A Statistical Study of Massive Cluster-forming Clumps

Tomomi Shimoikura; Kazuhito Dobashi; Fumitaka Nakamura; Tomoaki Matsumoto; Tomoya Hirota

doi:10.3847/1538-4357/aaaccd

1. Introduction

Young clusters with ages of a few Myr are deeply embedded in their natal molecular clumps. These clusters can be easily identified in near-infrared images, and we call such young clusters IR clusters. Although it is well known that stars are often born in clusters (e.g., Lada & Lada 2003; Gutermuth et al. 2009), the formation and evolution processes of clusters still remain unclear. Observational studies of IR clusters and their natal clumps provide a key to understanding the formation and evolution of clusters and their environments.

Cluster-forming clumps tend to exhibit complex velocity structures with multiple velocity components. Several hypotheses have been proposed to explain the velocity fields of cluster-forming clumps. For example, it is possible that the clumps can be affected by an expanding H ii region (e.g., Shimoikura et al. 2015) or by collisions of smaller clumps and/or filaments (e.g., Higuchi et al. 2009; Dobashi et al. 2014). Peretto et al. (2006, 2007) found two velocity components in the massive cluster-forming clump NGC 2264C, for which they suggested a large-scale collapsing motion of the clump. Similarly, we investigated the velocity structure of the cluster-forming clump S235AB, and found that the entire clump is infalling with rotation toward the clump center where the most massive star in the cluster is forming (Shimoikura et al. 2016).

How do the velocity structures of the natal clumps evolve along with the cluster formation? Considering the results we obtained for the clump S235AB (Shimoikura et al. 2016), we would expect that the clumps forming IR clusters should experience the clump-scale infalling motion with rotation in an early stage of cluster formation. In order to confirm if such a dynamical infall is a common phenomenon for the cluster-forming clumps, we need to carry out a statistical study with a rich sample of massive clumps with young clusters.

We also note the fact that there is a large variation in morphologies of the IR clusters and their natal clumps, which is believed to represent various evolutionary stages of cluster formation (e.g., Lada & Lada 2003). However, the quantitative relationships between the properties of clusters (e.g., age, size, number of constituent stars) and their natal clumps (e.g., mass, density, and velocity dispersion) still remain unclear. The relationships should change along with the evolution time, but it is generally difficult to assess the absolute ages of the natal clumps. There are, however, some molecules (e.g., CCS) for which the time variations of the abundances have been calculated (e.g., Suzuki et al. 1992), and they can be used as a measure of the clump ages. In order to study the relationships between the clusters and natal clumps, it is therefore very important to investigate systematically not only the physical properties but also the chemical compositions of the clumps.

In this study, we conducted systematic observations of 15 dust condensations selected from a catalog of dust condensations compiled by Dobashi (2011). We used the NRO 45 m telescope to observe the dust condensations with different tracers.

In the C¹⁸O data from the 45 m telescope, the condensations can be divided into smaller clumps. In one of the clumps named S235AB corresponding to No. 4423 in the 15 dust condensations, we detected the global infalling motion with rotation as noted previously. We show the results for S235AB in detail in a separate paper (Shimoikura et al. 2016). In this paper, we present the results for all of the clumps we identified.

Our primary goals in this paper are (i) to find differences between the clumps with and without IR clusters and to investigate how and under what physical conditions the cluster formation can occur, mainly by using the C¹⁸O data as a tracer of kinematics, and (ii) to infer the evolutionary stages of the clumps by comparing the abundances of CCS and HC₃N, as well as those of CS and SO. Since the CCS emission has been detected only in dark clouds (e.g., Nakamura et al. 2014) but not in active cluster-forming clumps (e.g., Lai & Crutcher 2000; Shimoikura et al. 2015), we are particularly interested in carrying out a CCS survey for our targets.

This paper is organized as follows. In Section 2, we describe the targets selected for the observations. We also describe our observations using the 45 m radio telescope. We identify 24 molecular clumps using the C¹⁸O (J = 1–0) data and derive their physical properties in Section 3. We analyze the chemical compositions and velocity structures of the clumps, and discuss how the clumps should evolve in Section 4. We present the summary of this paper in Section 5.

