GAS EMISSIONS IN PLANCK COLD DUST CLUMPS—A SURVEY OF THE J = 1–0 TRANSITIONS OF ¹²CO, ¹³CO, AND C¹⁸O

Most of the observed clumps have a single velocity component in CO emission. Among the 673 sources, 123 have double velocity components and 16 have possible double velocity components; 18 have three velocity components and 10 have possible triple velocity components. Multiple components or blend emission were detected in 52 cold sources. The spectral line of each distinguishable component was fitted with a Gaussian function. Centroid velocity V_lsr, antenna temperature T*_A, and FWHM $\Delta \hbox{\textit {V}}$ were obtained for all three CO lines, which are given in Table 3. Centroid velocity of ¹³CO was taken as the systemic velocity of each velocity component and listed in the second column of Table 4. Dense core masses are related to molecular line widths (Wang et al. 2009). We adopted an average value of ¹³CO line width of 1.3 km s⁻¹ for the nearby dark cores (Myers & Benson 1983) as a criterion to distinguish high-mass and low-mass clumps. If a clump contains one or more velocity components with a ¹³CO line width larger than 1.3 km s⁻¹, it is considered to be a candidate of high-mass clumps (group H), otherwise, it is taken as a candidate for low-mass clumps (group L). In some of the observed clumps, the spectral lines of the emission components depart from a Gaussian profile, which probably reflects the state of gas or originates from systematic motions and star formation activities. We classify the different non-Gaussian profiles with the following characters: BA⁺: blue profile; RA⁺: red profile; BA: blue asymmetric; RA: red asymmetric; De: possible depletion; BW: blue wing; RW: red wing; W: wings; P: pedestal; Dob: double components; T: three components; and M.B: multiple or blended components.

Table 4. Derived Parameters of Surveyed ECC Clumps

Name	Vlsr	R	D	Z	Tex	τ(13)	N(13)	τ(18)	N(18)	$N_{{\rm H}_{2}}$	Ratio(12/13)	X13/X18	σNT	σTherm	σ3D
	(km s−1)	(kpc)	(kpc)	(kpc)	(K)		(1015 cm−2)		(1015 cm−2)	(1021 cm−2)		(km s−1)	(km s−1)	(km s−1)
G001.38+20.94	0.74	7.47	1.1	0.39	14.8	1.2	7.3	0.2	1.6	6.5	2.1	4.6	0.32	0.21	0.67
G001.84+16.58	5.87	4.51	4.16	1.19	14.6	1.2	6.5	0.4	1.5	5.7	2.7	4.3	0.29	0.21	0.61
G003.73+16.39	6.17	5.87	2.75	0.78	14.6	0.9	5.7	0.1	1.0	5.0	2.5	5.9	0.29	0.21	0.63
G003.73+18.30	4.32	6.48	2.14	0.67	16.8	1.0	10.6	0.5	2.7	9.4	2.2	4.0	0.41	0.23	0.80
G004.02+16.64	5.86	6.10	2.52	0.72	14.4	1.2	4.3	0.1	0.6	3.9	2.0	7.7	0.20	0.21	0.50
G004.19+18.09	3.73	6.88	1.71	0.53	15.3	1.2	12.1	0.2	1.0	10.8	1.9	12.2	0.52	0.22	0.97
G004.19+18.09	6.69	5.92	2.73	0.85	16.7	0.6	4.9			4.4	3.0		0.25	0.23	0.59
G004.15+35.77	2.61	7.13	1.7	0.99	12.9	1.1	7.4			6.6	2.7		0.45	0.20	0.85
G004.17+36.67	2.47	7.19	1.64	0.98	13.6	1.0	5.2			4.7	2.0		0.29	0.20	0.62
G004.41+15.90	4.73	6.62	1.96	0.54	15.7	0.9	4.3			3.8	2.0		0.19	0.22	0.50
G004.46+16.64	5.55	6.37	2.23	0.64	15.6	0.9	10.6	0.3	1.5	9.4	2.3	7.1	0.50	0.22	0.95
G004.54+36.74	2.54	7.25	1.56	0.93	12.4	1.0	4.9	0.1	0.4	4.3	2.4	11.5	0.32	0.19	0.64
G004.81+37.02	3.82	6.79	2.15	1.30	12.3	1.0	6.6	0.1	0.7	5.9	2.2	9.9	0.44	0.19	0.83
G004.92+17.95	3.71	7.10	1.48	0.46	10.9	2.0	4.3	0.3	0.7	3.8	2.7	6.5	0.26	0.18	0.55
G005.03+19.07	3.81	7.08	1.5	0.49	17.8	0.8	9.9	0.1	1.2	8.8	2.3	8.0	0.41	0.23	0.82
G005.29+11.07	4.14	7.09	1.44	0.28	18.6	0.8	6.8	0.2	1.1	6.1	2.7	6.5	0.26	0.24	0.61
G005.29+14.47	3.74	7.20	1.35	0.34	13.6	0.3	0.8			0.7	5.6		0.11	0.20	0.40
G005.31+10.78	4.38	7.03	1.51	0.28	16.6	1.0	9.0			8.0	2.3		0.37	0.22	0.75
G005.69+36.84	0.6	8.33	0.21	0.13	11.1	0.2	1.6			1.4	6.9		0.40	0.18	0.77
G005.69+36.84	2.27	7.60	1.13	0.68	10.2	2.1	5.5	0.6	1.2	4.9	2.0	4.6	0.38	0.18	0.72
G005.80+19.92	2.96	7.52	1.05	0.36	15.7	1.0	8.3	0.2	1.1	7.4	2.5	7.4	0.37	0.22	0.75
G006.08+20.26	3.97	7.26	1.33	0.46	13.9	1.6	8.7	0.2	1.5	7.7	2.7	5.9	0.38	0.21	0.75

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

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The normalized velocity difference δV = (V_thick − V_thin)/δV_thin is applied to identify the blue and red profiles (Mardones et al. 1997), where V_thick is the peak velocity of ¹²CO (1–0), V_thin and δV_thin are the systemic velocity and the optical thin line width, respectively, of optically thin lines. We use ¹³CO (1–0) and C¹⁸O (1–0) as the optically thin lines. If δV < −0.25, the line is classified as a "blue profile," and if δV > 0.25, the line is classified as a "red profile." The sources with blue or red profiles are listed in Table 5. We define δV(12) = (V_thick − V₁₂)/δV_thin to investigate line blue or red asymmetries where δV₁₂ < −0.25 or >0.25, where V₁₂ is the center velocity of ¹²CO (1–0). The sources with asymmetric profiles are listed in Table 6. The spectrum characteristics are denoted in the last column of Table 3. Figure 1 presents the examples of the spectra of the J = 1–0 lines of the ¹²CO, ¹³CO, and C¹⁸O with red, green, and blue colors, respectively, including single, double, and triple components and the characteristics of the spectral profiles.

