Nobeyama 45-m Cygnus X CO Survey: II Physical Properties of $\mathrm{C^{18}O}$ Clumps

TL;DR

This study statistically analyzes the physical properties of C$^{18}$O clumps in Cygnus X, revealing differences in evolution stages, gravitational binding, and mass functions that relate to star formation activities.

Contribution

It provides the first comprehensive statistical analysis of C$^{18}$O clumps in Cygnus X, linking physical properties to star formation stages and mass functions.

Findings

North region clumps have higher H$_2$ density than south.

Clumps are gravitationally bound with a virial ratio of 0.3.

Mass function aligns with the low- and intermediate-mass IMF segments.

Abstract

We report the statistical physical properties of the C$^{18}$O($J=1-0$) clumps present in a prominent cluster-forming region, Cygnus X, using the dataset obtained by the Nobeyama 45-m radio telescope. This survey covers 9 deg$^2$ of the north and south regions of Cygnus X, and totally 174 C$^{18}$O clumps are identified using the dendrogram method. Assuming a distance of 1.4 kpc, these clumps have radii of 0.2-1 pc, velocity dispersions of $<2.2~\mathrm{km~s^{-1}}$, gas masses of 30-3000 $M_\odot$, and H$_2$ densities of (0.2-5.5)$\times10^4~\mathrm{cm^{-3}}$. We confirm that the C$^{18}$O clumps in the north region have a higher H$_2$ density than those in the south region, supporting the existence of a difference in the evolution stages, consistent with the star formation activity of these regions. The difference in the clump properties of the star-forming and starless clumps is also confirmed by the radius, velocity dispersion, gas mass, and H$_2$ density. The average virial ratio of 0.3 supports that these clumps are gravitationally bound. The C$^{18}$O clump mass function shows two spectral index components, $\alpha=-1.4$ in 55-140 $M_\odot$ and $\alpha=-2.1$ in $>140~M_\odot$, which are consistent with the low- and intermediate-mass parts of the Kroupa's initial mass function. The spectral index in the star-forming clumps in $>140~M_\odot$ is consistent with that of the starless clumps in 55-140 $M_\odot$, suggesting that the latter will evolve into star-forming clumps while retaining the gas accretion. Assuming a typical star formation efficiency of molecular clumps (10%), about ten C$^{18}$O clumps having a gas mass of $>10^3~M_\odot$ will evolve into open clusters containing one or more OB stars.