2. Observations

2.1. The Target Dust Condensations

Based on the catalog of dust condensations of Dobashi (2011) and Dobashi et al. (2013), we selected 15 dust condensations. Extinction maps of the 15 dust condensations selected for this study are shown in Figure 1. Numbers in the figure correspond to the condensation numbers given by Dobashi (2011). Except for No. 4678, the dust condensations we selected for the observations are regarded to include IR clusters by Dobashi (2011, and assigned Flag "3" in their catalog)—that is, the dust condensations appear as a "hole" in the A_J map due to the increase of star density compared to adjacent regions, but as a "bump" in the E(J–H) map because of the intrinsically red colors of young stars. We selected the 15 dust condensations from various star-forming regions within 2.4 kpc from the Sun. Except for No. 4398,⁵ the distances to the condensations were obtained from the literature. We selected relatively massive condensations observable from Nobeyama with a mass of greater than 100 M_☉, except for No. 4059 (∼50 M_☉).⁶

**Figure 1.** Extinction (A_V) maps of the 15 dust condensations generated by Dobashi (2011) shown in the Galactic coordinates. Contours are drawn from 0.5 mag with an increment of 1.0 mag. Plus signs indicate the positions of the identified IR clusters (see Section 3.4).
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Ten of the dust condensations are associated with known IR clusters in active cluster-forming regions such as S201 and Mon R2 (e.g., Bica et al. 2003a, 2003b; Kirsanova et al. 2008). Typical ages of the IR clusters are 1–5 Myr. We also conducted our own analyses using the 2MASS Point Source Catalog (PSC) to reveal the star density distribution around the selected condensations, which is described in detail in Section 3.4. Based on the analyses, we found that the rest of the five dust condensations are not associated with any apparent IR clusters.

The selected dust condensations and their main characteristics are summarized in Table 1.

Table 1. List of Observed Dust Condensations

Dust Condensation No. (1)	IR cluster^a	Associated Objects	Distance (kpc)
3645	Y	S172	2.4 (2)
3890	Y	S190, AFGL333, IC1805-W, BRC5	2.0 (3)
3921	Y	S199, AFGL4029	2.1 (4)
3923	Y	S201	2.1 (4)
3935	⋯	⋯	0.9 (For S202 (2))
3937	⋯	⋯	0.9 (For S202 (2))
4054	Y	BFS32	0.6 (2)
4059	⋯	⋯	0.6 (For BFS52 (2))
4398	⋯	⋯	0.81^b
4417	Y	S235	1.56 (5)
4423	Y	S235A, B	1.56 (5)
4565	Y	BFS51	1.6 (6)
4678	⋯	⋯	1.0 (For S268 (2))
4753	Y	Mon OB1-D, NGC 2264C, NGC 2264D	0.738 (7)
4974	Y	Mon R2	0.893 (8)

Notes.

^aSee Table 8 for the references of the IR clusters. ^bFor No. 4398, we calculated the kinematic distance using the ¹³CO peak velocity obtained with the 45 m observations (V_LSR = −2.2 km s⁻¹). The distance is calculated using the Galactic rotation model of Kerr & Lynden-Bell (1986), Wouterloot & Brand (1989), and Wouterloot et al. (1990), assuming the distance of the Sun from Galactic Center R₀ = 8.5 kpc and the rotation speed of the Galaxy Θ₀ = 220 km s⁻¹ at R₀.

References. (1) Dobashi (2011), (2) Russeil (2003), (3) Xu et al. (2006), (4) Chauhan et al. (2011), (5) Burns et al. (2015), (6) Carpenter et al. (1990), (7) Kamezaki et al. (2014), (8) Dzib et al. (2016).

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2.2. Observations with the NRO 45 m Telescope

The mapping observations of the 15 dust condensations using the NRO 45 m telescope were carried out during two separate observing periods. All of the observations were performed in on-the-fly mode. The observed molecular lines and the resulting noise levels for each line are summarized in Table 2.