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The histograms of the line center (peak) velocity difference between the lines of ¹²CO and ¹³CO (V₁₂–V₁₃) and those of ¹³CO and C¹⁸O (V₁₃–V₁₈) lines are shown in Figures 2(a) and (b). The distributions (blue solid histograms) of both the V₁₂ − V₁₃ and V₁₃ − V₁₈ are quite symmetric around the zero, and are fitted with a normal distribution (red curve). However, their distributions are much narrower than a standard normal distribution (red curve), but have a sharp peak at zero (see Figures 2(a) and (b)). Ninety-four percent of the clumps have V₁₂ − V₁₃ less than 3σ of the velocity resolution (0.17 km s⁻¹) given by the spectrometer, and 98% of the clumps have V₁₃ − V₁₈ less than 3σ of the velocity resolution. The velocity correlations between lines of ¹²CO–¹³CO and ¹³CO–¹⁸CO are shown in Figures 2(c) and (d). Y = (1.002 ± 0.001)X + (0.005 ± 0.016) for V₁₂ (Y) to V₁₃ (X) and Y = (0.992 ± 0.005)X + (0.140 ± 0.057) for V₁₃ (Y) to V₁₈ (X) show very good correlations and the correlation coefficient is 100%. This is the first time good agreement of the center velocities of the ¹²CO and its main isotopes, the ¹³CO and C¹⁸O lines, has been shown with such a large sample. These results show that the peak velocities of the three CO lines agree very well, and demonstrate that they originate from the same emission regions. Comparisons of Figures 2(a) and (b) with Figures 2(c) and (d) show the agreement between V_lsr of the ¹³CO and C¹⁸O lines is better than that of the ¹²CO and ¹³CO lines, which may suggest that the ¹²CO is easily affected by dynamic factors in the clump or its environment.

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Since there are fewer sources in which C¹⁸O lines were detected compared with those in which ¹³CO lines were detected, we adopt the center velocity of ¹³CO as the systemic velocity of the clumps in the following analysis. For the components without ¹³CO (1–0) emission, the center velocities of ¹²CO were adopted as the systemic velocity.

The main beam antenna temperatures of the three transitions for all the components detected were obtained. T₁₂ ranges from 0.5 to 12 K. The three clumps G209.28−19.62 (12 K), G192.54−11.56 (9.2 K), and G207.35−19.82 (8.8 K), temperatures which are all located in the Orion region, have the highest. Generally, the antenna temperatures of ¹³CO and C¹⁸O are also high in the ¹²CO emission strong clumps. For the above three clumps, T₁₃ and T₁₈ are 6.8, 1.4; 5.0, 0.6; and 3.1, 0.4 K, respectively. The ratio of T₁₂/T₁₃ is between 2.8 and 1.8, showing that the ¹²CO line emissions have large opacity. The ratio of T₁₃/T₁₈ ranges between 4.5 and 8.3, with an average value of 6.0 which is close to the terrestrial value. However, the ratio may be different in different regions, for example, in the Ophiuchus complex, the antenna temperatures of the three transitions are 6.7, 4.4, and 2.5 K for G003.73+18.30 and 5.9, 4.4, and 1.4 K for G006.41+20.56. The ratio of T₁₃/T₁₈ is 1.8 and 3.1 for the two clumps, respectively, which is much less than 5.5, suggesting that the ¹³CO lines are optically thick. For all the detected components, the histograms of T₁₂ and the ratios of T₁₂/T₁₃ and T₁₃/T₁₈ are present in Figures 3(a)–(c), respectively. The peak of T₁₂ is around 3 K. For the ratio of T₁₂/T₁₃, the mean value is 2.2 with a standard deviation of 1.4, showing that the ¹²CO (1–0) line emissions of the cold clumps are generally optically thick. The mean value of the ratio of T₁₃/T₁₈ is 3.9 with a standard deviation of 1.7.

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We found that all the distributions of the observed parameters as well as the derived parameters seemed to skew to the right with a long tail at the high value side. We try to depict their distributions with a lognormal distribution. The probability density function (PDF) of a lognormal distribution is

$$\begin{equation} f_{X}(x;\mu,\sigma)=\frac{1}{x\sigma ({2\pi })^{1/2}}e^{-\frac{(\ln x-\mu)^{2}}{2\sigma ^{2}}},\quad x>0, \end{equation} \tag{ 1 }$$

where x is the value of the variable, the parameters μ and σ are the mean and standard deviation, respectively, of the variable's natural logarithm. The Kolmogorov-Smirnov test (K-S test) is applied to identify whether the parameters follow a lognormal distribution. The decision to reject or accept the null hypothesis is based on comparing the P-value with the desired significance level, which is 0.05 in this paper. If the P-values from the K-S test are larger than 0.05, the parameter should follow the reference distribution. The statistics and K-S test results of the parameters are summarized in Table 7.

Table 7. A Statistical Analysis of Parameters

Stat	V12 − V13	V13 − V18	T12	T12/ T13	T13/ T18	FWHM(12)	FWHM(13)	FWHM(18)	$N_{{\rm H}_{2}}$	Tex	τ(13)	X13/X18	σNT	σTherm	σ3D	σNT/σTherm
	(km s−1)	(km s−1)	(K)			(km s−1)	(km s−1)	(km s−1)	(1021 cm−2)	(K)			(km s−1)	(km s−1)	(km s−1)
Statistics
Numbera	782	437	904	782	437	904	782	437	782	782	782	437	782	782	782	782
Mean	0.02	0	3.08	2.15	3.88	2.03	1.27	0.76	4.4	10.1	0.93	7.0	0.53	0.17	0.98	3.09
std	0.29	0.16	1.37	1.35	1.71	1.28	0.77	0.73	3.6	2.6	0.56	3.8	0.31	0.02	0.51	1.83
	Normal distribution fit		Lognormal distribution fit
μ	0.02	0	1.02	0.65	1.26	0.56	0.10	−0.44	1.22	2.29	−0.24	1.83	−0.77	−1.76	−0.12	0.99
σ	0.29	0.16	0.48	0.43	0.45	0.55	0.51	0.53	0.78	0.24	0.62	0.46	0.51	−0.12	0.43	0.53
P	0	0	0	0	0.234	0.636	0.830	0.515	0	0.227	0	0.388	0.889	0.227	0.374	0.822

Notes. ^aOnly the parameters of ¹³CO components are analyzed, but we also include those ¹²CO components without ¹³CO emission in statistics of T₁₂ and FWHM(12). Thirty-nine clumps without suitable reference positions in observations are excluded in statistics.

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The distributions of T₁₂ and T₁₂/T₁₃ have a similar characteristic. Both have a power-law-like long tail, but cannot be described well with a lognormal distribution. The tail of the distribution of T₁₃/T₁₈ is less than those of T₁₂ and T₁₂/T₁₃, suggesting that T₁₂ may be a more sensitive physical element than T₁₃ and T₁₈ for star formation. The distribution of T₁₃/T₁₈ has a lognormal shape with a P-value for the K-S test as high as 0.234.