Tables

Table 1. Table 1: C 18 O core catalog of the Cygnus-X survey

ID	$l_{\mathrm{peak}}$	$b_{\mathrm{peak}}$	$v_{\mathrm{peak}}$	$T_{\mathrm{mb}}^{C^{18}O}$	$T_{\mathrm{mb}}^{{}_{}{}^{12}\mathrm{CO}}$	$I^{C^{18}O}$	$R_{\mathrm{cl}}$	$M_{\mathrm{LTE}}$	$n_{H_2}$	$d{v}_{\mathrm{cl}}$	$M_{\mathrm{vir}}$	SF?	Region	Edge?
	(∘)	(∘)	(km s-1)	(K)	(K)	(K km s-1 pc2)	(pc)	(${10}^2{M}_{\odot }$)	(${10}^4$ cm-3)	(km s-1)	(${10}^2{M}_{\odot }$)
1	80.5080	0.7222	-30.12	1.96 $\pm$ 0.39	10.07 $\pm$ 1.79	0.294 $\pm$ 0.029	0.39	0.78	0.47	1.00	0.83	Y	North	$\cdots$
2	79.9782	0.8357	-10.12	2.52 $\pm$ 0.43	32.13 $\pm$ 4.88	0.675 $\pm$ 0.068	0.43	3.69	1.70	0.91	0.76	$\cdots$	South	$\cdots$
3	78.8873	0.7096	-6.12	1.98 $\pm$ 0.47	28.24 $\pm$ 4.37	7.069 $\pm$ 0.707	1.43	35.10	0.42	1.47	6.57	Y	AFGL2592	$\cdots$
4	81.5485	0.0980	-6.38	2.00 $\pm$ 0.36	24.89 $\pm$ 3.80	0.395 $\pm$ 0.040	0.36	1.79	1.38	0.76	0.45	Y	North	$\cdots$
5	81.4728	0.0223	-4.38	3.98 $\pm$ 0.48	37.64 $\pm$ 5.69	4.619 $\pm$ 0.462	0.82	28.60	1.88	1.34	3.12	Y	North	$\cdots$
6	81.5170	0.0476	-6.38	2.16 $\pm$ 0.34	27.83 $\pm$ 4.23	0.134 $\pm$ 0.013	0.25	0.66	1.58	0.42	0.10	Y	North	$\cdots$
7	81.3026	-0.1101	-5.88	2.42 $\pm$ 0.41	22.27 $\pm$ 3.43	1.458 $\pm$ 0.146	0.81	6.10	0.41	0.65	0.75	Y	North	$\cdots$
8	81.1197	-0.1416	-5.12	2.55 $\pm$ 0.42	24.50 $\pm$ 3.76	0.532 $\pm$ 0.053	0.37	2.38	1.69	0.66	0.35	Y	North	$\cdots$
9	81.1323	-0.1353	-3.88	2.22 $\pm$ 0.40	20.15 $\pm$ 3.12	0.759 $\pm$ 0.076	0.57	2.97	0.57	1.17	1.66	Y	North	$\cdots$
10	77.4680	-1.0811	-3.88	2.56 $\pm$ 0.51	14.84 $\pm$ 2.44	0.787 $\pm$ 0.079	0.45	2.54	0.98	1.18	1.33	$\cdots$	DR13S	$\cdots$
11	81.7503	0.5898	-4.12	4.29 $\pm$ 0.53	30.25 $\pm$ 4.60	1.036 $\pm$ 0.104	0.33	5.42	5.60	1.35	1.25	Y	DR13S	$\cdots$
12	80.6278	0.6844	-3.38	3.10 $\pm$ 0.49	25.86 $\pm$ 3.97	2.048 $\pm$ 0.205	0.71	9.53	0.94	1.96	5.74	Y	North	$\cdots$
13	81.5989	0.4259	-3.88	1.94 $\pm$ 0.33	31.04 $\pm$ 4.70	0.155 $\pm$ 0.016	0.26	0.83	1.66	0.42	0.11	$\cdots$	North	$\cdots$
14	78.3321	-1.0811	-3.12	1.92 $\pm$ 0.60	24.27 $\pm$ 3.78	0.280 $\pm$ 0.028	0.40	1.24	0.70	0.75	0.49	Y	South	$\cdots$
15	81.8512	0.7475	-3.12	2.47 $\pm$ 0.38	28.25 $\pm$ 4.29	0.614 $\pm$ 0.061	0.43	3.05	1.40	0.81	0.60	$\cdots$	North	$\cdots$
16	80.8801	0.3061	-2.88	2.26 $\pm$ 0.38	16.65 $\pm$ 2.61	0.968 $\pm$ 0.097	0.51	3.35	0.88	1.28	1.80	Y	North	$\cdots$
17	80.8612	0.4196	-2.88	2.34 $\pm$ 0.44	18.41 $\pm$ 2.91	0.802 $\pm$ 0.080	0.50	2.96	0.85	1.35	1.92	$\cdots$	North	$\cdots$
18	78.3636	-1.0811	-3.12	2.32 $\pm$ 0.51	24.14 $\pm$ 3.78	0.613 $\pm$ 0.061	0.48	2.71	0.89	1.11	1.25	Y	South	$\cdots$
19	80.8990	-0.2993	-2.62	2.22 $\pm$ 0.39	24.39 $\pm$ 3.72	0.824 $\pm$ 0.082	0.49	3.68	1.10	1.04	1.14	Y	North	$\cdots$
20	79.2722	-0.1416	-2.62	1.95 $\pm$ 0.36	7.72 $\pm$ 1.43	0.714 $\pm$ 0.071	0.56	1.69	0.34	0.67	0.56	Y	South	$\cdots$
21	81.7692	0.6718	-3.38	2.69 $\pm$ 0.39	25.39 $\pm$ 3.88	0.350 $\pm$ 0.035	0.33	1.61	1.66	0.42	0.14	Y	North	$\cdots$
22	81.9079	0.8547	-2.88	1.85 $\pm$ 0.34	20.88 $\pm$ 3.19	0.546 $\pm$ 0.055	0.57	2.19	0.42	0.58	0.43	Y	North	$\cdots$
23	81.8260	0.8168	-2.88	2.69 $\pm$ 0.39	21.51 $\pm$ 3.29	0.619 $\pm$ 0.062	0.42	2.53	1.24	0.96	0.82	Y	North	$\cdots$
24	79.3100	-0.3749	-2.62	1.85 $\pm$ 0.42	21.94 $\pm$ 3.39	0.166 $\pm$ 0.017	0.31	0.69	0.79	0.44	0.14	Y	South	$\cdots$
25	78.6605	0.1863	-1.88	2.40 $\pm$ 0.39	14.20 $\pm$ 2.28	1.494 $\pm$ 0.149	0.64	4.71	0.64	1.18	1.88	Y	South	$\cdots$
26	81.6746	0.5394	-1.88	3.50 $\pm$ 0.43	36.48 $\pm$ 5.51	1.507 $\pm$ 0.151	0.44	9.11	3.72	1.11	1.16	Y	North	$\cdots$
27	81.7188	0.5709	-2.62	3.95 $\pm$ 0.49	35.61 $\pm$ 5.37	0.385 $\pm$ 0.039	0.25	2.28	5.46	0.62	0.21	Y	North	$\cdots$
28	79.0892	0.4889	-2.62	1.79 $\pm$ 0.36	17.50 $\pm$ 2.72	0.153 $\pm$ 0.015	0.29	0.55	0.81	0.46	0.14	Y	South	$\cdots$
29	81.8386	0.8799	-1.88	4.41 $\pm$ 0.52	33.21 $\pm$ 5.04	3.217 $\pm$ 0.322	0.72	18.10	1.71	1.50	3.46	Y	North	$\cdots$
30	79.4358	1.0060	-1.62	2.43 $\pm$ 0.45	9.13 $\pm$ 1.63	0.477 $\pm$ 0.048	0.48	1.21	0.40	0.75	0.58	Y	South	$\cdots$
31	78.2435	-1.3081	-2.38	2.27 $\pm$ 0.63	19.73 $\pm$ 3.15	0.256 $\pm$ 0.026	0.33	0.99	1.02	0.68	0.33	$\cdots$	DR13S	Y
32	81.4350	0.7096	-1.62	2.43 $\pm$ 0.35	34.82 $\pm$ 5.28	1.399 $\pm$ 0.140	0.60	8.15	1.33	0.92	1.09	Y	North	$\cdots$
33	77.8779	-1.1253	-2.12	2.02 $\pm$ 0.48	13.32 $\pm$ 2.23	0.173 $\pm$ 0.017	0.31	0.53	0.61	0.64	0.28	Y	DR13S	$\cdots$
34	80.9116	0.3313	-2.12	2.01 $\pm$ 0.36	17.04 $\pm$ 2.67	0.176 $\pm$ 0.018	0.29	0.62	0.92	0.57	0.21	Y	DR13S	$\cdots$
35	79.7511	0.9934	-0.88	2.20 $\pm$ 0.43	9.29 $\pm$ 1.59	0.857 $\pm$ 0.086	0.51	2.18	0.57	1.00	1.10	Y	South	$\cdots$
36	78.2186	-1.0496	-1.62	1.77 $\pm$ 0.48	21.24 $\pm$ 3.35	0.291 $\pm$ 0.029	0.44	1.18	0.51	0.41	0.17	$\cdots$	DR13S	$\cdots$
37	80.8612	0.3565	-1.38	2.06 $\pm$ 0.41	21.54 $\pm$ 3.33	0.434 $\pm$ 0.043	0.38	1.78	1.16	1.25	1.26	Y	North	$\cdots$
38	78.3004	-1.1568	-1.62	1.88 $\pm$ 0.56	17.33 $\pm$ 2.77	0.154 $\pm$ 0.015	0.34	0.55	0.51	0.40	0.13	$\cdots$	DR13S	$\cdots$
39	77.9094	-1.1631	-0.62	2.28 $\pm$ 0.55	14.84 $\pm$ 2.42	1.610 $\pm$ 0.161	0.81	5.20	0.35	1.37	3.22	Y	DR13S	$\cdots$
40	78.7735	-1.0874	-0.88	2.26 $\pm$ 0.44	24.28 $\pm$ 3.79	0.740 $\pm$ 0.074	0.60	3.29	0.54	0.63	0.54	Y	South	$\cdots$
41	79.3478	-0.2993	-1.12	2.00 $\pm$ 0.41	9.99 $\pm$ 1.71	0.311 $\pm$ 0.031	0.30	0.82	1.06	0.88	0.51	Y	South	$\cdots$
42	78.2498	-1.3081	-1.12	2.03 $\pm$ 0.63	16.96 $\pm$ 2.78	0.188 $\pm$ 0.019	0.35	0.66	0.56	0.42	0.14	Y	DR13S	Y
43	77.8778	-1.2009	-1.12	2.26 $\pm$ 0.47	15.33 $\pm$ 2.49	0.165 $\pm$ 0.017	0.31	0.54	0.63	0.42	0.13	$\cdots$	DR13S	$\cdots$
44	78.2752	-1.1505	-1.38	1.84 $\pm$ 0.54	17.00 $\pm$ 2.76	0.500 $\pm$ 0.050	0.56	1.75	0.36	0.88	0.93	$\cdots$	DR13S	$\cdots$
45	78.0422	-0.9046	-1.12	1.92 $\pm$ 0.46	18.67 $\pm$ 2.93	0.373 $\pm$ 0.037	0.42	1.39	0.68	0.88	0.70	$\cdots$	DR13S	$\cdots$
46	78.8497	-0.3875	-1.12	1.83 $\pm$ 0.35	19.79 $\pm$ 3.08	0.182 $\pm$ 0.018	0.29	0.70	1.04	0.49	0.16	Y	South	$\cdots$
47	81.3530	0.5709	-1.62	1.84 $\pm$ 0.35	29.87 $\pm$ 4.56	0.159 $\pm$ 0.016	0.33	0.83	0.85	0.44	0.15	$\cdots$	North	$\cdots$
48	78.2246	-1.3081	-1.12	1.83 $\pm$ 0.53	13.65 $\pm$ 2.27	0.141 $\pm$ 0.014	0.35	0.43	0.37	0.30	0.08	$\cdots$	DR13S	Y
49	78.2813	-1.2892	-1.12	1.91 $\pm$ 0.47	17.03 $\pm$ 2.75	0.176 $\pm$ 0.018	0.35	0.62	0.52	0.26	0.06	Y	DR13S	Y
50	78.1053	-0.7848	-0.88	1.93 $\pm$ 0.51	26.34 $\pm$ 4.08	0.334 $\pm$ 0.033	0.51	1.58	0.43	0.37	0.17	$\cdots$	DR13S	$\cdots$
51	78.0422	-0.8857	-0.62	1.92 $\pm$ 0.50	18.66 $\pm$ 2.94	0.364 $\pm$ 0.036	0.47	1.35	0.47	0.47	0.24	$\cdots$	DR13S	$\cdots$
52	79.3226	-0.1479	-0.62	1.84 $\pm$ 0.37	7.89 $\pm$ 1.41	0.460 $\pm$ 0.046	0.54	1.09	0.24	0.50	0.31	Y	South	$\cdots$
53	80.9116	0.3187	-0.88	1.80 $\pm$ 0.38	18.83 $\pm$ 2.93	0.130 $\pm$ 0.013	0.31	0.49	0.56	0.28	0.06	Y	North	$\cdots$
54	80.6972	0.6970	-1.12	2.00 $\pm$ 0.42	19.81 $\pm$ 3.10	0.590 $\pm$ 0.059	0.52	2.28	0.57	0.70	0.57	Y	North	$\cdots$
55	81.8575	0.9619	-0.88	2.01 $\pm$ 0.35	19.93 $\pm$ 3.10	0.194 $\pm$ 0.019	0.36	0.75	0.58	0.30	0.08	Y	North	$\cdots$
56	77.9033	-1.0433	-0.62	1.79 $\pm$ 0.53	9.31 $\pm$ 1.72	0.136 $\pm$ 0.014	0.33	0.35	0.36	0.29	0.07	$\cdots$	DR13S	$\cdots$
