (${N}_{{{\rm{H}}}_{2}}$), cloud mass (M_CO), and number density (${n}_{{{\rm{H}}}_{2}}$). The total M_CO is the sum of M_CO in each category.

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The total number and M_CO of the starless sources correspond to ∼8% and ∼2%, respectively, with respect to the total population (see Table 3). σ_v and M_CO appear to be larger as the star formation activity becomes energetic. The typical σ_v in the Spitzer + Herschel YSO sources is indeed larger than the value that we expect from the global size–linewidth relation (Section 3.2) at the R_deconv. Figure 6 shows the comparison histogram of the physical properties. The general trend is that large physical quantities are in the two categories: Spitzer + Herschel YSO candidate, and other Spitzer catalog source.

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Single-dish Galactic and ALMA LMC studies also obtained a higher velocity dispersion and a larger radius/mass at star-forming clouds (Kawamura et al. 1998; Ikeda & Kitamura 2009; Nayak et al. 2016; Naslim et al. 2018). They discussed that feedback from protostellar objects, such as high-radiation pressure of shocks and molecular outflow/jets, enhances the linewidth. The increase in M_CO suggests that there is a mass accumulation during the star and/or cloud formation phase. The possible mass-supply sources are CO-dark-H₂ and/or H i gas around the CO clouds, as suggested in LMC studies (e.g., Fukui et al. 2019; Tokuda et al. 2019, 2022). According to some theoretical studies, atomic gas is a more important reservoir to promote star formation in a lower-metallicity environment (e.g., Krumholz 2012; Fukushima et al. 2020).

Interestingly, we found many compact CO clouds whose location is relatively isolated from the larger clouds in the field (see also Paper I). In these clouds, massive YSOs do exist at some of the isolated compact clouds, and they could be suitable targets in which to explore the initial condition of high-mass star formation because the relatively simple configuration provides an easier way than typical molecular cloud complexes that harbor well-developed H ii regions and/or supernova remnants. Extragalactic studies are more appropriate for discovering such an object, and recent ALMA observations have been studying similar targets in the LMC (Harada et al. 2019). Follow-up ALMA 12 m array observations in the SMC are desired to further understand the nature of these isolated clouds and the star formation therein.

Bolatto et al. (2008) already described that the velocity dispersions are smaller for clouds with the same sizes compared with the MW relation by a factor of two in lower-metallicity targets of their sample (see also Saldaño et al. 2023). They probably overestimated the cloud sizes due to the larger beam size of ∼10 pc. Our ACA observations show that the size–linewidth relation is closer to that in the MW than the Bolatto et al. (2008) result, possibly thanks to the improved spatial resolution. However, we still see a departure from the MW relation toward the lower side in velocity dispersions with a factor of ∼1.5. Bolatto et al. (2008) discussed two possibilities for this trend: (1) the column density is lower than the MW under the condition of virial equilibrium, or (2) the turbulent motion is not strong enough to stabilize the core, and the clouds are supposed to be unstable against the freefall collapse. In the former case, the column density is proportional to the square of linewidth, i.e., our finding of ∼1.5 times lower velocity dispersion in the SMC predicts a factor of ∼2 lower column density. The second idea is highly unlikely in the MW because statistical counting methods using a large number of starless cores with respect to star-forming cores tell us that the lifetime of dense objects until protostar formation is generally longer than the freefall time (Onishi et al. 2002; Ward-Thompson et al. 2007) unless their central density exceeds ∼10⁶ cm⁻³ (Tokuda et al. 2020). The derived density range of the CO clouds is on the order of 10² cm⁻³ (Table 3), and although it might be slightly higher, around 10⁴ cm⁻³, as suggested by early studies (Muraoka et al. 2017; Paper I), it is unlikely that all of these less-dense clouds are undergoing freefall collapse. We note that the above-mentioned dense core surveys in the MW (e.g., Ward-Thompson et al. 2007) constrained the starless cloud densities using multiple molecular lines with a higher spatial resolution as well as independent measurements, such as millimeter/submillimeter continuum observations. Our current SMC study has a single CO line with a lower spatial resolution, and thus it is likely that the uncertainty of the density estimation is quite large compared to the above MW surveys. Moreover, it is difficult to prove whether the starless sources are truly "starless" down to a low-mass star regime in the SMC as well. These observational limitations should be overcome to constrain the timescale of starless molecular clouds more precisely and to further explore the implications of the size–linewidth relations by future studies.

The frequency distribution of the mass of the molecular cloud is presented as ${dN}/{dM}\propto {M}^{-\alpha }$ or in the cumulative form, N(> M) ∝ M^−(α−1). This observed quantity is relevant to the fundamental problem of star formation, how molecular clouds transform into stars, i.e., the origin of the initial mass function. From a galactic perspective, an ensemble of formation and destruction processes of molecular clouds likely determines the cloud mass function (Inutsuka 2015; Kobayashi & Inutsuka 2017). Although various CO surveys have been revealed, the cloud population along the MW Galactic plane and nearby galaxies, weak CO emission in metal-poor environments, such as the SMC, makes it difficult for us to accumulate a sufficient sample to know the cloud mass function. Saldaño et al. (2023) obtained a sufficient number (>100) of CO clouds in the SMC for the first time and derived the mass spectrum. Our ACA observations still give us further constraints down to the low-mass regime where the CO emission is not clearly visible in the previous single-dish measurement.