From Table 3 one can see that the line widths of the emission components are generally narrow. Most of the clumps have line widths smaller than 1.3 km s⁻¹. There are 162 high-mass clump candidates; among these, 68 have 2 or more velocity components. The clumps at high latitude all are low-mass clump candidates with a single component except for G159.23−34.49, which is in the high-mass group and has two components. Figure 4(a) presents the distributions of the FWHM of all three lines: the mean values and the standard deviations of the three line widths are 2.0 ± 1.3, 1.3 ± 0.8, and 0.8 ± 0.7 km s⁻¹, respectively. The shapes of all the distributions are similar to each other and are lognormally distributed.

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The excitation temperature derived from the radiation transfer equation is

$$\begin{eqnarray} T_{r}&=& \frac{T_{a}^{*}}{\eta _{b}}=\frac{h\nu }{k}\left[\frac{1}{\exp (h\nu /kT_{{\rm ex}})-1}-\frac{1}{\exp (h\nu /kT_{bg})-1}\right]\nonumber \\ \ms && \times [1-\exp (-\tau)]f. \end{eqnarray} \tag{ 2 }$$

Here, T_r is the brightness temperature corrected with beam efficiency η_b. Assuming ¹²CO emission is optically thick (τ ≫ 1) and a filling factor of f = 1, the excitation temperature T_ex can be straightforwardly obtained. The T_ex is given in Column 6 of Table 4. We assume that the excitation temperatures of ¹³CO and C¹⁸O are the same as that of the ¹²CO (1–0) in the following analysis. The values range from 3.9 K to 27 K, wider than the dust temperature range 7–17 K (Planck Collaboration et al. 2011a). The mean value with the standard deviation is 10 ± 2.6 K, which is smaller than the mean value of the dust temperature (12.8 ± 1.6 K) based on aperture photometry with a local background subtraction by Herschel photometric observations toward 71 Planck cold fields (Juvela et al. 2012), indicating the gas may be heated by the dust. There are 12 clumps with T_ex > 17 K. All of the hottest clumps are located in the Orion and Taurus regions, which suggests that high excitation temperature may be related to star formation conditions. Ninety-three components with T_ex < 7 K are referred to as coldest clumps among which G093.66+04.66 (3.9 K) is in the first quadrant, and G098.10+15.83 (5.0 K) and G112.63+20.80 (5.8 K) are in Cepheus. All other coldest clumps are the weaker components of the clumps with double or three emission components. The T_ex histogram and its lognormal fit are shown in Figure 5. Its distribution can be well fitted by a lognormal shape with a P-value of the K-S test as large as 0.227, but the tail of the distribution seems to be much smaller than that of line widths and velocity dispersions. In the following analysis T_ex was taken as the gas kinetic temperature assuming the local thermodynamic equilibrium (LTE) holds.

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Both the optical depths τ₁₃ and τ₁₈ at the emission peak of the corresponding lines were calculated with Equation (2) assuming the filling factor f = 1; these are listed in Columns 7 and 9 in Table 4. τ₁₃ ranges from 0.1 to 4.1. The clumps with the largest τ₁₃ include G026.45−08.02 (3.2) and G058.07+03.29 (3.2) of the first quadrant, G164.94−08.57 (4.1) and G179.10−06.27 (3.9) in Taurus, and G182.04+00.41 (3.8) located at anticenter. For the 10 clumps with the smallest optical depth (0.1), all of them are the minor components of the multiple-component sources except for G121.88−08.76. Figure 6(a) shows the histogram of τ₁₃ and its lognormal fitting. The mean value is 0.93  ±  0.56.

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The column density of a molecular line can be obtained with the theory of radiation transfer and molecular excitation as follows (Garden et al. 1991):

$$\begin{eqnarray} N &=& \frac{3k}{8\pi ^{3}B\mu ^{2}}\frac{\exp [hBJ(J+1)/kT_{{\rm ex}}]}{(J+1)} \nonumber \\ && \times \frac{(T_{{\rm ex}}+hB/3k)}{[1-\exp (-h\nu /kT_{{\rm ex}})]}\int \tau _{V}dV, \end{eqnarray} \tag{ 3 }$$

where B, μ, and J are the rotational constant, the permanent dipole moment, and the rotational quantum number of the lower state of the molecular transition. Column densities of the ¹³CO and C¹⁸O molecules were calculated and given in Columns 8 and 10 of Table 4. The maximum C¹⁸O column densities of the Planck clumps are 1.1 × 10¹⁶ cm⁻² and 1.3 × 10¹⁵ cm⁻² in G028.56−00.24 and G160.51−16.84, respectively, and the smallest ones are 1.0 × 10¹⁴ cm⁻² in G26.93−20.68 and G102.72−25.96. The column densities of the C¹⁸O span a wider range than those of the nearby dark clouds (Myers et al. 1983) which are from 3 × 10¹⁴ to 2.7 × 10¹⁵ cm⁻². The different column density ranges between our sample and the nearby dark clouds may be attributed to the larger space distribution of Planck cold clumps than the nearby dark clouds.

The ¹³CO column densities were calculated for 782 velocity components. For the 437 components with both C¹⁸O and ¹³CO column densities, the abundance ratio of X₁₃/X₁₈ was calculated and listed in Column 13 of Table 4. The histogram and the lognormal distribution of X₁₃/X₁₈ fitting are presented in Figure 6(b). The distribution shape of the ratio X₁₃/X₁₈ is similar to that of τ₁₃. The mean value of X₁₃/X₁₈ is 7.0 ± 3.8, higher than that of the terrestrial ratio 5.5. The distribution of X₁₃/X₁₈ can be well depicted by a lognormal distribution with a P-value of the K-S test as high as 0.388.

Molecular hydrogen column densities of each velocity component were derived according to the column densities of the ¹³CO. The fractional abundance of [H₂]/[¹³CO] = 89 × 10⁴ was adopted. We also calculated the $N_{{\rm H}_{2}}$ for the components without ¹³CO emission by assuming ¹²CO (1–0) emission to be optically thin, the excitation temperature of 10 K and [H₂]/[¹²CO] = 10⁴, but these components are excluded in further statistics. Figure 6(c) presents the plots of the $N_{{\rm H}_{2}}$ histogram and its lognormal fitting. It spans from 10²⁰ to 4.5 × 10²² cm⁻², which is larger than that of the eight sources on average (Planck Collaboration et al. 2011b). From Herschel follow-up observations, the peak column densities of 71 clumps range from 4 × 10²⁰ to 7.4 × 10²² (Juvela et al. 2012), which are slightly larger than the column densities obtained in this work. The four clumps with the largest ¹³CO column densities are G209.28−19.62, G028.56−00.24, G033.70−00.01, and G158.37−20.72. The $N_{{\rm H}_{2}}$ of G209.28−19.62 located in the Orion complex is as high as 4.5 × 10²² cm⁻². G028.56−00.24 and G033.70−00.01, with $N_{{\rm H}_{2}}$ of 3.4 and 2.8 × 10²² cm⁻², are located in the first quadrant. G158.37−20.72, with $N_{{\rm H}_{2}}$ of 2.3 × 10²² cm⁻², is in Taurus, which is 7' north of NGC 1333 (Strom et al. 1976) and has a very red young star, SSV 13 (Harvey et al. 1998). The ¹²CO lines of all these clumps have large line widths of 2.57–9.35 km s⁻¹, showing turbulence support for these clumps. The column density distribution (Figure 6(c)) cannot be fitted with a unique lognormal distribution, but exhibits a power-law-like tail, similar to that identified from active star formation regions (Kainulainen et al. 2009), indicating that some Planck cold clumps are located in active star-forming regions.