57	78.0737	-0.8668	-0.38	2.68 $\pm$ 0.53	20.73 $\pm$ 3.25	0.809 $\pm$ 0.081	0.52	3.23	0.81	1.28	1.81	Y	DR13S	$\cdots$
58	78.0928	-0.6713	-0.12	3.23 $\pm$ 0.60	21.00 $\pm$ 3.31	0.581 $\pm$ 0.058	0.37	2.34	1.66	0.69	0.39	Y	DR13S	$\cdots$
59	78.1118	-0.6334	-0.38	3.25 $\pm$ 0.52	23.88 $\pm$ 3.72	0.607 $\pm$ 0.061	0.37	2.67	1.89	0.70	0.39	Y	DR13S	$\cdots$
60	79.2784	0.3817	1.38	2.28 $\pm$ 0.39	13.29 $\pm$ 2.12	0.893 $\pm$ 0.089	0.50	2.71	0.78	2.16	4.92	Y	South	$\cdots$
61	79.2406	0.5268	0.38	3.76 $\pm$ 0.49	9.69 $\pm$ 1.62	5.040 $\pm$ 0.504	0.97	13.10	0.51	1.05	2.30	Y	South	$\cdots$
62	77.8715	-1.2073	0.12	1.99 $\pm$ 0.52	15.89 $\pm$ 2.56	0.293 $\pm$ 0.029	0.39	0.99	0.60	0.54	0.26	$\cdots$	DR13S	$\cdots$
63	79.5181	0.0034	0.12	1.91 $\pm$ 0.39	8.86 $\pm$ 1.58	0.798 $\pm$ 0.080	0.68	1.99	0.23	1.07	1.66	Y	South	$\cdots$
64	79.4613	0.1989	0.12	2.57 $\pm$ 0.40	9.45 $\pm$ 1.61	2.137 $\pm$ 0.214	0.97	5.48	0.22	0.73	1.11	Y	South	$\cdots$
65	79.4929	0.2619	-0.12	1.83 $\pm$ 0.33	7.19 $\pm$ 1.28	0.641 $\pm$ 0.064	0.54	1.48	0.33	0.99	1.14	$\cdots$	South	$\cdots$
66	77.8273	-1.2640	-0.12	2.13 $\pm$ 0.50	16.44 $\pm$ 2.63	0.505 $\pm$ 0.051	0.54	1.73	0.39	1.36	2.14	$\cdots$	DR13S	$\cdots$
67	78.1367	-0.9046	0.62	3.48 $\pm$ 0.51	23.77 $\pm$ 3.70	4.214 $\pm$ 0.421	0.93	18.50	0.81	1.34	3.54	Y	DR13S	$\cdots$
68	78.9506	-0.1858	1.62	2.41 $\pm$ 0.41	13.25 $\pm$ 2.14	0.717 $\pm$ 0.072	0.50	2.17	0.62	1.38	2.01	Y	South	$\cdots$
69	79.3226	0.3313	1.38	3.85 $\pm$ 0.51	15.23 $\pm$ 2.37	2.975 $\pm$ 0.298	0.60	9.76	1.64	1.28	2.08	Y	South	$\cdots$
70	79.1712	0.5898	0.12	2.26 $\pm$ 0.41	8.55 $\pm$ 1.50	1.092 $\pm$ 0.109	0.76	2.68	0.22	0.53	0.49	Y	South	$\cdots$
71	81.8701	1.0375	0.12	2.40 $\pm$ 0.38	24.16 $\pm$ 3.75	1.019 $\pm$ 0.102	0.63	4.52	0.65	0.70	0.67	Y	North	$\cdots$
72	78.0549	-0.7217	0.38	1.94 $\pm$ 0.46	18.57 $\pm$ 3.03	0.193 $\pm$ 0.019	0.37	0.72	0.51	0.44	0.16	$\cdots$	DR13S	$\cdots$
73	78.1622	-0.5578	0.12	1.83 $\pm$ 0.45	24.34 $\pm$ 3.78	0.190 $\pm$ 0.019	0.42	0.84	0.41	0.07	0.02	Y	DR13S	$\cdots$
74	79.3100	-0.1668	0.12	2.03 $\pm$ 0.36	8.87 $\pm$ 1.53	0.456 $\pm$ 0.046	0.48	1.14	0.38	0.80	0.66	Y	South	$\cdots$
75	79.7829	0.0728	0.12	2.09 $\pm$ 0.44	7.66 $\pm$ 1.44	0.415 $\pm$ 0.042	0.49	0.98	0.29	0.49	0.27	$\cdots$	South	$\cdots$
76	79.1144	0.6466	-0.12	2.10 $\pm$ 0.39	8.83 $\pm$ 1.54	0.149 $\pm$ 0.015	0.36	0.37	0.29	0.10	0.02	Y	South	$\cdots$
77	78.9630	0.7412	0.12	1.84 $\pm$ 0.48	8.27 $\pm$ 1.63	0.128 $\pm$ 0.013	0.34	0.31	0.29	0.18	0.04	$\cdots$	South	$\cdots$
78	79.4046	0.1421	0.38	1.87 $\pm$ 0.38	6.88 $\pm$ 1.30	0.275 $\pm$ 0.027	0.40	0.62	0.35	0.40	0.15	$\cdots$	South	$\cdots$
79	79.4109	0.2619	0.62	1.83 $\pm$ 0.35	5.70 $\pm$ 1.17	0.354 $\pm$ 0.035	0.44	0.76	0.31	0.51	0.26	Y	South	$\cdots$
80	79.2532	0.4007	0.38	2.19 $\pm$ 0.44	8.91 $\pm$ 1.52	0.215 $\pm$ 0.022	0.30	0.54	0.70	0.54	0.20	Y	South	$\cdots$
81	78.9251	0.7853	0.62	2.58 $\pm$ 0.44	10.49 $\pm$ 1.83	1.218 $\pm$ 0.122	0.73	3.27	0.30	0.52	0.45	Y	South	$\cdots$
82	81.7124	1.6807	0.38	1.83 $\pm$ 0.45	20.75 $\pm$ 3.26	0.168 $\pm$ 0.017	0.30	0.67	0.87	0.78	0.40	$\cdots$	North	Y
83	78.1620	-0.8415	0.62	2.12 $\pm$ 0.49	18.50 $\pm$ 2.89	0.275 $\pm$ 0.028	0.36	1.02	0.79	0.51	0.21	$\cdots$	DR13S	$\cdots$
84	79.7073	0.1295	0.88	2.32 $\pm$ 0.40	8.85 $\pm$ 1.47	0.968 $\pm$ 0.097	0.74	2.41	0.21	0.46	0.37	Y	South	$\cdots$
85	77.8968	-1.1946	1.38	2.00 $\pm$ 0.51	15.22 $\pm$ 2.50	0.626 $\pm$ 0.063	0.59	2.05	0.36	0.72	0.66	Y	DR13S	$\cdots$
86	79.3667	0.3817	0.88	3.14 $\pm$ 0.43	11.75 $\pm$ 1.88	0.255 $\pm$ 0.026	0.30	0.73	0.94	0.28	0.06	$\cdots$	South	$\cdots$
87	79.2532	0.4448	1.12	2.82 $\pm$ 0.42	9.13 $\pm$ 1.55	0.633 $\pm$ 0.063	0.48	1.60	0.53	0.65	0.44	Y	South	$\cdots$
88	80.0225	-0.4254	1.38	2.30 $\pm$ 0.40	9.24 $\pm$ 1.64	0.540 $\pm$ 0.054	0.46	1.37	0.50	0.62	0.40	Y	South	$\cdots$
89	81.8827	1.1321	1.88	2.08 $\pm$ 0.44	11.50 $\pm$ 1.95	0.599 $\pm$ 0.060	0.56	1.69	0.34	0.76	0.71	$\cdots$	North	$\cdots$
90	79.3415	-0.4695	1.62	1.94 $\pm$ 0.44	8.59 $\pm$ 1.56	0.517 $\pm$ 0.052	0.52	1.27	0.32	0.80	0.72	Y	South	$\cdots$
91	79.8901	-0.2236	1.38	2.06 $\pm$ 0.41	9.89 $\pm$ 1.74	0.173 $\pm$ 0.017	0.34	0.45	0.42	0.30	0.08	$\cdots$	South	$\cdots$
92	79.2406	0.4196	1.88	3.09 $\pm$ 0.45	11.56 $\pm$ 1.91	1.216 $\pm$ 0.122	0.56	3.43	0.68	0.74	0.67	Y	South	$\cdots$
93	78.0737	-0.8920	1.38	2.36 $\pm$ 0.53	16.34 $\pm$ 2.61	0.175 $\pm$ 0.018	0.34	0.60	0.56	0.25	0.06	$\cdots$	DR13S	$\cdots$
94	77.8208	-1.3586	3.38	2.06 $\pm$ 0.54	17.29 $\pm$ 2.78	1.513 $\pm$ 0.151	0.84	5.36	0.32	1.20	2.57	Y	DR13S	$\cdots$
95	78.5531	0.6907	2.12	1.83 $\pm$ 0.44	10.68 $\pm$ 1.88	0.166 $\pm$ 0.017	0.30	0.45	0.59	0.25	0.05	$\cdots$	South	$\cdots$
96	81.3845	0.8862	2.88	1.78 $\pm$ 0.34	17.44 $\pm$ 2.71	0.237 $\pm$ 0.024	0.35	0.85	0.72	0.51	0.21	Y	North	$\cdots$
97	77.9850	-1.2577	3.12	1.78 $\pm$ 0.50	10.34 $\pm$ 1.81	0.391 $\pm$ 0.039	0.47	1.04	0.36	0.86	0.75	Y	DR13S	$\cdots$
98	79.2406	0.2367	2.88	1.84 $\pm$ 0.40	27.47 $\pm$ 4.19	0.308 $\pm$ 0.031	0.38	1.50	0.98	1.06	0.91	$\cdots$	South	$\cdots$
99	81.7061	1.2141	2.88	2.22 $\pm$ 0.39	11.50 $\pm$ 1.98	0.166 $\pm$ 0.017	0.31	0.47	0.54	0.34	0.09	$\cdots$	North	$\cdots$
100	81.7818	1.2519	2.88	2.05 $\pm$ 0.39	16.18 $\pm$ 2.62	0.190 $\pm$ 0.019	0.33	0.65	0.67	0.55	0.23	$\cdots$	North	$\cdots$
101	77.9470	-1.3460	3.12	1.87 $\pm$ 0.52	15.73 $\pm$ 2.61	0.327 $\pm$ 0.033	0.44	1.09	0.47	0.64	0.40	$\cdots$	DR13S	$\cdots$
102	79.4864	-0.6587	3.38	1.90 $\pm$ 0.33	12.69 $\pm$ 2.11	0.354 $\pm$ 0.035	0.45	1.05	0.41	0.55	0.31	Y	South	$\cdots$
103	81.3530	0.3817	3.12	1.84 $\pm$ 0.33	10.16 $\pm$ 1.67	0.215 $\pm$ 0.022	0.45	0.57	0.22	0.01	0.01	$\cdots$	North	$\cdots$
104	81.2773	0.5394	3.12	2.13 $\pm$ 0.32	10.41 $\pm$ 1.67	1.354 $\pm$ 0.135	0.86	3.63	0.20	1.01	1.88	$\cdots$	North	$\cdots$
105	77.9660	-1.3144	3.88	2.52 $\pm$ 0.51	12.73 $\pm$ 2.21	0.325 $\pm$ 0.033	0.39	0.96	0.58	0.67	0.38	Y	DR13S	$\cdots$
106	81.3845	0.4133	3.88	1.91 $\pm$ 0.34	11.42 $\pm$ 1.83	0.648 $\pm$ 0.065	0.52	1.82	0.46	0.57	0.38	Y	North	$\cdots$
107	81.7629	1.3528	3.88	3.65 $\pm$ 0.50	11.21 $\pm$ 1.90	2.011 $\pm$ 0.201	0.76	5.59	0.45	1.35	2.96	Y	North	$\cdots$
108	81.7314	1.2961	3.62	2.22 $\pm$ 0.39	13.84 $\pm$ 2.26	0.881 $\pm$ 0.088	0.57	2.74	0.53	0.69	0.59	$\cdots$	North	$\cdots$
109	81.6998	1.3528	3.62	2.06 $\pm$ 0.40	10.02 $\pm$ 1.73	0.232 $\pm$ 0.023	0.29	0.61	0.91	0.47	0.14	$\cdots$	North	$\cdots$
110	79.3036	-0.6713	4.12	3.39 $\pm$ 0.49	15.93 $\pm$ 2.63	1.521 $\pm$ 0.152	0.76	5.13	0.41	0.79	1.04	Y	South	$\cdots$
111	77.9849	-1.2829	3.88	2.12 $\pm$ 0.55	13.90 $\pm$ 2.30	0.175 $\pm$ 0.018	0.35	0.54	0.46	0.20	0.04	$\cdots$	DR13S	$\cdots$
112	78.9442	-0.5515	4.38	1.91 $\pm$ 0.33	8.63 $\pm$ 1.60	0.149 $\pm$ 0.015	0.34	0.37	0.34	0.31	0.08	Y	South	$\cdots$
113	81.9521	-0.3308	4.62	2.04 $\pm$ 0.63	8.65 $\pm$ 2.45	0.217 $\pm$ 0.022	0.37	0.54	0.38	0.42	0.15	$\cdots$	North	Y
114	78.9695	0.3565	5.38	2.98 $\pm$ 0.43	27.45 $\pm$ 4.20	2.278 $\pm$ 0.228	0.70	11.10	1.14	1.59	3.76	Y	South	$\cdots$
115	79.5557	-0.8037	5.12	3.23 $\pm$ 0.47	13.98 $\pm$ 2.27	1.617 $\pm$ 0.162	0.60	5.05	0.85	1.20	1.83	Y	South	$\cdots$