Table 2. NRO 45 m Observations

Molecule	Transition	Frequency	Beam	ΔT_mb
		(GHz)	(arcsec)	(K)
CCS	J_N = 4₃–3₂	45.379033	368	0.1–0.3
HC₃N	J = 5−4	45.490316	367	0.1–0.3
C³⁴S	J = 2–1	96.412950	173	0.3–0.6
CS	J = 2−1	97.980953	170	0.4–0.7
SO	J_N = 3₂–2₁	99.299905	168	0.3–0.6
C¹⁸O	J = 1–0	109.782176	152	0.4–0.8
¹³CO	J = 1–0	110.201354	151	0.5–0.9
¹²CO	J = 1–0	115.271202	145	1.2–1.8

Note. The rest frequency for the CCS line is taken from Yamamoto et al. (1990), and those of the other lines are taken from the website of Lovas (1992).

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2.2.1. Observations of ${}^{12}{CO},{}^{13}{CO}\,{C}^{18}O,SO,CS,$ and ${C}^{34}S$

Observations of the 15 dust condensations with six emission lines at 100 GHz (¹²CO, ¹³CO, C¹⁸O, SO, CS, and C³⁴S) were conducted for 10 days in 2013 February. The beam size of the telescope is ∼15'' at 110 GHz. The two-beam Superconductor-Insulator-Superconductor receiver TZ (Nakajima et al. 2013) was used as the front end, and the digital spectrometer SAM45 with 4096 channels covering a total bandwidth of 31 MHz and a velocity resolution of ∼0.02 km s⁻¹ was used as the back end. The overall system temperature (T_sys) typically ranged from 150 to 300 K.

During the first part of the observations, the receiver was tuned to the ¹²CO (J = 1–0) line, and ∼6' × 6' mapping observations centered on each of the dust condensations were performed along the equatorial coordinates to investigate the molecular distributions. Afterward, the receiver was tuned to the ¹³CO, C¹⁸O, SO, CS, and C³⁴S lines to perform simultaneous ∼5' × 5' mapping observations centered on the same peaks as those for the ¹²CO observations.

An ambient-temperature chopper wheel was employed to determine the antenna temperature scale. The telescope pointing for each region was checked every 1.5 hr using SiO maser sources at 43 GHz, ensuring that the pointing remained accurate within ∼3''. The sideband ratios of the receiver at the rest frequencies of the observed molecular lines were also checked every day to further calibrate the spectral data, which fluctuated within ∼10% each time the receiver was tuned. Calibration was also checked by taking the average spectra of the central 100'' × 100'' of the dust condensation No. 4423 for all of the molecular lines, confirming consistent calibration within 10% error.

The baselines of the spectral data were removed by fitting the emission-free velocity ranges with linear functions, and the data were converted into three-dimensional data with a spheroidal convolution at a angular grid size of 7 farcs 5 using the software package NOSTAR.

The data were then corrected for the main-beam efficiency of the telescope into the T_mb scale, for which main-beam efficiencies (η_mb) were assumed to be 0.27, 0.30, 0.30, 0.37, 0.38, and 0.39 for the ¹²CO, ¹³CO, C¹⁸O, SO, CS, and C³⁴S lines, respectively.

We finally obtained the spectral data with an effective angular resolution of approximately 22''–24'' and a velocity resolution of 0.05 km s⁻¹ for each emission line. The typical 1σ noise level in the ¹²CO spectra was ΔT_mb = 1.2 K, and ΔT_mb = 0.2–0.5 K for the other lines.

2.2.2. Observations of CCS and ${{HC}}_{3}N$

Observations of the 15 dust condensations were also carried out with the CCS and HC₃N emission lines at 45 GHz using the NRO 45 m telescope for 3 days in 2017 March. We obtained ∼5' × 5' maps for the 15 dust condensations in both of the lines simultaneously, covering the same areas as for the 100 GHz observations. The dual-polarization receiver Z45 (Nakamura et al. 2015) was used, which provided T_sys ≃ 160 K. Spectral data were obtained with the 4096 channels using the SAM45 spectrometer operating at a resolution of 0.1 km s⁻¹. At 45 GHz, the beam size of the telescope was ∼37'' and η_mb was 0.7.