The one-dimensional nonthermal (σ_NT) and thermal (σ_Therm) velocity dispersions can be estimated as follows:

$$\begin{equation} \sigma _{{\rm NT}} = \left[\sigma _{^{13}{\rm CO}}^{2}-\frac{kT_{{\rm ex}}}{m_{^{13}{\rm CO}}}\right]^{\frac{1}{2}} \end{equation} \tag{ 4 }$$

$$\begin{equation} \sigma _{{\rm Therm}} = \left[\frac{kT_{{\rm ex}}}{m_{{\rm H}}\mu }\right]^{\frac{1}{2}}, \end{equation} \tag{ 5 }$$

where $\sigma _{^{13}{\rm CO}}=({\Delta V_{13}}/{8\ln (2)})$ and T_ex are the one-dimensional velocity dispersion of the ¹³CO (1–0) and excitation temperature, respectively. k is the Boltzmann's constant, $m_{^{13}{\rm CO}}$ is the mass of ¹³CO, m_H is the mass of atomic hydrogen, and μ = 2.72 is the mean molecular weight of the gas. Then the 3D velocity dispersion σ_3D can be estimated as

$$\begin{equation} \sigma _{{\rm 3D}} = \big({3\big(\sigma _{{\rm Therm}}^{2}+\sigma _{{\rm NT}}^{2}\big)} \big)^{1/2}. \end{equation} \tag{ 6 }$$

The 3D and nonthermal velocity dispersions shown in Figures 4(b) and (c) also present a similar distribution as line widths. As shown in Table 7, the P-values of the K-S test for a lognormal hypothesis for line widths and velocity dispersions are all much larger than 0.05, indicating that their distributions can be remarkably well described by a lognormal fit. The lognormal behaviors of volume or column density in molecular clouds were frequently reported in recent observations (Ridge et al. 2006; Froebrich et al. 2007; Goodman et al. 2009), which are often interpreted as a consequence of supersonic turbulence in the observed clouds (Vázquez-Semadeni 1994). From our results, the effect of supersonic turbulence in the clouds should be more likely reflected in the lognormal behaviors of the distributions of line widths and velocity dispersions than in the distributions of column density. Figure 4(d) plots the distribution for the ratios of σ_NT to σ_Therm. One can see that most of the clumps have σ_NT larger than σ_Therm, indicating that turbulent motions dominate in these clouds. The shape of their ratio distribution is similar to the distributions of the FWHM of the three transitions, the σ_3D and σ_NT, but the tail part is narrower than the others, which may suggest that the thermal motions may not be as sensitive as nonthermal motions for revealing star formation activity.

In the 10 mapped clumps, 12 velocity components were detected. Six of them have FWHMs of ¹³CO (1–0) larger than 1.3 km s⁻¹ and the other four belong to group L. The CO line profiles of the clump G089.64−06.59, one of the velocity components of G157.60−12.17, G179.29+04.20, and G196.21−15.50, show a blue asymmetric signature. The integrated intensities are shown in the contour maps in Figure 7. The morphologies of these clumps are different. G001.38+20.94 and G180.92+04.53 show both diffuse features and a dense clump. G108.85−00.80, G157.60−12.17b, and G196.21−15.50 exhibit a filamentary shape with a chain of dense clumps. G161.43−35.59 and G194.80−03.41 also appear as a dumbbell in filamentary structure. Four cores are detected in G006.96+00.89a and G161.43−35.59, respectively. G049.06−04.18 is an isolate clump while G089.64−06.59 shows a cometary-like structure. Filamentary structures are the majority among these clumps, which is consistent with the Herschel follow-up observation results (Juvela et al. 2012). Juvela et al. (2012) also found that the filaments often fragment into substructures. Such behavior is revealed in the gas emission too as in G006.96+00.89a shown in Figure 7.

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There are 22 cores identified with two-dimensional Gaussian fits to the 10 mapped sources. The physical parameters of these cores are presented in Table 8. The positions of the cores are shown as offset relative to the reference positions in Column 4. Deconvolved sizes a and b (Column 5) are the major and minor angular sizes of the cores and measured from the contours at half of the maximum intensity of the ¹³CO (1–0) lines. The radius R = ((ab)^1/2/2)D, where D is the distance, in Column 6 distributes from several tenths to about 3 of kpc. Columns 7–12 list the clump parameters: T_ex, $N_{{\rm H}_{2}}$, velocity dispersions, and volume density $n_{{\rm H}_{2}}=N_{{\rm H}_{2}}$/2R, respectively. Then the core mass can be derived as $M=({4}/{3})\pi \cdot R^{3}\cdot n_{{\rm H}_{2}}\cdot m_{{\rm H}_{2}}\cdot \mu _{g}$, where $m_{{\rm H}_{2}}$ is the mass of a hydrogen molecule and μ_g = 1.36 is the mean atomic weight of the gas. Core mass calculated with LTE assumption is given in Column 13. Columns 14 and 15 are the virial mass and the Jeans mass, respectively (see the next section). The final three columns are the morphology, the group, and the location of the clumps. The column density of the cores ranges from 1.3 to 7.7 × 10²¹ cm⁻². The LTE masses of the cores range from 9 to 1.5 × 10⁴ M_☉ with a median value of 110 M_☉. In the Herschel follow-up observations, the 26 identified filaments have column densities ranging from 0.9 to 19.2 × 10²¹ cm⁻² and masses ranging from 3.2 × 10³ with a median value of 120 M_☉ (Juvela et al. 2012), which are consistent with the case of the cores in this work.