116	80.8927	-0.3308	5.12	2.06 $\pm$ 0.39	8.95 $\pm$ 1.59	1.163 $\pm$ 0.116	0.80	2.91	0.20	0.57	0.57	$\cdots$	North	$\cdots$
117	80.8423	-0.1921	5.88	1.81 $\pm$ 0.35	8.71 $\pm$ 1.53	0.944 $\pm$ 0.094	0.55	2.34	0.50	1.50	2.60	Y	North	$\cdots$
118	81.0756	-0.4758	5.62	2.49 $\pm$ 0.39	11.47 $\pm$ 1.89	0.514 $\pm$ 0.051	0.50	1.44	0.41	0.52	0.31	Y	North	$\cdots$
119	81.0062	-0.3749	5.12	1.89 $\pm$ 0.40	8.18 $\pm$ 1.45	0.195 $\pm$ 0.020	0.35	0.47	0.40	0.25	0.06	$\cdots$	North	$\cdots$
120	81.2837	-0.2740	5.38	2.01 $\pm$ 0.40	6.81 $\pm$ 1.33	0.491 $\pm$ 0.049	0.52	1.11	0.28	0.55	0.35	$\cdots$	North	$\cdots$
121	79.0324	0.6592	6.88	3.14 $\pm$ 0.46	31.35 $\pm$ 4.77	2.735 $\pm$ 0.274	0.73	14.70	1.33	1.44	3.20	Y	South	$\cdots$
122	81.0503	-0.5199	5.88	2.10 $\pm$ 0.39	10.59 $\pm$ 1.72	0.261 $\pm$ 0.026	0.34	0.71	0.66	0.76	0.42	$\cdots$	North	$\cdots$
123	79.1334	-0.3749	6.62	1.91 $\pm$ 0.36	24.84 $\pm$ 3.80	0.338 $\pm$ 0.034	0.35	1.53	1.29	1.17	1.01	Y	South	$\cdots$
124	81.1954	-0.2866	5.38	2.58 $\pm$ 0.44	7.88 $\pm$ 1.45	0.694 $\pm$ 0.069	0.58	1.65	0.30	0.49	0.32	Y	North	$\cdots$
125	81.0251	-0.4506	5.88	2.60 $\pm$ 0.41	11.05 $\pm$ 1.84	1.832 $\pm$ 0.183	0.87	5.05	0.27	0.51	0.52	Y	North	$\cdots$
126	80.9873	-0.4064	5.88	2.27 $\pm$ 0.38	8.67 $\pm$ 1.54	0.195 $\pm$ 0.020	0.39	0.48	0.29	0.23	0.06	$\cdots$	North	$\cdots$
127	81.0504	0.2998	5.62	1.93 $\pm$ 0.39	10.44 $\pm$ 1.79	0.147 $\pm$ 0.015	0.36	0.39	0.30	0.18	0.04	$\cdots$	North	$\cdots$
128	79.7325	-0.2614	6.38	2.09 $\pm$ 0.40	11.15 $\pm$ 1.89	0.386 $\pm$ 0.039	0.41	1.07	0.56	0.82	0.59	Y	South	$\cdots$
129	78.6164	-0.1038	6.38	2.00 $\pm$ 0.45	8.44 $\pm$ 1.63	0.215 $\pm$ 0.022	0.38	0.53	0.34	0.35	0.11	$\cdots$	South	$\cdots$
130	78.9631	0.5331	6.38	2.41 $\pm$ 0.44	21.47 $\pm$ 3.30	0.395 $\pm$ 0.040	0.36	1.61	1.25	0.84	0.55	Y	South	$\cdots$
131	78.9757	0.6087	6.38	1.93 $\pm$ 0.41	19.34 $\pm$ 3.04	0.183 $\pm$ 0.018	0.30	0.70	0.91	0.43	0.13	Y	South	$\cdots$
132	78.5786	-0.0281	6.88	2.22 $\pm$ 0.40	8.69 $\pm$ 1.53	0.927 $\pm$ 0.093	0.72	2.29	0.22	0.51	0.43	Y	South	$\cdots$
133	79.7577	-0.1542	6.88	1.79 $\pm$ 0.36	11.29 $\pm$ 1.89	0.256 $\pm$ 0.026	0.38	0.72	0.47	0.76	0.48	$\cdots$	South	$\cdots$
134	81.4539	0.4637	7.88	2.18 $\pm$ 0.36	40.61 $\pm$ 6.13	0.502 $\pm$ 0.050	0.47	3.31	1.15	0.93	0.87	Y	North	$\cdots$
135	79.2214	0.9556	7.38	3.00 $\pm$ 0.49	28.31 $\pm$ 4.33	1.077 $\pm$ 0.108	0.58	5.36	0.99	0.79	0.78	Y	South	$\cdots$
136	79.1773	0.9556	7.12	2.85 $\pm$ 0.47	26.65 $\pm$ 4.11	0.499 $\pm$ 0.050	0.39	2.38	1.44	0.70	0.42	Y	South	$\cdots$
137	82.0277	-0.2614	7.62	2.30 $\pm$ 0.40	11.29 $\pm$ 1.91	0.571 $\pm$ 0.057	0.47	1.59	0.55	0.57	0.34	Y	North	Y
138	81.5296	0.2241	8.88	2.60 $\pm$ 0.36	24.69 $\pm$ 3.75	3.347 $\pm$ 0.335	0.78	15.10	1.14	1.68	4.65	Y	North	$\cdots$
139	79.0764	0.9303	7.88	2.11 $\pm$ 0.43	30.59 $\pm$ 4.65	0.245 $\pm$ 0.025	0.31	1.29	1.49	0.73	0.37	Y	South	$\cdots$
140	79.0261	0.6214	8.12	1.92 $\pm$ 0.37	19.46 $\pm$ 3.01	0.150 $\pm$ 0.015	0.29	0.57	0.85	0.65	0.27	$\cdots$	South	$\cdots$
141	79.1205	0.9556	7.62	2.16 $\pm$ 0.42	30.58 $\pm$ 4.67	0.661 $\pm$ 0.066	0.47	3.48	1.21	0.73	0.55	Y	South	$\cdots$
142	81.4161	0.4196	8.12	2.38 $\pm$ 0.38	27.91 $\pm$ 4.23	0.594 $\pm$ 0.059	0.44	2.92	1.27	0.61	0.36	$\cdots$	North	$\cdots$
143	80.3693	0.4448	8.62	2.45 $\pm$ 0.41	35.86 $\pm$ 5.46	0.810 $\pm$ 0.081	0.44	4.83	1.97	0.94	0.85	Y	North	$\cdots$
144	81.6494	0.7222	8.38	2.06 $\pm$ 0.35	24.10 $\pm$ 3.68	0.367 $\pm$ 0.037	0.34	1.63	1.52	0.56	0.23	Y	North	$\cdots$
145	78.3768	0.3187	8.38	2.38 $\pm$ 0.47	12.54 $\pm$ 2.18	0.533 $\pm$ 0.053	0.54	1.57	0.36	0.50	0.31	Y	South	$\cdots$
146	81.8701	0.7790	9.62	2.76 $\pm$ 0.37	24.96 $\pm$ 3.81	3.070 $\pm$ 0.307	0.72	13.90	1.35	1.48	3.32	Y	North	$\cdots$
147	81.7061	-0.0344	8.88	2.82 $\pm$ 0.38	21.94 $\pm$ 3.38	0.475 $\pm$ 0.048	0.42	1.97	0.97	0.43	0.18	$\cdots$	North	$\cdots$
148	81.6872	-0.0218	9.38	2.42 $\pm$ 0.36	30.22 $\pm$ 4.58	0.369 $\pm$ 0.037	0.45	1.93	0.75	0.63	0.40	Y	North	$\cdots$
149	78.3578	0.3187	8.88	1.94 $\pm$ 0.40	12.44 $\pm$ 2.18	0.828 $\pm$ 0.083	0.69	2.43	0.26	0.56	0.48	Y	South	$\cdots$
150	81.4602	0.4637	9.38	2.29 $\pm$ 0.35	36.78 $\pm$ 5.55	0.324 $\pm$ 0.032	0.39	1.97	1.19	0.49	0.21	Y	North	$\cdots$
151	81.5359	0.1043	9.38	2.22 $\pm$ 0.37	22.38 $\pm$ 3.43	0.454 $\pm$ 0.045	0.44	1.91	0.83	0.46	0.22	Y	North	$\cdots$
152	78.3074	0.1674	9.38	2.34 $\pm$ 0.50	10.59 $\pm$ 1.87	0.210 $\pm$ 0.021	0.34	0.57	0.53	0.34	0.10	$\cdots$	South	$\cdots$
153	78.3579	0.1989	9.12	2.15 $\pm$ 0.44	13.31 $\pm$ 2.25	0.570 $\pm$ 0.057	0.48	1.73	0.54	0.51	0.29	$\cdots$	South	$\cdots$
154	78.4020	0.2556	9.12	2.24 $\pm$ 0.42	13.13 $\pm$ 2.13	1.601 $\pm$ 0.160	0.85	4.83	0.28	0.67	0.85	Y	South	$\cdots$
155	82.2484	0.1674	9.38	2.34 $\pm$ 0.41	13.54 $\pm$ 2.20	0.254 $\pm$ 0.025	0.38	0.78	0.51	0.26	0.07	Y	North	Y
156	82.2547	0.2052	9.38	2.99 $\pm$ 0.54	14.26 $\pm$ 2.51	0.306 $\pm$ 0.031	0.31	0.97	1.12	0.41	0.12	$\cdots$	North	Y
157	82.1980	0.1232	10.12	2.04 $\pm$ 0.35	14.02 $\pm$ 2.31	0.801 $\pm$ 0.080	0.65	2.51	0.33	0.81	0.91	Y	North	$\cdots$
158	78.2885	0.1737	10.12	2.57 $\pm$ 0.43	12.72 $\pm$ 2.10	0.510 $\pm$ 0.051	0.44	1.51	0.66	0.53	0.27	$\cdots$	South	$\cdots$
159	81.8260	1.2645	10.62	2.02 $\pm$ 0.37	28.87 $\pm$ 4.44	0.792 $\pm$ 0.079	0.54	4.00	0.89	1.19	1.63	Y	North	$\cdots$
160	82.2673	0.1547	9.88	1.93 $\pm$ 0.51	11.13 $\pm$ 2.18	0.148 $\pm$ 0.015	0.31	0.41	0.47	0.27	0.06	$\cdots$	North	Y
161	78.1876	0.0980	10.62	2.63 $\pm$ 0.44	14.45 $\pm$ 2.38	0.390 $\pm$ 0.039	0.47	1.24	0.43	0.42	0.20	Y	South	$\cdots$
162	78.2255	0.1737	10.38	2.21 $\pm$ 0.50	14.73 $\pm$ 2.41	0.211 $\pm$ 0.021	0.34	0.68	0.63	0.23	0.05	Y	South	$\cdots$
163	79.3223	-0.9866	11.38	1.89 $\pm$ 0.38	18.30 $\pm$ 2.93	0.124 $\pm$ 0.013	0.30	0.46	0.60	0.36	0.10	Y	South	$\cdots$
164	81.9016	0.7916	11.62	2.17 $\pm$ 0.35	26.91 $\pm$ 4.10	0.637 $\pm$ 0.064	0.45	3.05	1.18	0.99	0.95	Y	North	$\cdots$
165	81.8890	1.2393	11.88	1.89 $\pm$ 0.36	24.54 $\pm$ 3.80	0.141 $\pm$ 0.014	0.29	0.63	0.94	0.54	0.19	Y	North	$\cdots$
166	79.2970	-1.0244	12.12	2.33 $\pm$ 0.50	16.03 $\pm$ 2.61	0.533 $\pm$ 0.053	0.48	1.80	0.59	0.43	0.21	Y	South	Y
167	81.1386	0.6970	12.12	1.90 $\pm$ 0.35	14.74 $\pm$ 2.34	0.521 $\pm$ 0.052	0.44	1.68	0.69	0.68	0.44	Y	North	$\cdots$
168	81.8323	1.2015	13.12	3.74 $\pm$ 0.48	29.73 $\pm$ 4.54	1.851 $\pm$ 0.185	0.56	9.55	1.97	1.32	2.05	Y	North	$\cdots$
169	81.2205	0.8988	13.62	2.73 $\pm$ 0.45	28.82 $\pm$ 4.43	2.346 $\pm$ 0.235	0.86	11.80	0.66	2.02	7.39	Y	North	$\cdots$
170	81.2584	0.9871	13.62	2.01 $\pm$ 0.40	33.48 $\pm$ 5.12	0.706 $\pm$ 0.071	0.53	3.99	0.96	0.76	0.67	Y	North	$\cdots$
171	81.2647	0.9114	13.88	2.27 $\pm$ 0.46	31.95 $\pm$ 4.90	0.512 $\pm$ 0.051	0.47	2.79	0.97	0.79	0.64	Y	North	$\cdots$
172	81.3467	0.7412	15.62	2.24 $\pm$ 0.36	27.66 $\pm$ 4.21	0.603 $\pm$ 0.060	0.46	2.95	1.08	0.72	0.52	Y	North	$\cdots$
173	81.1638	0.8042	15.88	1.98 $\pm$ 0.37	19.17 $\pm$ 3.05	0.223 $\pm$ 0.022	0.36	0.85	0.65	0.57	0.26	$\cdots$	North	$\cdots$
174	81.2962	1.0564	16.12	1.82 $\pm$ 0.42	32.73 $\pm$ 5.01	0.166 $\pm$ 0.017	0.23	0.92	2.69	0.67	0.23	Y	North	$\cdots$