The telescope pointing and data reduction were performed in the same manner used for the 100 GHz observations. We smoothed the obtained spectral data to an effective angular and velocity resolutions of ∼49'' and 0.2 km s⁻¹, respectively. The resulting 1σ noise level is ΔT_mb ≃ 0.2 K for these resolutions.

3. Results

3.1. Identification of Molecular Clumps and Estimation of Their Physical Properties

Figures 2–7 show integrated intensity maps of the molecular emission lines observed with the 45 m telescope. In the figures, only molecular lines significantly detected at the 3σ noise level are shown. It is seen that the C¹⁸O line was detected in all of the target regions, although some lines such as C³⁴S, CCS, and HC₃N were not detected in some of the dust condensations, especially in those without IR clusters (e.g., No. 4398 in Figure 5).

**Figure 2.** Maps of the integrated intensity of the observed molecular lines around the dust condensation No. 3645 obtained with the 45 m telescope, shown in the equatorial coordinates. Molecules, transitions, and the velocity ranges in units of km s⁻¹ used for the integration are indicated above the maps. The lowest contours and the contour intervals in units of K km s⁻¹ are indicated in the square brackets in each panel. No obvious CCS emission is detected in this dust condensation. The map resolution is indicated by the open circle in panels for the ¹³CO and HC₃N emission lines. The last panel on the lower right shows the star density map of the cluster 3645cl overlaid with the *WISE* 3.4 μm image (grayscale). The lowest contour and the contour interval in units of arcmin⁻² are indicated in the panel. The red dot denotes the position of the selected *IRAS* source.
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**Figure 3.** Same as Figure 2, but for the dust condensations Nos. 3890 and 3921.
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**Figure 4.** Same as Figure 2, but for the dust condensations Nos. 3923, 3935, 3937, 4054, and 4059. No obvious C³⁴S emission is detected in all of the dust condensations. No obvious IR cluster is seen in the dust condensations Nos. 3935, 3937, and 4059.
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**Figure 5.** Same as Figure 2, but for the dust condensations Nos. 4398, 4417, and 4423. No obvious SO, CS, C³⁴S emission or IR cluster are seen in the dust condensation No. 4398.
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**Figure 6.** Same as Figure 2, but for the dust condensations Nos. 4565, 4678, and 4753. No obvious C³⁴S emission is detected in the dust condensations Nos. 4565 and 4678. No obvious IR cluster is seen in the dust condensation No. 4678.
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**Figure 7.** Same as Figure 2, but for the dust condensation No. 4974.
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Based mainly on the C¹⁸O data, we identified molecular clumps and estimated their physical parameters. We used the following four-step procedure to define the molecular clumps in this study:

1.
We first searched for pixels having intensities greater than the 3σ noise level in the C¹⁸O intensity map, and regarded a set of continuous pixels as a clump.
2.
We then searched for the peak intensity position in each clump, and defined S the surface area of the clump as the region enclosed by the contour at 50% of the peak intensity.
3.
In step 2, we found that four clumps (Nos. 3645, 3890, 4417, and 4565) have two local peaks within S, each of which is well separated from the other peak in other molecular lines such as SO and/or CS. In addition, the two local peaks have different radial velocities separated by >0.5 km s⁻¹. We believe that the two local peaks should originate from two distinct clumps lying along the same line of sight. We therefore divided each of the four clumps into two smaller clumps at the valley in the C¹⁸O contours, and re-measured S for the smaller clumps in the same way as described in step 2.
4.
Among the clumps selected by the above steps, we chose only the clumps having S greater than 0.3 arcmin² (corresponding to 20 pixels in the C¹⁸O intensity maps) to analyze in this paper, in order to ensure the definite detection.

Using the above procedure, we identified 24 clumps in total in the observed 15 dust condensations. We refer to the clumps as 3645a, 3645b, and so on, in the order of increasing right ascension.

To examine the star formation activity in the clumps, we investigated the young stellar objects (YSOs) associated with each clump. The YSOs were searched for by referring to the catalogs of IRAS point sources. Eleven clumps were found to be associated with one YSO selected from the IRAS catalog based on the selection criteria proposed by Dobashi et al. (1994), and they have a bolometric luminosity greater than 10²L_☉.