Table 8. Parameters of the 10 Mapped Clumps

Name	Vlsr	d	Offset	Deconvolved Size	R	Tex	$N_{{\rm H}_{2}}$	σTherm	σNT	σ3D	n	MLTE	Mvir	MJ	Group	Region
	(km s−1)	(kpc)	('', '')	('' × ''(°))	(pc)	(K)	(1021 cm−2)	(km s−1)	(km s−1)	(km s−1)	(103 cm−3)	(M☉)	(M☉)	(M☉)
G001.38+20.94	0.74	1.1	(−110,−41)	677 × 428(67.9)	1.4	14.1(0.9)	5.3(1.7)	0.21(0.01)	0.33(0.09)	0.67(0.13)	0.6	751	150	43	L	Ophiuchus
G006.96+00.89a_1	9.33	2.21	(5,−91)	187 × 119(−8.1)	0.8	9.9(0.4)	3.2(0.7)	0.17(0.00)	0.88(0.19)	1.56(0.32)	0.6	141	453	496	H	Fourth quad
G006.96+00.89a_2	9.33	2.21	(−90,30)	149 × 102(−42.5)	0.7	9.7(0.5)	2.6(0.9)	0.17(0.00)	0.70(0.20)	1.25(0.34)	0.6	78	240	260		Fourth quad
G006.96+00.89a_3	9.33	2.21	(−207,39)	301 × 64(−70.9)	0.7	9.4(0.3)	3.2(1.0)	0.17(0.00)	0.92(0.01)	1.61(0.17)	0.7	122	449	544		Fourth quad
G006.96+00.89a_4	9.33	2.21	(−334,66)	268 × 143(89.1)	1.0	8.9(0.7)	2.7(0.7)	0.16(0.01)	1.02(0.30)	1.79(0.51)	0.4	204	783	945		Fourth quad
G006.96+00.89b	41.67	5.36	(−64,−1)	203 × 161(38.2)	2.3	10.7(1.1)	6.8(2.6)	0.18(0.01)	1.52(0.22)	2.66(0.37)	0.5	2579	3873	2905	H	Fourth quad
G049.06−04.18	9.93	0.6	(16,41)	239 × 194(−51.9)	0.3	8.9(1.2)	1.3(0.5)	0.16(0.01)	0.15(0.04)	0.39(0.05)	0.7	9	11	7	L	First quad
G089.64−06.59	12.51	0.6	(81,−20)	320 × 187(−0.9)	0.4	10.2(0.9)	3.4(1.5)	0.18(0.01)	0.40(0.09)	0.74(0.15)	1.5	30	45	38	L	First quad
G108.85−00.80	−49.51	5.4	(−20,−12)	776 × 213(45.1)	5.3	11.5(3.7)	7.7(5.4)	0.18(0.03)	0.89(0.28)	1.58(0.46)	0.2	14993	3096	858	H	Second quad
G157.60−12.17a	−7.75	1.17	(−38,−44)	432 × 283(16.4)	1.0	10.4(0.9)	3.6(1.2)	0.18(0.01)	0.40(0.01)	0.76(0.12)	0.6	243	133	61	L	Taurus
G157.60−12.17b_1	−2.58	0.47	(−83,−63)	535 × 421(41.7)	0.5	14.7(1.6)	4.1(1.5)	0.21(0.01)	0.43(0.11)	0.83(0.17)	1.2	82	87	55	L	Taurus
G157.60−12.17b_2	−2.58	0.47	(−197,−278)	301 × 196(52.2)	0.3	14.6(1.3)	4.1(1.4)	0.21(0.01)	0.60(0.13)	1.11(0.21)	2.4	22	79	92		Taurus
G161.43−35.59_1	−5.83	1.49	(60,212)	269 × 143(−12.5)	0.7	9.8(0.4)	2.3(0.5)	0.17(0.00)	0.29(0.06)	0.59(0.09)	0.5	79	57	29	L	High Glat
G161.43−35.59_2	−5.83	1.49	(−3,−49)	261 × 150(82)	0.7	12.0(1.2)	2.6(0.8)	0.19(0.01)	0.18(0.03)	0.46(0.04)	0.6	91	35	13		High Glat
G161.43−35.59_3	−5.83	1.49	(−166,−71)	387 × 168(87.6)	0.9	10.5(0.9)	2.2(0.5)	0.18(0.01)	0.20(0.03)	0.47(0.04)	0.4	128	47	17		High Glat
G161.43−35.59_4	−5.83	1.49	(−303,−86)	141 × 140(−21.1)	0.5	10.7(0.9)	1.9(0.6)	0.18(0.01)	0.25(0.06)	0.53(0.09)	0.6	34	33	21		High Glat
G180.92+04.53	0.98	3.62	(0,−12)	359 × 339(62.2)	3.1	9.1(0.6)	3.4(1.1)	0.17(0.01)	0.59(0.11)	1.07(0.19)	0.2	2191	817	303	H	Third quad
G194.80−03.41_1	12.84	2.89	(−4,−19)	690 × 341(81.3)	3.4	9.8(0.5)	4.5(1.7)	0.18(0.01)	0.86(0.31)	1.52(0.52)	0.2	3573	1829	812	H	Third quad
G194.80−03.41_2	12.84	2.89	(−132,331)	355 × 242(61.3)	2.1	10.3(0.9)	5.3(2.4)	0.17(0.01)	0.78(0.20)	1.28(0.34)	0.4	1536	784	436		Third quad
G196.21−15.50_1	3.76	0.8	(−79,5)	276 × 203(54.2)	0.5	14.5(0.8)	3.1(0.9)	0.21(0.01)	0.32(0.12)	0.68(0.16)	1.1	45	49	30	H	Orion
G196.21−15.50_2	3.76	0.8	(104,126)	228 × 84(3.5)	0.3	15.1(0.8)	2.8(0.7)	0.21(0.01)	0.31(0.07)	0.65(0.11)	1.7	14	26	22		Orion
G196.21−15.50_3	3.76	0.8	(265,85)	256 × 89(60.8)	0.3	14.6(0.6)	2.5(0.9)	0.21(0.00)	0.30(0.12)	0.66(0.15)	1.4	15	30	23		Orion

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The coincidence of three transitions observed toward the Planck clumps is not usual in star formation regions. Line center velocities of different molecular species could be significantly offset from the systematic velocity in active star-forming regions. In the six NH₃ clumps of G084.81−01.09, the deviations between the ¹²CO and ¹³CO are all larger than 1 km s⁻¹ (Zhang et al. 2011). V_lsr of the ¹²CO deviated from that of ¹³CO or C¹⁸O are also seen in IRDCs. In 61 IRDCs, there are 10% of sources with V_lsr deviation of ≳ 1 km s⁻¹ from the ¹²CO and the C¹⁸O lines (Du & Yang 2008). The rather large discrepancy between the V_lsr of ¹²CO and ¹³CO can also be seen in the submillimeter clumps (Qin et al. 2008). The line center velocity difference of various molecular species may originate from molecular layers with different temperatures or trace different kinematical gas layers (Bergin et al. 1997; Muller et al. 2011). The deviation between V₁₃ and V₁₈ of the Planck clumps also tends to be smaller than those of Myers et al. (1983). All of these suggest that the cold clumps are the quietest molecular regions found so far as a whole.