Table 2. Table 2: Averages and 1 σ 𝜎 \sigma deviations of physical properties of the C 18 O clumps.

	All	North	South	Star-forming	Starless
Samples	133	68 (51.1 %)	65 (48.9 %)	98 (73.7 %)	35 (26.3 %)
$R_{\mathrm{cl}}$(pc)	0.49 $\pm$0.17	0.49 $\pm$0.17	0.49 $\pm$0.17	0.52 $\pm$0.17	0.42 $\pm$0.13
$d{V}_{\mathrm{cl}}$($\mathrm{km}{s}^{-1}$)	0.75 $\pm$0.39	0.79 $\pm$0.42	0.71 $\pm$0.37	0.83 $\pm$0.40	0.54 $\pm$0.29
$M_{\mathrm{LTE}}$ (${10}^2{M}_{\odot }$)	1.9 ${}_{-1.1}{}^{}{}_{}{}^{+3.0}$	2.2 ${}_{-1.4}{}^{}{}_{}{}^{+3.6}$	1.5 ${}_{-0.9}{}^{}{}_{}{}^{+2.3}$	2.3 ${}_{-1.4}{}^{}{}_{}{}^{+3.6}$	1.0 ${}_{-0.5}{}^{}{}_{}{}^{+1.1}$
$n_{H_2}$(${10}^3{\mathrm{cm}}^{-3}$)	6.6 ${}_{-3.2}{}^{}{}_{}{}^{+6.1}$	7.9 ${}_{-3.9}{}^{}{}_{}{}^{+7.8}$	5.5 ${}_{-2.4}{}^{}{}_{}{}^{+4.2}$	7.1 ${}_{-3.4}{}^{}{}_{}{}^{+6.7}$	5.4 ${}_{-2.4}{}^{}{}_{}{}^{+4.3}$
${\alpha }_{\mathrm{vir}}$	0.30 $\pm$0.24	0.28 $\pm$0.21	0.33 $\pm$0.27	0.32 $\pm$0.41	0.27 $\pm$0.29

Table 3. Table 3: Fitting results of the CMF parameters. [This table was updated.]

Sample	Fitting mass range	$\alpha$	$a(\times {10}^3)$
All		-1.39 $\pm$ 0.04	$0.57\pm 0.10$
All		-2.07 $\pm$ 0.04	$17.4\pm 3.6$
Star-forming		-1.30 $\pm$ 0.04	$0.31\pm 0.05$
Star-forming		-2.00 $\pm$ 0.04	$10.6\pm 2.2$
Starless		-1.94 $\pm$ 0.06	$1.19\pm 0.37$

Equations

$$R_{\mathrm{cl}}=D{\theta }_{\mathrm{pix}}\sqrt{\frac{n_{\mathrm{sky}}}{\pi }},$$

$$I=\sum _{i=1}^{n_{\mathrm{vox}}}{T}_{\mathrm{mb}}^{i}d{v}_{\mathrm{spec}}(D{\theta }_{\mathrm{pix}}{)}^2$$

$$M_{\mathrm{LTE}}({\mathrm{M}}_{\odot })=13.2\frac{X_{{\mathrm{C}}^{18}\mathrm{O}}}{5.9\times 10^6}\frac{T_{\mathrm{ex}}}{1\mathrm{K}}{e}^{\frac{5.27\mathrm{K}}{T_{\mathrm{ex}}}}\frac{I}{1\mathrm{K}\mathrm{km}{\mathrm{s}}^{-1}\mathrm{p}{\mathrm{c}}^2},$$

$$T_{\mathrm{ex}}(\mathrm{K})=\frac{5.53}{\ln (1+\frac{5.53}{T_{\mathrm{mb}}^{{}^{12}\mathrm{CO}}+0.83})},$$

$$n_{{\mathrm{H}}_2}=\frac{3M_{\mathrm{LTE}}}{4\pi 2\mu m_{\mathrm{p}}{R_{\mathrm{cl}}}^3},$$

$$M_{\mathrm{vir}}=\frac{3(5-2k)}{G(3-k)}{R}_{\mathrm{cl}}{{\sigma }_{\mathrm{cl}}}^2,$$

$$\frac{dN}{dM}\propto M^{\alpha },$$

$$N(>M_{\mathrm{LTE}})\equiv {\int }_{M_{\mathrm{LTE}}}^{\infty }\frac{dN}{dM}dM=a{M_{\mathrm{LTE}}}^{\alpha +1},$$

Full text

ISM: clouds — ISM: individual objects (Cygnus X) — stars: mass function

††facilities: No:45m, Spitzer††software: Astropy(Astropy Collaboration et al., 2013), NumPy(Walt et al., 2011), SciPy(Jones et al., 2001), Matplotlib(Hunter, 2007), astrodendro

1 Introduction

Stars are formed in dense molecular cores and clumps, which are defined as compact ($\sim$0.1, and 1 pc, respectively) and dense ($\gtrsim 10^{4}$–$10^{5}~{}\mathrm{H_{2}~{}cm^{-3}}$) structures (Motte et al., 2018; Ohashi et al., 2016; Zhang et al., 2009; Williams et al., 2000). Understanding the physical and chemical properties of dense cores and clumps is one of the most important astrophysical topics in regard to the star formation process connecting a molecular cloud and protostar, mechanism to determine the initial stellar mass function (IMF), and enrichment of interstellar molecules. Therefore, observational studies of dense cores toward various star-forming regions have been conducted by some methods. In particular, thermal dust continuum observations using space and ground-based imaging arrays at sub-millimeter wavelengths identify hundreds of dense cores in nearby star-forming regions and reveal their statistical properties (e.g., Motte et al., 1998; Enoch et al., 2006). Dust extinction also provides a similar observational approach to exhibit the statistical properties of the dense cores in nearby molecular clouds(e.g., Alves et al., 2007).

Concurrently, molecular line mapping using dense molecular gas tracers, such as C18O, CS, NH3, and H13CO+, is a complementary approach to reveal the dense core and clump properties of star-forming regions. This method assists in decomposing spatially overlapping components using the velocity information and in diagnosing the kinematic properties of the dense cores (e.g., Myers & Benson, 1983; Myers et al., 1983; Stutzki & Guesten, 1990; Tatematsu et al., 1993; Onishi et al., 1996, 2002; Tafalla et al., 2004). In particular, C18O ($J=1$–[math]) surveys performed by the 4-m NANTEN and Nagoya University telescopes were promoted toward the high-density regions traced by a 13CO line (e.g. Onishi et al., 1996; Hara et al., 1999; Tachihara et al., 2000; Onishi et al., 2002) for nearby low-mass star-forming regions ($<200$ pc). The C18O cores identified by these observations exhibit densities of $10^{4}$–$10^{5}~{}\mathrm{cm^{-3}}$, radii of 0.1–0.5 pc, and gas masses of 1–100 $M_{\odot}$, typically with a spatial resolution of $\sim 0.1$ pc.