In the following, we estimate the physical parameters of the individual clumps. To derive column densities from the observed emission lines, we assumed the local thermodynamic equilibrium (LTE). Details of the derivations are described in Appendix A. Based on the ¹²CO data, we calculated excitation temperature T_ex at the individual positions of each clump for the observed emission lines. Using Equation (7) and assuming that the ¹²CO emission line is optically thick (τ ≫ 1), T_ex can be derived as

$\begin{eqnarray}&&{T}_{\mathrm{ex}}=5.53{\left\{\mathrm{ln}\left[1+\displaystyle \frac{5.53}{{T}_{\mathrm{mb}}^{\mathrm{co}}+0.819}\right]\right\}}^{-1}\,{\rm{K}},\end{eqnarray} \tag{ 1 }$

where ${T}_{\mathrm{mb}}^{\mathrm{co}}$ is the peak brightness temperature in K of the ¹²CO data estimated by a single Gaussian fit at the individual observed positions. The maximum T_ex for each clump ranges from 28.0 K (clump 4059) to 82.1 K (clump 4974), and the average T_ex within S, ${\overline{T}}_{\mathrm{ex}}$ , ranges from 24.5 K (clump 4059) to 59.4 K (clump 4974).

Using Equation (8) and the derived values of T_ex, we calculated the column densities of C¹⁸O, SO, CS, and C³⁴S of the clumps on the assumption of LTE and the optically thin cases (τ ≪ 1).

The molecular hydrogen column density N(H₂) was derived from the C¹⁸O column density N(C¹⁸O) by assuming the relation N(C¹⁸O) = 1.7 × 10⁻⁷N(H₂) (Frerking et al. 1982). The LTE mass of the clumps within S, M_LTE, was derived as

$\begin{eqnarray}&&{M}_{\mathrm{LTE}}=\overline{\mu }{m}_{{\rm{H}}}{\int }_{S}N({{\rm{H}}}_{2}){dS},\end{eqnarray} \tag{ 2 }$

where m_H is the hydrogen mass, and $\overline{\mu }$ is the mean molecular weight, which is assumed to be 2.8. The mean volume density in the clumps, n(H₂), was estimated by dividing M_LTE by the clump volume V = (4/3)πR³, where R is the radius of the clump defined as $R=\sqrt{S/\pi }$ .

We also calculated the virial mass, M_vir, as

$\begin{eqnarray}&&{M}_{\mathrm{vir}}=\displaystyle \frac{5R}{G}\displaystyle \frac{\overline{{\rm{\Delta }}V}{({{\rm{C}}}^{18}{\rm{O}})}^{2}}{8\,\mathrm{ln}2},\end{eqnarray} \tag{ 3 }$

where G is the gravitational constant, and $\overline{{\rm{\Delta }}V}({{\rm{C}}}^{18}{\rm{O}})$ is the mean line width (FWHM) in the composite profile obtained by averaging all of the spectra of the clump within S. We further derived the average fractional abundances of SO, CS, and C³⁴S within S by estimating the column densities and dividing them by N(H₂) derived from the C¹⁸O data.

Using this approach, we found that the clumps have sizes ranging from 0.1 to 0.6 pc, masses ranging from 5 to 4397 M_☉, and volume densities ranging from 1.2 × 10⁴ to 1.9 × 10⁵ cm⁻³. These physical properties are summarized in Table 3.