Distance is essential for investigating the spatial distribution and physical conditions of the clumps. The Planck Collaboration et al. (2011d) have estimated the distance for 2619 C3PO clumps using various extinction signatures. They also found that there are 127 Planck cold clumps associated with IRDCs which have a kinematic distance from Simon et al. (2006). In our sample there are only two clumps close to the sources of Simon et al. (2006) at the zero latitude Galactic layer. There is certainly a part of the ECC clumps with distance estimated using extinction methods. We estimated the kinematic distances of the clumps using the V_lsr of the clumps which could be a comparison for those with known distance. We adopt the rotation curve of Clemens (1985) R_☉ = 8.5 kpc and Θ_☉ = 220 km s⁻¹ in our calculation. To see the possible physical relation of the components in clumps with double and triple peaks, the distance of each component was calculated. For the clumps within the inside of the solar circle there are two solutions. The clumps are perhaps located at the front of the Galactic bulk of the diffuse background, since extinction is rising along a line of sight that crosses a dust clump (Planck Collaboration et al. 2011a). For this reason, the near value of the distances was adopted. Among our sample there are a number of clumps that are located in molecular complexes with known distances. Since these complexes have rather large areas and clumps residing inside them have different V_lsr, the kinematic distances of the clumps within one complex are quite different as well. Therefore, for every clump within the same complex, their distances are also given as the kinematic distances. However, in a case where there is some ambiguity about the distance of the clump, the one close to the known distance of the complex was adopted.

The histogram of the kinematic distances is plotted in Figure 8. Distances were obtained for 741 ¹³CO components. Of the components, 51% have distances within 0.5 and 1.5 kpc. The mean value is 1.57 kpc, lower than those associated with IRDCs by Simon et al. (2006). The reason for this may be due to cloud properties; most of our clumps or components belong to the low-mass group and the IRDCs of Simon et al. (2006) are at the fourth quadrant of the mid-plane and with distances between 0.4 and 7.8 kpc (Simon et al. 2006).

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4.3.1. Excitation Temperature and the Ratio of Line Strengths of ¹²CO and ¹³CO

Figure 9 presents the distribution of the T_ex and the ratio of T₁₂/T₁₃. Figures 9(a) and (c) are for radial changes and (b) and (d) are for the altitude from the Galactic plane. The excitation temperature is higher than 10 K from 4 to 8 kpc. Early observations also showed the high excitation of the gas emission at the 3–7 kpc molecular ring (Scoville & Sanders 1987). Around 8 kpc, T_ex is also larger than 10 K, which may be related to the emission of the giant molecular clouds near the Sagittarius arm. The ratio of T₁₂ to T₁₃ is high at R ∼ 5 kpc, then deceases with R and has a valley between 5 and 8 kpc, then a lowest value at ∼6 kpc, suggesting that the brightness temperature of ¹³CO (1–0) is relatively high in this region.

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Figure 9(b) shows that excitation temperature changes with the altitude. There are two peaks 11 and 13 K at Z ∼ 350 pc and ∼470 pc, respectively. The changes of the ratio of T₁₂/T₁₃ shown in Figure 9(d) are rather smooth and reach a low value at Z ∼ 470 pc, suggesting the brightness temperature of ¹³CO is relatively high at this altitude.

4.3.2. Velocity Dispersion

Variations of the velocity dispersion with the distance from the Galactic center and the altitude from the Galactic plane are investigated. The radial variations of σ_3D, σ_NT, and the ratio of σ_NT/σ_Therm are plotted in Figures 10(a), (c), and (e), respectively. The variation of the σ_3D and σ_NT as well as the ratio of σ_NT/σ_Therm with R are about the same and they reached the maximum at R ∼ 5 kpc, which suggests that the dynamic process is most violent at the 5 kpc Galactic ring. From 6 kpc, the σ_3D, σ_NT, and the ratio of σ_NT/σ_Therm seem to linearly increase with R, indicating that turbulence becomes more violent in the outer part of the Galaxy.

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Figures 10(b), (d), and (f) present changes of the velocity dispersions σ_3D, σ_NT, and the ratio of σ_NT/σ_Therm with the altitude. One can see that they all decrease with increasing altitude from the Galactic disk to heights of 475–525 pc, showing that the turbulent process is stronger closer to the Galactic plane. At Z ∼ 680 pc all of them reached a minor peak. We found the clumps at this minor peak are distributed around (l ∼ 174°, b ∼ 17°) or (l ∼ 4°, b ∼ −17°); this minor peak may be concerned with the emission regions of Taurus and ρ Oph. From panels (e) and (f), one can see that nonthermal motion dominates the line broadening. This is the first time evidence for nonthermal line broadening has been obtained from a survey of the ¹³CO (1–0) lines.

One can see that there are some differences among the radial variations of the velocity dispersion and excitation temperature. The maximum of T_ex–R variation is at rather high values around 4–8 kpc and reaches maximum at 6 kpc. The T_ex variation is milder than that of σ_NT suggesting that the gas heating and cooling occur in a wider spatial region than the turbulence.

4.3.3. ¹³CO Opacity, X₁₃/X₁₈, and H₂ Column Density

Figure 11(a) shows the radial variation of the optical depth of the ¹³CO (1–0) lines. The smallest value is at the 5 kpc ring. Between 5.5 and 8 kpc there is a high feature, then it decreases until 14 kpc. One reason for the low valley is that T_ex is rather high around 5 kpc (see Figure 9(a)). Besides, its emission is relatively low compared with that of ¹²CO. For example, G017.22−01.47 at R = 4.90 kpc is τ₁₃ = 0.3, T_ex = 10.1 K, and T₁₃ = 0.88 K; G033.70−00.01, R = 5.05 kpc, τ₁₃ = 0.5, T_ex = 9.2 K, and T₁₃ = 1.12 K; and G028.56−00.24, R = 4.96 kpc, τ₁₃ = 0.3, T_ex = 10.1 K, and T₁₃ = 0.92 K.

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The ratio of X₁₃ to X₁₈ presented in Figure 11(c) is rather low, between 5 and 7 kpc, and its corresponding values range from ∼6 to 7, still higher than the terrestrial value. At 8 kpc and >10 kpc the value is near 8.

Figure 11(e) shows the radial variation of the column density of hydrogen molecules. Clearly, it presents an enhancement at 5 kpc where the densest and most massive star formation regions within our Galaxy are located. Then it is almost at a similar level until it reaches the outer region except at 9 kpc where there is a minor low valley. Owing to the small τ₁₃ around 5 kpc (see Figure 11(a)) the column density is mainly affected by the velocity dispersion σ_3D or σ_NT shown in Figure 10. To confirm the Galactic distribution of the column density, the radial distribution of the flux density at 857 GHz dust emission detected by Planck was plotted in Figure 11(g). The variations agree with that of the column density very well. At 9 kpc the 857 GHz flux is a little higher, showing another dense structure (Scoville & Sanders 1987).

The variation of τ₁₃ with altitude is shown in Figure 11(b). It exhibits a high feature between 350 and 550 pc and reaches its maximum at 450 pc. The change of the ratio of X₁₃/X₁₈ seen in Figure 11(d) seems to be opposite to that of τ₁₃ with its lowest point at Z = 450 pc. Figure 11(f) presents the variation of the molecular hydrogen column density with Z. At Z = 300 and 500 pc, the values are higher than in the other regions. There is a low valley at Z = 450. Combining the altitude variation of τ₁₃ and the velocity dispersion of Figures 10(b), (d), and (f) where σ_NT is at low values, again shows that nonthermal line width is the major factor in determining the gas column density. Between 350 and 550 pc the flux at 857 GHz is higher too, which is consistent with the variation of $N_{{\rm H}_{2}}$ as a whole. These results revealed that the column density reaches the maximum at R = 5 kpc, a low valley at Z = 450 pc, and is mainly caused by nonthermal velocity dispersion, which also has not been reported before.