By contrast, understanding of the statistical core and clump properties in high-mass star-forming regions using molecular lines is still limited. Although C18O mapping observations have investigated the statistical core and clump properties in some active centers of high-mass star-forming regions (e.g., Stutzki & Guesten, 1990; Kramer et al., 1998; Wong et al., 2008; Ikeda & Kitamura, 2009, 2011), the observed field size in each case is only a few hundred square arcminutes. Thus, previous studies are probably biased to the core and clump properties in massive filaments. Such filaments are expected to be affected by the efficient mass accretion by the large-scale conversing flows (André et al., 2016; Fukui et al., 2018; Tokuda et al., 2018) as well as by the strong feedback and phenomena associated with high-mass star formation, such as strong ultra-violet (UV) radiation feedback, jet and outflow from a protostar, and supernova explosions. Therefore, determining the physical properties of the C18O cores and clumps in high-mass star-forming regions with a large-field ($>1~{}\mathrm{deg}^{2}$) survey is important to obtain the complete mechanism of a high-mass star formation in giant molecular clouds (GMCs).

Cygnus X is one of the most massive complexes of GMCs in our galaxy. Its environment is characterized by the current extremely active star formation, and a close distance of 1.4 kpc(Rygl et al., 2012) provides an opportunity to investigate the cluster formation process and ISM affected by strong stellar UV feedback by high-mass stars. At the center of the Cygnus X complex is the Cygnus OB2 association, which is known as one of the most massive associations of young stars in our galaxy containing $>200$ OB stars (Wright et al., 2015). The total molecular gas mass of Cygnus X is estimated to be $3\times 10^{6}~{}\mathrm{M_{\odot}}$(Schneider et al., 2006).

Cygnus X is divided into northern and southern molecular cloud complexes (hereafter referred as North and South, respectively), which have 13CO($J=2-1$)-traced dense gas masses of 2 and 3$\times 10^{5}\ \mathrm{M_{\sun}}$, respectively (Schneider et al., 2006). Cygnus X North shows an extremely filamentary structure of dust and molecular gas (e.g., Schneider et al., 2011, 2016), and contains well-known star-forming regions represented as DR21 and W75N, consisting of numerous fragmentary structures and massive dense cores, which can form high-mass stars. Compared to Cygnus X North, the South region shows a relatively weak star-forming activity, but the existence of a large amount of molecular gas component suggests the possibility of formation of stellar clusters in the South region (Yamagishi et al., 2018; Schneider et al., 2006). Thus, the Cygnus X complex, which contains these various environments, is the best target to investigate the star formation process from molecular gases to a massive stellar cluster and the stellar radiation feedback to the GMCs. Previously, molecular gas distribution in Cygnus X was investigated by 12/13CO lines (Schneider et al., 2006, 2011), and Herschel revealed the dust distribution via imaging of the sub-millimeter continuum emission(Schneider et al., 2016). However, it is important to investigate the gas properties of dense clumps using an optically thin line emission to reveal the formation process of high-mass stars and stellar clusters from molecular cores.

In this study, we investigated C18O clump properties using multi-line CO and CN survey data at 3 mm wavelength toward the main part of the Cygnus X GMC complex using the Nobeyama 45 m telescope (Yamagishi et al., 2018). Section 2 describes the details of the C18O observation, clump identification method, and estimation of the physical properties of the identified clumps. The result of data analysis is presented in Section 3. In Section 4, we discuss the physical properties of the C18O clumps obtained by this survey. Finally, Section 5 summarizes the main results of this study.

2 Observation and Analysis

2.1 FOREST/NRO 45-m Data

The C18O ($J=$1–0) data of the Cygnus X region were obtained by the FOREST receiver (Minamidani et al., 2016) mounted on the Nobeyama 45 m radio telescope, along with the 12CO ($J=$1–0), 13CO ($J=$1–0), and CN ($N=$1–0) data111The datasets are publicly available at https://cygnus45.github.io (Yamagishi et al., 2018). The observations covered a $\sim 9$ deg2 field, which included the main parts of the North and South GMCs, by connecting $1^{\circ}\times 1^{\circ}$ patches (FUGIN scan, Umemoto et al., 2017). The angular resolution of the telescope was $\sim 16^{\prime\prime}$ FWHM at the C18O band.

To improve the sensitivity, we convolved the cube to a spatial resolution of $46^{\prime\prime}$ FWHM with a pixel grid of $22.7^{\prime\prime}$ and binned to a velocity resolution of $0.25~{}\mathrm{km~{}s^{-1}}$. Consequently, the median rms noise level of the final C18O image $T_{\mathrm{rms}}$ became 0.35 K on the $T_{\mathrm{mb}}$ scale. The observation and data analysis procedures are described in Yamagishi et al. (2018) in detail.

2.2 C18O clump identification

We identify C18O clumps from the C18O cube using the astrodendro package, which is based on the dendrogram algorithm (Rosolowsky et al., 2008). A dendogram is used to construct a tree structure consisting of trunks, branches, and leaves. A “trunk” is defined as a set of voxels such that $T_{\mathrm{mb}}$ is larger than $T_{\mathrm{min}}$ and the voxel number, $n_{\mathrm{vox}}$, is not less than the integer, $n_{\mathrm{vox}}^{\mathrm{min}}$. A trunk is split into one or more leaves by a “branch”, which is a node of more compact structures (leaf or branch). A “leaf” is defined as a local peak such that its height is higher than $T_{\mathrm{delta}}$ from the skirt of the peak and the voxel number is not less than $n_{\mathrm{vox}}^{\mathrm{min}}$. From the definition, leaves are identified as compact clumps that do not have multiple peaks, and therefore, a dendrogram is available as an identification algorithm for molecular clumps and cores. Cheng et al. (2018) used the dendrogram method to identify the dense cores and clumps in G 286.21+0.27 and reported that the dendrogram-identified cores showed a spectral index of the core mass function that was more consistent with the Salpeter-IMF than that of the clumpfind-identified cores. Thus, it is reasonable to adopt the dendrogram algorithm as a core and clump identification procedure.

In the analysis, we adopted $T_{\mathrm{min}}=3T_{\mathrm{rms}}$ and $T_{\mathrm{delta}}=2T_{\mathrm{rms}}$ to identify C18O clumps with a reliable signal-to-noise ratio. We also used $n_{\mathrm{vox}}^{\mathrm{min}}=16$ to avoid false detection of clumps by picking up random noise.

2.3 Physical property estimation

We estimated C18O clump properties such as radius $R_{\mathrm{cl}}$, local thermal equilibrium (LTE) mass $M_{\mathrm{LTE}}$, FWHM velocity width $dv_{\mathrm{cl}}$, and virial mass $M_{\mathrm{vir}}$. We followed the method generally adopted by previous C18O core studies (Onishi et al., 1996; Ikeda & Kitamura, 2009, 2011; Shimajiri et al., 2015) and made further refinements to improve the reliability of the estimated physical properties, motivated by Nishimura et al. (2015).

The radius of a C18O clump is defined using the pixel number projected on the sky ($l$-$b$ plane of the galactic coordinate), $n_{\mathrm{sky}}$, assuming a spherically symmetric clump:

[TABLE]

where $\theta_{\mathrm{pix}}=22.7^{\prime\prime}$ is the pixel grid spacing along with the galactic coordinate of the data cube and $D$ is the distance to the clump from the solar system.

We define the integrated intensity of an object as

[TABLE]

where $i$ is the voxel number of each core, $T_{\mathrm{mb}}^{i}$ is the main beam temperature at voxel $i$ and $dv_{\mathrm{spec}}=0.25~{}\mathrm{km~{}s^{-1}}$ is the spectral velocity width. The LTE mass is estimated using the equation:

[TABLE]

where $T_{\mathrm{ex}}$ is the excitation temperature of the C18O molecules. We assumed that 12CO was optically thick and the $T_{\mathrm{ex}}$ of 12CO and C18O was the same. Thus,

[TABLE]

where $T_{\mathrm{mb}}^{\mathrm{{}^{12}CO}}=\max\{T^{\mathrm{{}^{12}CO},~{}i}_{\mathrm{mb}};i=1,2,...,n_{\mathrm{vox}}\}$. We used the isotopic abundance ratio of the C18O molecules relative to the $\mathrm{H_{2}}$ molecules, $X_{\mathrm{C^{18}O}}=5.9\times 10^{6}$(Frerking et al., 1982). Assuming a spherical clump shape, we also defined the mean gas density as

[TABLE]

where $\mu=1.36$ is the mean molecular weight per proton and $\mathrm{m_{p}}=1.67\times 10^{-24}~{}\mathrm{g}$ is a proton mass.

To calculate the virial masses, we removed the effect of the velocity width broadening by the limitation of the spectral resolution, $dv_{\mathrm{spec}}$. The spectral window function obtained by a SAM45 spectrometer can be approximated by a rectangular window function. Thus, we estimated the actual velocity widths of the clumps, $dv_{\mathrm{cl}}$, by deconvolving the intensity-weighted velocity dispersions, $dv_{\mathrm{obs}}$, with a rectangular function.

Following Solomon et al. (1987) and Bolatto et al. (2013), we estimated the virial masses of the identified clumps with the radial density profile of $\rho(R)\propto R^{-k}$:

[TABLE]

where $G$ is the gravitational constant, $k$ is a parameter of the density profile, and $\sigma_{\mathrm{cl}}=dv_{\mathrm{cl}}/(2\sqrt{2\ln 2})$, which is assuming a Gaussian line profile. We used $k=0$ for the calculation, which assumes a spherically uniform clump that has no external pressure, by following the previous C18O studies (e.g., Ikeda & Kitamura, 2009, 2011; Shimajiri et al., 2015; Tachihara et al., 2002). The possible bias of the virial mass estimate by the selection of $k$ is a factor of 1–1.4 in the possible range of $0<k<2$ for an isothermal gas sphere (e.g., Shu, 1977). We also defined the virial ratio, $\alpha_{\mathrm{vir}}\equiv M_{\mathrm{vir}}/M_{\mathrm{LTE}}$.

Finally, we used the canonical distance, $D=1.4$ kpc, from the sun to the clumps, which was determined by parallax measurements by a very long baseline interferometry observation toward four major star-forming regions, as a representative value of the Cygnus X GMC complex. The exception was the distance to a corresponding object of background star-forming region AFGL 2592 at $D=3.3$ kpc (Rygl et al., 2012).