Table 3. Physical Properties of the Clumps

Clump	α(J2000)^a	δ(J2000)^a	R	$\overline{{\rm{\Delta }}V}$ (C¹⁸O)^b	$\overline{{T}_{\mathrm{ex}}}$ ^b	M_LTE	M_vir	n(H₂)^b	$\overline{N}({{\rm{H}}}_{2})$ ^b	$\overline{N}$ (C¹⁸O)^b	$\overline{f}$ (SO)^b	$\overline{f}$ (CS)^b	$\overline{f}$ (C³⁴S)^b
	(^{h m s})	(° ' '')	(pc)	(km s⁻¹)	(K)	(M_☉)	(M_☉)	(10⁴ cm⁻³)	(10²² cm⁻²)	(10¹⁵ cm⁻²)	(10⁻⁹)	(10⁻⁹)	(10⁻¹⁰)
3645a	00:15:25.0	61:13:17	0.43	2.7	35.8	398	681	1.7	3.9	6.3	1.7	0.9	<1.1
3645b	00:15:29.2	61:14:02	0.41	1.9	38.4	474	347	2.4	3.6	5.8	1.8	1.5	1.7
3890a	02:28:03.1	61:27:39	0.61	2.1	36.0	3432	573	5.2	13.5	23.6	1.7	0.5	2.8
3890b	02:28:04.1	61:29:16	0.62	2.4	35.6	4397	721	6.4	17.3	30.4	1.1	0.3	2.2
3890c	02:28:57.7	61:33:01	0.23	1.1	35.9	113	56	3.2	3.0	4.7	3.3	1.4	<2.0
3921	03:01:30.4	60:29:11	0.57	1.9	50.5	1508	439	2.8	6.7	11.4	1.8	1.8	2.0
3923	03:03:22.5	60:28:03	0.28	1.6	43.0	249	141	3.9	4.6	7.7	2.4	1.2	<0.6
3935	03:15:41.4	60:02:23	0.19	0.9	28.8	25	35	1.2	2.7	4.2	1.3	0.3	<0.3
3937	03:20:38.9	60:17:54	0.21	0.9	26.4	86	32	3.2	2.8	4.4	1.0	0.4	<0.6
4054	03:51:42.7	51:27:52	0.16	1.0	34.9	48	31	4.0	2.7	4.1	1.1	0.4	<0.4
4059	03:56:50.4	51:47:19	0.20	1.3	24.5	71	67	3.1	2.5	3.9	1.7	0.5	<0.8
4398	05:14:09.6	32:45:07	0.10	0.9	34.2	5	14	1.6	1.0	1.2	<0.9	<0.1	<0.9
4417a	05:40:59.7	35:49:20	0.64	3.1	54.4	1852	1464	2.4	6.5	11.1	2.8	1.4	1.3
4417b	05:41:26.9	35:52:12	0.46	1.5	54.8	994	253	3.5	7.6	13.1	2.7	1.1	<0.7
4417c	05:41:29.3	35:48:57	0.40	2.5	56.5	993	609	5.4	8.7	15.0	3.6	1.7	1.7
4423a	05:40:52.9	35:41:35	0.41	2.5	47.7	955	617	4.8	7.9	13.5	4.0	2.9	4.3
4423b	05:40:53.5	35:38:28	0.25	1.5	55.7	177	142	3.9	4.2	6.8	<1.1	<0.8	<1.2
4565a	06:18:36.7	23:18:32	0.19	1.7	58.1	131	115	6.6	5.3	8.8	3.3	1.5	<1.2
4565b	06:18:42.7	23:20:02	0.31	1.6	38.9	331	172	3.8	5.1	8.5	2.1	0.8	<1.0
4565c	06:18:46.0	23:21:17	0.22	1.4	32.9	161	92	5.2	3.7	6.0	2.1	0.7	<0.8
4678	06:09:52.5	13:44:48	0.14	1.4	36.7	26	59	3.3	2.1	3.1	2.0	0.3	<0.9
4753a	06:41:05.0	09:35:15	0.27	2.9	50.6	1123	486	19.8	20.6	36.5	2.1	1.0	1.2
4753b	06:41:10.6	09:29:38	0.35	3.3	50.8	1203	810	9.7	13.6	23.8	4.0	2.0	2.1
4974	06:07:44.4	−06:23:26	0.50	3.3	59.4	2581	1076	7.2	13.3	23.3	1.2	2.2	1.7

Notes. For the fractional abundance of SO, we calculated the mean partition function Q to be 76.3–176.9 for the assumed T_ex of 24.5–82.1 K using the parameters measured by Tiemann (1974).

^aPeak position of the C¹⁸O (J = 1–0) integrated intensity in the equatorial coordinates. ^bThe average value of the clumps.