4.3.4. Parameters of the Clumps in Different Molecular Complexes

There are 16 clumps having an absorption dip at the line center, which is rather symmetric relative to the V_lsr. Nine of them show a dip in all three transitions. They may be the candidates for the ¹²CO depletion. In the other seven clumps, only the ¹²CO line has the center dips that may originate from self-absorption. Mapping is needed to further examine the properties of the line center dips. Eighteen cores with blue profiles and fifteen cores with red profiles were identified (see Table 5). Blue profiles are a kind of typical feature of molecular clump collapse (Zhou et al. 1993) whereas the red profile could originate from the expansion of the clump or outflow motion. The ratios of the clump with the blue and red profiles to the total clump numbers of clumps are small—2.7% and 2.2%, respectively. The blue excess E = (N_b − N_r)/N_t is 0.004; here N_b, N_r, and N_t are the clump numbers with the detected blue and red profiles and the surveyed sample (Mardones et al. 1997). E of the Class -I, 0, and I clumps is 0.31, 0.30, and 0.30 shown in the HCN (3–2) line, respectively (Evans 2003), while it is 0.15–0.17 for UC H ii region precursors and 0.58 for UC H ii regions detected with HCO⁺(1–0) lines (Wu et al. 2007; Fuller et al. 2005). Nevertheless, in a sample of 27 Orion starless clumps, 9 have blue profiles and 10 have red ones, implying that the blue excess E is −0.04 (Velusamy et al. 2008). The ratios of the blue and red profiles to these cores are 33% and 37%, greatly exceeding those of our sample, suggesting that star formation activities occur more frequently in the Orion cores than in the Planck cold clumps. The small ratio of the blue and red profiles means that most of the Planck cold clumps do not yet have systematic star-forming motion. We also identified 19 and 13 cores with blue and red line asymmetry, respectively. Different from blue and red profiles, line asymmetry reflects the whole gas motion of the core, which may result in interaction of the core and its environment.

High velocity wings are rare in Planck cold clumps. Among the surveyed clumps, only three were detected with blue wings, six with red ones, eight with both blue and red wings, and six with a pedestal feature, showing rather rare star formation feedback activities.

There are 41 clumps located at latitudes higher than 25°. Six clumps have two velocity components and one has three. Nine of the clumps belong to the high-mass group. T_ex is intermediate among the 12 complexes (see Table 2). The column density is 3 × 10²¹ cm⁻² on average. σ_NT tends to be smaller among the 12 complexes but still larger than those in the Ophiechs and Oph-Sgr. Core G089.03−41.28 has a blue profile while cores G182.54−25.34 and G210.67−36.77 have a red profile. Their altitudes are 2.4, 0.64, and 0.15 kpc, respectively, showing that star formation signatures also exist in clumps at high latitudes. Here the kinematic distance was adopted.

Since the diffuse emission was found over the whole Galactic sky (Hauser et al. 1984), many high-latitude clouds such as infrared cirrus were also detected (Low et al. 1984). Heithausen et al. (1993) made a survey for 16° ⩽ b ⩽ 44°, 117° ⩽ l ⩽ 160° in the second quadrant. They found that clouds with CO emission are 13% of the survey sample. Yamamoto et al. (2003) also carried out a CO survey toward the MBM 53, 54, and 55 complex, which are within the latitude −30°–(43°). They identified 110 ¹²CO clouds with a total mass of 1200 M_☉, in which all of the clouds are not dense enough to form stars. The conditions of our 41 Planck samples are closer to star-forming states. Additionally, the latitudes of the Planck clumps exceed those of the above samples. These results suggest that the ECC clumps are a good guide for investigating initial conditions or searching for star formation.

The different morphologies of the contour maps of the 10 mapped clumps show that the Planck clumps contain a rather long evolution stage, which includes diffuse and elongated regions, a filament structure or cometary shape, multiple cores, and an isolated core.

Assuming that the core is a gravitationally bound isothermal sphere with uniform density and is supported solely by random motions, the virial mass M_vir can be calculated following Ungerechts et al. (2000):

$$\begin{equation} \frac{M_{{\rm vir}}}{M_{\odot }}=2.10\times 10^{2}\left(\frac{R}{{\rm pc}}\right)\left(\frac{\Delta V}{{\rm km\,s^{-1}}}\right), \end{equation} \tag{ 7 }$$

where R is the radius of the clump and ΔV is the line width of the ¹³CO (1–0). The virial masses are listed in Column 14 of Table 8.

In molecular clouds, many factors including thermal pressure, turbulence, and magnetic field support the gas against gravity collapse. The Jeans mass, which takes into account the thermal and turbulent support, can be expressed as (Hennebelle & Chabrier 2008)

$$\begin{equation} M_{J}\approx 1.0a_{J}\left(\frac{T_{{\rm eff}}}{10\,{\rm K}}\right)^{3/2}\left(\frac{\mu }{2.33}\right)^{-1/2}\left(\frac{n}{10^4\,{\rm cm^{-3}}}\right)^{-1/2}\,M_{\odot }, \end{equation} \tag{ 8 }$$

where a_J is a dimensionless parameter of order unity which takes into account the geometrical factor, μ = 2.72 is the mean molecular weight, $n={N_{{\rm H}_{2}}}/{2R}$ is the volume density of H₂, and T_eff = (C²_{s, eff}μm_H/k) is the effective kinematic temperature. The effective sound speed C_{s, eff} including turbulent support can be calculated as

$$\begin{equation} C_{s,{\rm eff}}=[(\sigma _{{\rm NT}})^{2}+(\sigma _{{\rm Therm}})^{2}]^{1/2}. \end{equation} \tag{ 9 }$$

The calculated Jeans masses are listed in Column 15 of Table 8.

There are ten cores with M_LTE larger than M_vir and M_J, which may be under going collapse. There are also seven cores having an M_LTE that agrees with M_vir and M_J within a factor of three. Considering the uncertainties in mass estimation, these cores may be in magical states. The remaining cores seem to be gravitationally unstable. One should keep in mind that these 10 clumps are not a representative sample for the whole ECC, but include the morphologies of the majority of the Planck clumps. Most of the ECC clumps show diffuse molecular emission or harbor gravitationally stable dense cores (Liu et al. 2012).

The mapped clumps are noted individually as the following.

G001.38+20.94. This clump is located in ρ Oph. The gas emission is diffuse and it has a size >1 pc. The density is lower than 10³ cm⁻³ and the mass >750 M_☉. The excitation temperature is rather high (14 K). The average σ_3D is only 0.67 km s⁻¹. Actually, it is located at (0.5, −1.0) with respect to L43B, a mixture of isolated globules and complexes (Benson & Myers 1989). It may be in a transition between diffuse interstellar medium (ISM) and a dense molecular cloud.