3 Result

Figures 1 and 2 show the C12O and C18O peak main beam temperature images obtained by the observation. The dense gas traced by the C18O emission shows a filamentary and compact distribution. By contrast, the 12CO emission traces a more diffuse gas component than the C18O emission.

Based on the dendrogram analysis, we identified 177 C18O clump candidates as leaves. From these samples, we excluded three clump candidates that had no corresponding 13CO emission at the velocity of the C18O line, because these would be false detections. Thus, we identified 174 C18O clumps in total. The positions of the C18O clumps are shown in Figures 1 and 2. The C18O clump catalog is provided in Table 1.

We show the line profiles of the C18O clumps in Figure 3. In the South region, we find that isolated clump #3 shows a different peak velocity ($v_{\mathrm{peak}}=30~{}\mathrm{km~{}s^{-1}}$) from those of the other identified clumps. The source position of #3 corresponds to background star-forming region AFGL 2592 at $D=3.3$ kpc(Rygl et al., 2012); thus, we exclude clump #3 from the South objects.

For the statistical analysis presented in Section 4, we did not use the eleven objects that were located at the edge of the map. We also excluded the clumps in a patch around $(l,b)=(+78,-1)$, which included DR13S filaments (Schneider et al., 2006), in the statistical analysis to avoid a systematic bias in the physical properties owing to the difference in the map sensitivity. We defined the border of the Cygnus X North and South regions at a galactic longitude of $80.2\deg$, with which the Cygnus OB2 association is associated. Excluding the objects that were located in the DR13S regions and at the map edge, we used 68 and 65 C18O clump samples as the North and South clumps, respectively.

The star formation activities of the C18O clumps were determined by existence of a protostar using the catalog obtained by Spitzer (Kryukova et al., 2014). Thus, we found 98 clumps that were associated with one or more protostars and 35 starless clumps in the North and South regions that were not located at the map edge.

4 Discussion

In section 3, we discussed the estimated physical properties of the C18O clumps and the classification into North and South and star-forming and starless objects. Here, we discuss in detail the physical properties of the molecular cloud clumps identified by this survey.

4.1 Difference in the physical properties of the North and South regions

Although both the Cygnus X North and South regions are known as large reservoirs of molecular gases ($\sim 10^{6}~{}M_{\sun}$), the North region shows an extremely filamentary 12/13CO structure compared to the South region (Schneider et al., 2006, 2011) and contains numerous active star-forming regions represented by DR21 and W75N. The above seem to reflect a difference in the star formation activity and evolution stages of each molecular cloud complex, and therefore, a difference in the statistical properties of the C18O clumps of the North and South regions is suggested.

Figure 4 shows the probability densities and histograms of the physical properties of the identified C18O clumps of the North and South regions. The mean and standard deviation of the physical properties classified by the regions are listed in Table 2. The distributions of the radius and velocity dispersion are very similar for the North and South clumps. By contrast, the C18O clumps in the North region show a slightly larger LTE mass and higher $\mathrm{H_{2}}$ density than those in the South region. The $p$-values of Welch’s $t$-test for the radii, velocity dispersions, LTE masses, and $\mathrm{H_{2}}$ densities of the North and South cores are 0.959, 0.241, 0.070, and 0.002, respectively. This does not support that the average values of the radii and velocity dispersions of the North and South clumps are significantly different. Contrastingly, the average $\mathrm{H_{2}}$ density of the C18O clumps of the North region is significantly higher than that of the C18O clumps of the South region, with a significance level of 5%. Thus, we can expect that the statistical difference in the $\mathrm{H_{2}}$ density reflects that of the clump evolution stages, and therefore, the difference in the star formation activities of the North and South regions, as suggested by Schneider et al. (2006) and Yamagishi et al. (2018).

4.2 Difference in the physical properties by the presence of star formation activity

We also investigated the quantitative difference in the physical properties of star-forming and starless clumps, which seemed to reflect the evolution sequences of the C18O clumps.

Figure 5 shows the probability densities and histograms of the physical properties of the identified C18O clumps of the star-forming and starless clumps. In Table 2, we also list the average and standard deviation classified by the star formation activity of the clumps. The star-forming clumps show a larger radius, velocity dispersion, LTE mass, and $\mathrm{H_{2}}$ density than the starless clumps. In fact, the significant difference in the mean values of these properties is strongly supported by Welch’s $t$-test, whose $p$-values are $<$0.01, $<$0.01, $<$0.01, and 0.01, respectively.

In nearby ($\leq 200$ pc) star-forming regions, Tachihara et al. (2002) reported a similar tendency of the C18O core radii, velocity dispersions, LTE masses, $\mathrm{H_{2}}$ densities, and $\mathrm{H_{2}}$ column densities between the starless, star-forming, and cluster-forming cores. This tendency is naturally expected to arise from difference of gas accretion time scale between starless and star-forming cores. Our result also supports that the general trends of the core properties, which evolve with star formation, are applicable to the C18O clumps in an extremely active high-mass star-forming region.

4.3 Virial ratio

Here, we discuss the virial ratio, which is an important indicator to determine whether stars will form cores/clumps, in comparison with previous C18O studies. As references of the previous C18O surveys, we use the results of nearby ($D\leq 200$ pc) molecular clouds, including the low-mass star-forming regions of Taurus, Ophiuchus, Lupus, Lynds 1333, Corona Australis, Southern Coalsack, and the Pipe nebula, observed by NANTEN(Tachihara et al., 2002). We also refer to the C18O cores properties observed by the NRO 45m telescope in Orion A ($D=440$ pc, Shimajiri et al., 2015; Hirota et al., 2007), the nearest high-mass star-forming GMC, which has about 1/10 of the total molecular gas mass of the Cygnus X GMC complex (Motte et al., 2018). We also consider the Sharpless 2-140 (S 140) HII region, a compact high-mass star-forming region located at the edge of the Lynds 1204 molecular cloud ($D=760$ pc, Ikeda & Kitamura, 2011; Hirota et al., 2008). The above is done to compare with smaller and less active high-mass star-forming regions than Cygnus X. We followed the assumption of a uniform and spherical core structure that had no support of rotation, magnetic field, and external pressure, which is assumed in the previous studies. By considering the most compact clumps ($n_{\mathrm{vox}}=16$) with relatively high excitation temperature of 36 K, corresponds to the $2\sigma$ value of all samples, the detection limit of the LTE mass is estimated to be $\sim 55~{}M_{\sun}$ with $3\sigma$ intensity detection, which covers the 95th percentile of the identified clumps. Therefore, we defined 95th percentile as induces of relative sensitivity limit for the Cygnus X, S140, Orion A, and nearby low-mass samples. Thus, the relative sensitivity limits of the LTE masses in the Cygnus X samples are $\sim$10 and 20 times worse than S 140, and Orion A/nearby studies.

We also consider the systematic bias of $\alpha_{\mathrm{vir}}$ caused by different spatial and velocity resolutions of data set. From the definition of the LTE and virial masses, we can assume that $\alpha_{\mathrm{vir}}$ is proportional to spatial resolution and inversely proportional to velocity resolution. The spatial and velocity resolutions of the Cygnus X clumps were 3 and 2.5 times worse than previous core studies. Thus, systematic bias of the virial ratio estimate can be estimated to be a factor of $\sim$1.2, and would not affect our discussion.

The relation between the LTE and virial masses is shown in Figure 6. While the NANTEN and Orion A C18O cores are located at $\alpha_{\mathrm{vir}}\gtrsim 1$, most of the C18O core/clumps in Cygnus X and S 140 show a virial ratio of $\alpha_{\mathrm{vir}}<1$. The average and standard deviation values of the virial ratio of the star-forming and starless clumps in Cygnus X are $0.32\pm 0.26$, $0.27\pm 0.19$ respectively, and the difference is not significant with Welch’s $t$-test ($p=0.32$). The average value of both the star-forming and starless cores is $0.30\pm 0.24$, which is consistent with the virial ratio of S 140 ($\alpha_{\mathrm{vir}}=0.35\pm 0.23$) and, therefore, supports that these C18O clumps are gravitationally bound. The observing region of S 140 is only $20\arcmin\times 18\arcmin$, and it will be very biased to the center of the active star-forming region. This result suggests that the C18O clumps in Cygnus X have very similar properties at the center of the high mass star-forming region. Thus, the C18O clumps in Cygnus X traces a dense molecular gas clump that directly connects to an extremely active future and current star formation activity. In addition, the virial ratios in Cygnus X and S 140 are smaller than those in the nearby molecular clouds ($\alpha_{\mathrm{vir}}=2.8\pm 3.6$) and Orion A ($\alpha_{\mathrm{vir}}=2.4\pm 2.2$). This might reflect the difference in the star formation mode: low-mass single star or high-mass cluster formation.

Another important feature is that the distribution of the virial or LTE mass of the C18O clumps in Cygnus X is dispersed widely compared to those in the previous studies. In fact, the mean and standard deviation of LTE masses in the previous studies were $22^{+25}_{-12}$, $11^{+14}_{-6}$, and $12^{+23}_{-8}~{}\mathrm{M_{\sun}}$ in S 140, Orion A, and nearby star-forming regions, respectively. These values are much smaller than those in the Cygnus X ($190^{+300}_{-110}~{}\mathrm{M_{\sun}}$) by more than one order of magnitude. This result is consistent with our estimate of the relative sensitivity limits, which would be attribute to the lower spatial resolution, spectral resolution, and image sensitivity than the previous studies.

While the typical LTE and virial masses are larger than the previous studies, the fact that the clumps in Cygnus X show $\alpha_{\mathrm{vir}}<1$ supports that these clumps are gravitationally bound objects, which are directly related to star formation. In particular, some of the massive clumps are assumed to be the formation sites of high-mass stars and stellar clusters. Thus, this feature could be related to the extremely active star formation in Cygnus X.

4.4 Clump mass function

We also examined the core/clump mass function (CMF) in Cygnus X to reveal the detailed mass properties and relation between the IMF and galactic field stars. Based on the definition of Offner et al. (2014), the IMF and CMF are defined as

[TABLE]

where $N$ is the number of stars or cores/clumps, $M$ is the mass of the stars or cores/clumps, and $\alpha$ is the spectral index of the IMF or CMF. As an integral form of the CMF for the case of $\alpha<-1$, we define a cumulative number,

[TABLE]

where $a$ is the factor of proportionality.