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We note that the ¹²CO spectra at some positions around the peak intensities in the clumps 3890a, 4423a, 4753a, and 4974 are optically thick and suffer from self-absorption. For these positions, we cannot determine T_ex precisely, which is a source of uncertainty in our mass estimates. Here we compare our estimates with those in the literature. Sakai et al. (2006) estimated the LTE mass of clump 3890b (which they called AFGL333 core A) to be 2300M_☉ based on the C¹⁸O data obtained with the NRO 45 m telescope and assuming a uniform T_ex of 20 K. For the same clump, we estimated 4000 M_☉ at their assumed distance of 1950 pc, ∼70% larger than their value. As another example, Peretto et al. (2006) derived a mass of 1650M_☉ for clump 4753b (NGC 2264C) using 1.2 mm continuum data, assuming a dust temperature of 15 K. Our value for the same clump would be rescaled to 1400M_☉ at their assumed distance of 800 pc, which is ∼20% smaller than their value. We found that these differences are mainly due to the difference of the adopted T_ex and the definition of the surface areas of the clumps.

We also derived fractional abundances of the CCS and HC₃N molecules of the clumps. The CCS emission was found only in four clumps (3890a, 4753a, 4753b, and 4974), whereas the HC₃N emission was found in nine clumps (3645b, 3890a, 3890b, 3921, 4423a, 4565b, 4753a, 4753b, and 4974). All of the clumps detected in CCS were also detected in HC₃N. At an rms noise level of 0.1–0.2 K and a resolution of 0.2 km s⁻¹, there was no detection of both CCS and HC₃N in the other 15 clumps.

For the nine clumps detected in CCS and/or HC₃N, the emission lines were detected only in compact regions in the clumps, and their peak positions in the integrated intensity maps do not match with those of the C¹⁸O line. Therefore we decided to derive physical properties using these lines at the HC₃N intensity peak positions. To derive the column densities of CCS and HC₃N of the clumps, N(CCS) and N(HC₃N), we tried to estimate T_ex by fitting three main hyperfine components of the HC₃N spectra. However, we could not fit the spectra well because of the low signal-to-noise ratios. We therefore derived N(CCS) and N(HC₃N) using Equation (8) on the assumption of a uniform T_ex of 5 K measured in dark clouds (e.g., Hirota et al. 2009), as well as much higher T_ex (≃34–66 K) measured from the ¹²CO spectra, which should give the lower and upper limits of the column densities, respectively. We then smoothed the C¹⁸O spectrum at the HC₃N peak position of each clump to 49'', the same resolution as at 45 GHz, and derived N(H₂) from the smoothed C¹⁸O spectrum in the same manner as for deriving the clump masses. Finally, we derived the fractional abundances of CCS and HC₃N of the clumps, f(CCS) and f(HC₃N), by dividing their column densities by N(H₂). The range of f(CCS) in the four clumps lies between 0.5 × 10⁻¹⁰ and 4.1 × 10⁻¹⁰, and that of f(HC₃N) in the nine clumps lies between 0.4 × 10⁻¹⁰ and 6.2 × 10⁻¹⁰. For the clumps detected in HC₃N but not in CCS, we derived the upper limits of N(CCS) and f(CCS) from the noise levels to be <1 × 10¹² cm⁻² and <1 × 10⁻¹¹, respectively. The derived column densities and fractional abundances for the nine clumps are shown in Table 4.