G006.96+00.89. This clump is located in the fourth quadrant. Two velocity components with V_lsr 9.33 and 41.67 km s⁻¹ were detected in the clump and both have FWHMs larger than 1.3 km s⁻¹. The two velocity components have four and one cores, respectively. No astronomical object was found associated with this clump so far. G006.96+00.89a, with a 9.33 km s⁻¹ velocity component, appears to be elongated from SE to NW and has a chain of at least four clumps. The other component has an isolated clump near the mapping center, and the clumps are not very dense with n lower than 10³ cm⁻³.

G049.06−04.18. This is an isolated clump and located in the first quadrant. The mass calculated with LTE is close to the Jeans and virial masses. It has been identified as CB 198 and contains IRAS 19342+1213 (J2000 = 19 36 37.8 +12 19 59) located at (8'', 43'') of the clump (Gómez et al. 2006).

G089.64−06.59. This is a clump in the first quadrant. Its gas clump tends to be cometary. The starless clump CB 232 AMM 1 is located at (20'', −36'') of the clump. It harbors an infrared source, IRAS 21352+4307 (Huard et al. 1999). At about 15'' eastern there is a near-infrared source, YC1-I. The LTE mass, Jeans mass, and virial mass all are close to each other.

G108.85−00.80. This clump belongs to the second quadrant. There are no associated objects and no known cloud was found for this clump. It shows a filamentary structure and is compact. The ¹³CO (1–0) line width is 2.7 km s⁻¹ and it is a typical high-mass clump. The LTE mass is larger than both the Jeans and virial masses. It seems very likely to be in gravitational collapse.

G157.60−12.17. This clump is located in the Taurus complex and has two components belonging to the L group. Contours of their integrated intensity show that the first component is rather diffuse and the second one contains two cores. TGU 1064 is located at 65'' east and south (Dobashi et al. 2005).

G161.43−35.59. This is a high-latitude clump and belongs to the L group. It contains at least four cores. No associated object was found.

G180.92+04.53. This is at the side of the anticenter of the Galaxy and belongs to the H group.

G194.80−03.41. The dumbbell gas emission region elongates in the northwest direction. Two large clumps are connected and each contains at least two cores. There was no associated object found. All the cores should be starless. The clump masses are all larger than the corresponding Jeans and virial masses, suggesting that they are at the gravitational bound states. TGU H1364 P8 is about 2' away (Dobashi et al. 2005).

G196.2−15.5. This clump has a blue asymmetry line (see Table 6). It is associated with L1595 and a reflection nebula VDB 40 (Maddalena et al. 1986). Three cores were found in this filamentary structure. All belong to the group L. Except for the M_J < M_LTE for core 1, M_LTE is less than M_J and M_vir, but all these masses are close to each other.

The morphology, structure, and physical parameters of the small set of 10 mapped clumps show that Planck cold clumps cover different phases that may be (1) a transition phase from diffuse ISM to cloud, (2) a state close to gravitationally bound, (3) an isolated clump or multiple clumps, (4) starless clumps, and (5) a state that harbors infrared sources. Among the 10 clumps, 4 are in a filamentary or elongated shape which shows that filamentary clumps may be the majority in C3PO clumps. In total, 22 cores were found and 20 of these are starless.

The clump kinetic temperature ranges from 4 to 27 K, wider than that of dust temperatures (7–17 K; Planck Collaboration et al. 2011a). However, there are only 12 clumps with T_k > 17 K. The ∼98% of the clumps have T_k ⩽ 17 K, showing that both the dust and gas are cold and couple well. Figure 12(a) shows a comparison of the T_d and T_k. Most of the clumps have T_d > T_k, indicating that gas could be heated by dust (Goldreich & Kwan 1974). For clumps with T_d < T_k, the gas may be due to ongoing protostellar process. For example, for the 27 clumps with T_k > 16 K > T_d, 6 are in or close to Ophiuchs, 8 in Taurus, and 10 in Orion, may be due to an ongoing protostellar process. The column densities deduced from dust emission and CO lines were plotted in Figure 12(b). One can see that the range of the values from dust is about three orders in total and that from CO lines is about 2.5 orders, slightly narrower. However, both the column densities concentrate on 10²¹–10²² cm⁻². According to Hartquist & Williams (1998), such column density is just about the critical value of the cloud collapse.

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To investigate the physical conditions and examine the possibility of stars forming in the cold clumps, we compare the line widths of ¹³CO (1–0) and column densities with the following CO molecular line surveys toward different kind of targets.

• 1.  
  Methanol maser sources (Liu et al. 2010),
• 2.  
  Candidates of a UC H ii region chosen with the IRAS color index and flux limit (Wu et al. 2001; Wood & Churchwell 1989),
• 3.  
  Candidates of extremely young stellar objects chosen with a redder color IRAS index and smaller flux density than those of UC H ii regions (Wang et al. 2009),
• 4.  
  IRDCs (Simon et al. 2006), and
• 5.  
  Extended green objects (EGOs) identified from the Spitzer GLIMPSE survey (Chen et al. 2010).

Figure 13(a) plots a cumulative fraction of the FWHM of ¹³CO (1–0). It shows that the methanol maser sources have the largest FWHMs and the smallest slopes. The IRDCs and EGOs have a shape similar to the methanol maser sources but with slightly larger slopes. When the FWHM is less than 3 km s⁻¹, the slope of IRDCs is almost the same as those of the UC H ii candidates and the redder, weaker IRAS sources. When the FWHM becomes larger than 3 km s⁻¹, the changes of the UC H ii candidates and the redder, weaker IRAS sources are much steeper than IRDCs, EGOs, and the methanol maser sources. The slope of the fraction of the redder, weaker IRAS is large and its maximum value is at 6 km s⁻¹. The variation of the cumulative fraction function of FWHM for the Planck cold clumps is the narrowest. The FWHM of the Planck cold clumps are the smallest compared with the other samples. For all the samples used in the comparison with Planck cold clumps, their FWHMs are almost larger than 2 km s⁻¹ while the cumulative fraction at FWHM > 2 km s⁻¹ of the cold clumps is less than 10%.

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The comparison of column densities for the samples of (1), (3), (4), and (5) is presented in Figure 13(b). The cumulative fraction distribution also produces the smallest column density range for the Planck cold clumps. IRDCs have nearly the same shape as Planck cold clumps when the column density is below 10²¹ cm⁻², but are similar to the redder, weaker IRAS sources at high densities, indicating that IRDCs may be at a transition phase between Planck cold clumps and redder, weaker IRAS sources. The methanal maser sources and EGOs have the largest column densities, indicating active star formations in them.

These results show that the Planck cold clumps are quiescent and have the smallest column densities among these star formation samples on the whole. Most of them seem to be in transition from clouds to dense clumps.