The observational studies of dense dust core surveys using (sub)millimeter dust continuum and dust extinction (e.g., Motte et al., 1998; Enoch et al., 2006; Nutter & Ward-Thompson, 2007; Alves et al., 2007) have revealed that multiple spectral index components of the CMF are similar to the $\alpha=-1.3\pm 0.5$ ($0.08<M_{*}/M_{\sun}<0.5$, $M_{*}$ is a stellar mass) and $\alpha=-2.3\pm 0.3$ ($0.5<M_{*}/M_{\sun}<1$) components of the Kroupa IMF(Kroupa, 2001). For a C18O core observation, Tachihara et al. (2002) has also reported multiple spectral index components of the CMF ($\alpha=1.25$ and $2.5$) corresponding to the Kroupa IMF components at $0.08<M_{*}/M_{\sun}<0.5$ and $0.5<M_{*}/M_{\sun}<1$ ranges toward nearby low-mass star-forming regions. Our observation in Cygnus X provides large samples of C18O clumps in an extremely active cluster-forming region. Lada & Lada (2003) suggest that cluster formation activity in GMCs is the dominant (70%–90%) supplier of field low-mass stars in the galactic disk. Thus, it is important to investigate the relationship between the IMF of the galactic field stars and CMF obtained by our C18O clump samples, which are more massive and larger than those in the previous C18O studies.

Figure 7 shows the cumulative number count of the C18O clumps and suggests that the spectral index of the CMF changes around $\log(M_{\mathrm{LTE}}/M_{\odot})=2.15$. The fitting parameters are shown in Figure 3. Considering the detection limit of the C18O clumps, $\log(M_{\mathrm{LTE}}/M_{\odot})=1.75$, we fit with two mass functions with ranges of $1.75<\log(M_{\mathrm{LTE}}/M_{\odot})<2.15$ and $2.15<\log(M_{\mathrm{LTE}}/M_{\odot})$. From the least-$\chi^{2}$ fittings, which are shown in Figure 7, the cumulative number count of the C18O clumps fits well in each mass range. We obtained $\alpha=-1.39\pm 0.04$ for $1.75<\log(M_{\mathrm{LTE}}/M_{\odot})<2.15$, and $\alpha=-2.07\pm 0.04$ for $2.15<\log(M_{\mathrm{LTE}}/M_{\odot})$. The errors (1$\sigma$) were estimated by Monte Carlo simulation by considering the random errors of the estimated LTE masses of the C18O clumps. These spectral indices are consistent with the $\alpha=-1.3$ and $-2.3$ components of the Kroupa IMF. This confirms the similarity of the IMF in the galactic field stars and clump-scale CMF in a high-mass star-forming region.

We also investigate the difference in the spectral indices of the star-forming and starless clumps. The mass function of the star-forming clumps well fits the two components of the spectral indices: $\alpha=-1.30\pm 0.04$ for $1.75<\log(M_{\mathrm{LTE}}/M_{\odot})<2.15$ and $\alpha=-2.00\pm 0.04$ for $2.15<\log(M_{\mathrm{LTE}}/M_{\odot})$, which are also consistent with the IMF. However, for the starless clumps, we can fit the CMF with a single spectral index of $\alpha=-1.94\pm 0.06$ at the mass range of $1.75<\log(M_{\mathrm{LTE}}/M_{\odot})$, and the index of the starless clumps is consistent with the spectral index of a star-forming clump at a high mass range. Thus, we can assume that the starless clumps will evolve into star-forming clumps with further gas mass accretion. This is also supported by the fact that $\sim 2$ times lowers the average mass of the starless clumps more than that of the star-forming ones, as can be seen from Table 2.

4.5 Star formation efficiency of the C18O clumps

We can estimate the molecular gas mass fraction that contribute to the stellar mass in a clump, which is called the star formation efficiency (SFE), from the boundary gas mass that changes the spectral index. Here, we assume that the clumps with a boundary mass of $\log(M_{\mathrm{LTE}})=2.15$ (i.e., $M_{\mathrm{LTE}}\simeq 140~{}M_{\odot}$) evolve into a single star that has a boundary mass of the Kroupa IMF of 0.5 $M_{\sun}$ or into a cluster that has a maximal stellar mass of 0.5 $M_{\sun}$. In case cluster formation, using the relation between maximal stellar mass $M_{\mathrm{*,max}}$ and cluster mass $M_{\mathrm{cluster}}$: $M_{\mathrm{*,max}}=0.39M_{\mathrm{cluster}}^{2/3}$, assuming the hierarchical cluster formation model (Bonnell et al., 2003, 2004; Weidner & Kroupa, 2006; Weidner et al., 2010), the total cluster stellar mass of the cluster is expected to be $1.5~{}M_{\sun}$. Thus, the SFE of the typical C18O clumps is expected to be 0.3–1%. This is very unlikely because the SFE is excessively lower than that estimated for the low-mass star-forming regions observed by NANTEN from the comparison of the CMF and IMF, with the assumption of a single star formation in the C18O cores ($\sim$10%, Tachihara et al., 2002).

It is known that some studies of massive clumps also reveal a high SFE ($\sim$10%, e.g., Lada & Lada, 2003) by comparing the gas amount with the stellar content in GMCs. Assuming an SFE of 10%, the $\sim$10 C18O clumps that have gas masses of $\gtrsim 10^{3}~{}M_{\sun}$ will evolve into open clusters having a total stellar mass of $\gtrsim 100~{}M_{\sun}$ and containing one or more high-mass stars ($>8~{}M_{\sun}$). This scenario is consistent with a high-resolution interferometry study of massive dense cores in Cygnus X North (Bontemps et al., 2010), which revealed numerous fragmentary structures inside massive dense cores.

The discrepancy between the SFEs of the NANTEN C18O cores and our samples could be explained in terms of the physical spatial resolution of our dataset of Cygnus X ($\sim$0.3 pc) being worse than those of the NANTEN observations ($\sim$0.1 pc). This is because the identified C18O clumps in Cygnus X are larger than in the NANTEN study, and therefore, the mass of these clumps is higher than of those in the latter study. Thus, we can also expect that most of the C18O clumps in Cygnus X have an internal structure, and our predicted SFE using the relation of the IMF and CMF might be underestimated. Further high-resolution, high-sensitivity, and wide-field survey of C18O and other dense gas tracers toward high-mass star-forming regions is important to understand the complete mechanism of star formation across a GMC.

5 Summary

We investigated the physical properties of the C18O clumps identified in a multi-line CO ($J=$1–0) survey toward the Cygnus X regions using the Nobeyama 45-m radio telescope. The main results are summarized below.

We identified 174 C18O clumps in total. Ninety eight out of the 133 objects, except for the objects that were located at the map edge or in the DR13S region, were accompanied by one or more protostars. 2. 2.

The C18O clump properties showed clump radii of 0.2–1 pc, velocity dispersions of $<2.2\mathrm{km\ s^{-1}}$, LTE masses of 30–3000 $M_{\sun}$, and H2 densities of (2–55) $\times 10^{3}\ \mathrm{cm^{-3}}$. 3. 3.

We detected statistical differences in the physical properties of the clumps of the North and South regions in terms of the H2 density. This was consistent with difference in the actual star formation activities of these regions and suggested to be caused by the difference in the evolution stages in the North and South regions. 4. 4.

The statistical differences in the physical properties of the star-forming and starless clumps were confirmed to be significant. The larger radius and velocity dispersion and higher LTE mass and H2 density in the star-forming clumps compared to those in the starless ones reflected the difference in the clump evolution stages. 5. 5.

The average value of the virial ratio was $0.30\pm 0.24$. This supported that the C18O clumps in Cygnus X were gravitationally bound and served as formation sites of a star or stellar cluster. In addition to Cygnus X, an active cluster-forming region, S 140, also reported a lower virial ratio than the nearby low-mass star-forming molecular clouds and Orion A GMC. This tendency seemed to be characterized by the difference in the star formation mode in these observing regions. 6. 6.

We confirmed two spectral index components of the clump-scale CMF, $\alpha=-1.39\pm 0.04$ ($1.75<\log(M_{\mathrm{LTE}}/M_{\odot})<2.15$) and $\alpha=-2.07\pm 0.04$ ($2.15<\log(M_{\mathrm{LTE}}/M_{\odot})$), which were consistent with the $\alpha=-1.3$ ($0.08<M_{*}/M_{\sun}<0.5$, $M_{*}$) and $\alpha=-2.3$ ($0.5<M_{*}/M_{\sun}<1$) components of the IMF of the galactic field stars, respectively. 7. 7.

The mass function spectral index of the star-forming clumps, $\alpha=-2.00\pm 0.04$, at $2.15<\log(M_{\mathrm{LTE}}/M_{\odot})$ was consistent with that of the starless clumps, $\alpha=-1.94\pm 0.06$ at $1.75<\log(M_{\mathrm{LTE}}/M_{\odot})$, suggesting that the starless clumps would evolve into star-forming clumps with further gas mass accretion. 8. 8.

By comparing the boundary masses of the CMF and IMF, the SFE of the C18O clumps was estimated to be 0.3–1%, which was excessively lower than that reported in previous studies ($\sim$10%) and very unlikely. Assuming an likely SFE of 10%, about ten C18O clumps that had a gas mass of $>10^{3}~{}M_{\sun}$ were expected to evolve into open clusters containing one or more high-mass stars.

K. T. would like to thank the University of Virginia for providing the funds for her postdoctoral fellowship in the VICO research program. The Nobeyama 45-m radio telescope is operated by Nobeyama Radio Observatory, a branch of the National Astronomical Observatory of Japan. Data analysis was in part carried out on the open-use data analysis computer system at the Astronomy Data Center, ADC, of the National Astronomical Observatory of Japan. This research made use of Astropy, a community-developed core Python package for astronomy (http://www.astropy.org/, Astropy Collaboration et al., 2013), and astrodendro, a Python package to compute dendrograms of astronomical data (http://www.dendrograms.org/). This work was supported by JSPS KAKENHI Grant Numbers JP17H06740, JP18K13580, JP18K13582, and JP18K13595.