We use the trunks, which are spatially or velocity-isolated components defined by a low-level contour and are assumed to be less sensitive against the astrodendro parameters. Figure 7 represents the cloud mass spectra of the luminosity and virial mass with the cumulative form. The features are very similar between the two spectra, except for the presence of massive clouds in the virial mass plot. We performed the ODR fitting to the mass spectra and reasonably characterized them by a single power law across two of three orders of magnitudes in the mass range with an exponent of ∼0.7, corresponding to α ∼1.7. Takekoshi et al. (2017) reported a similar value, α = 1.76, with their completeness limit of 8 × 10³ M_⊙, by compiling the 1.1 mm continuum selected Giant Molecular Clouds (GMCs) across the SMC.

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We compare the derived mass spectrum index, ∼1.7 with the previous CO study in the SMC. Saldaño et al. (2023) reported a steeper power-law index of α = 3.1–3.5 in the same region, N66 + NE, in their paper. The discrepancy is presumably caused by the following three factors. (1) The field coverage of our ACA study is wider than that of the APEX observations (Saldaño et al. 2023). The molecular clouds in the SMC northern region are more sparsely distributed than in the southwestern region. The limited field coverage with APEX did not capture some of the massive CO clouds. The SW region, where many CO clouds are densely packed into almost the same area as the NE coverage, shows shallower mass spectra. (2) The fitting mass ranges are different from each other. We performed a fitting to the M_vir function of our data in the same range as Saldaño et al. (2023), >8.6 × 10³ M_⊙, and obtained a steeper index, α ∼2 (see Figure 7(b)). (3) The resultant index of the cloud mass function somewhat depends on the observation sensitivity and the decomposition algorithm (e.g., Pineda et al. 2009). Their analysis using CPROPS (Rosolowsky & Leroy 2006) extracted local maxima of the CO emission, possibly causing an oversegmentation for larger clouds. It is not necessarily consistent with our trunk-based identification, whose cloud boundaries are well characterized by the lowest contour level. Considering some observational and methodological limitations, α ∼1.7 derived by our study in the SMC northern region and/or α ∼2 derived by Saldaño et al. (2023) in the other SMC regions would currently be appropriate values to represent the CO cloud mass function of the galaxy.

We subsequently compare the CO cloud mass spectrum in the SMC with the spectra in the MW and LMC studies at galactic scales. Heyer et al. (2001) and Fukui et al. (2008) reported that the indices α of CO cloud spectra are ∼1.8 in the MW and LMC. These are consistent with our results. Note that a higher-resolution survey in the LMC by Wong et al. (2011) reported a much steeper value, possibly because the larger clouds are resolved into smaller ones, which probably is the same as the third issue in the previous paragraph. Although the CO emission likely cannot trace a large amount of molecular material in the metal-poor environment (e.g., Glover & Clark 2012; Bisbas et al. 2021; Fukushima et al. 2020, see also Paper I), it is still intriguing that the Local Group of galaxies shows a similar behavior in CO cloud mass function. M. I. N. Kobayashi et al. (2023, in preparation) numerically demonstrated that mass functions of cold neutral medium, which eventually evolve into molecular clouds, show a spectrum index of 1.7 and do not largely depend on the metallicity condition with Z = 0.2–1.0 Z_⊙ after sufficient cooling time under the same conversing H i flow setting. It will be important in the future to develop a theory and/or numerical models of molecular cloud formation that take into account the CO abundance and compare these models with observations.

Inutsuka (2015) formulated that the exponent of the mass function is determined by the ratio of the formation and destruction timescale (T_f, and T_d) of molecular clouds and suggested that the theory explains the observed indices of α = 1.5–2.0 well if T_d is longer than T_f (see also Kobayashi & Inutsuka 2017). We also remark that there is a mass truncation at ∼10⁴–10⁵ M_⊙ in the SMC northern spectra. The mass truncation is determined by the total amount of parental material, i.e., H i (Kobayashi & Inutsuka 2017). These environments do not harbor many high-mass stars, making superbubble-type H i flows, which would be a supply source that might trigger massive GMC formation, and thus can provide the mass truncation in quiescent interarm regions in the MW and in M51 (Kobayashi & Inutsuka 2017; Kobayashi et al. 2018). Because Saldaño et al. (2023) also argued that low-mass clouds are dominant in the SMC, additional interferometric studies such as our ACA observations toward other regions would provide further insight into the CO cloud mass function and its regional dependence in the low-metallicity SMC.