Table 4. Physical Properties Derived from CCS and HC₃N

Clump	α(J2000)	δ(J2000)	T_ex^a	N(H₂)	N(CCS)^b	N(HC₃N)^b	f(CCS)^b	f(HC₃N)^b
	(^{h m s})	(° ' '')	(K)	(10²² cm⁻²)	(10¹² cm⁻²)	(10¹² cm⁻²)	(10⁻¹⁰)	(10⁻¹⁰)
3645b	00:15:30.1	61:14:30	35.9	2.1	<1.4–<4.9	4.7–6.5	<0.7–<2.3	2.2–3.1
3890a	02:28:4.9	61:27:45	36.2	15.6	8.6–29.7	8.5–11.7	0.5–1.9	0.5–0.7
3890b	02:28:7.0	61:29:15	34.2	19.1	<3.0–<6.4	6.9–9.5	<0.2–0.3	0.4–0.5
3921	03:01:30.0	60:29:15	52.1	6.9	<1.7–<9.4	11.5–21.2	<0.2–1.4	1.7–3.1
4423a	05:40:53.0	35:41:35	47.8	8.9	<4.5–<5.4	16.1–27.9	<0.5–0.6	1.8–3.1
4565b	06:18:43.3	23:19:45	37.4	4.0	<2.6–<9.2	6.0–8.5	<0.7–<2.3	1.5–2.1
4753a	06:40:58.4	09:36:8	50.2	13.4	10.1–46.5	30.2–53.9	0.8–3.5	2.2–4.0
4753b	06:41:10.6	09:29:23	55.3	18.2	10.3–50.9	38.8–75.1	0.6–2.8	2.1–4.1
4974	06:07:39.0	−06:22:60	66.1	14.2	10.1–57.6	38.6–87.4	0.7–4.1	2.7–6.2

Notes. The parameters were derived at the peak position of the HC₃N integrated intensity. To estimate the column densities of CCS, we calculated Q to be 24.302–651.75970 for the assumed T_ex of 5.0–66.1 K, using the parameters measured by Yamamoto et al. (1990).

^aT_ex calculated using the ¹²CO data. ^bMinimum and maximum estimates for parameters assuming a flat T_ex of 5 K and that calculated using the ¹²CO data, respectively.

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We note that f(CCS), f(HC₃N), f(CS), and f(SO) derived in the above may be overestimated, because we derived N(H₂) from N(C¹⁸O), assuming their flat ratios. In very dense regions, C¹⁸O can be less abundant due to adsorption onto dust grains (e.g., Bergin et al. 2002) or due to selective destruction by the strong UV radiation from young massive stars (e.g., Shimajiri et al. 2014), which may cause an underestimation of N(H₂). Taking into account all of the uncertainties in distance, T_ex, and N(H₂), we conclude that our estimates of mass and fractional abundances for the 24 clumps have an uncertainty of 50% at most.

3.2. Velocity Dispersion of the Clumps

We investigated the velocity dispersion of the clumps. The velocity dispersion σ_obs of the observed emission lines at each observed position was derived as

$\begin{eqnarray}&&{\sigma }_{\mathrm{obs}}=\sqrt{\displaystyle \frac{\int {(V-{V}_{0})}^{2}{T}_{\mathrm{mb}}\,{dV}}{\int {T}_{\mathrm{mb}}\,{dV}}},\end{eqnarray} \tag{ 4 }$

where V₀ is the intensity-weighted mean velocity measured as ${V}_{0}=\int {{VT}}_{\mathrm{mb}}\,{dV}/\int {T}_{\mathrm{mb}}\,{dV}$ .

Based on the C¹⁸O data, we derived σ_obs of the emission line, ${\sigma }_{\mathrm{obs}({{\rm{C}}}^{18}{\rm{O}})}$ , from the above equation. We regard that ${\sigma }_{\mathrm{obs}({{\rm{C}}}^{18}{\rm{O}})}$ consists of the thermal (σ_therm) and non-thermal (σ_NT) components (e.g., Myers 1983), and can be expressed as

$\begin{eqnarray}&&{\sigma }_{\mathrm{obs}({{\rm{C}}}^{18}{\rm{O}})}^{2}={\sigma }_{\mathrm{therm}}^{2}+{\sigma }_{\mathrm{NT}}^{2}+{\sigma }_{\mathrm{reso}}^{2}.\end{eqnarray} \tag{ 5 }$

Here, σ_reso (=0.05 km s⁻¹) is the velocity resolution of the data, and σ_therm can be calculated as

$\begin{eqnarray}&&{\sigma }_{\mathrm{therm}}=\sqrt{\displaystyle \frac{{{kT}}_{\mathrm{ex}}}{{\mu }_{({{\rm{C}}}^{18}{\rm{O}})}{m}_{{\rm{H}}}}},\end{eqnarray} \tag{ 6 }$

where ${\mu }_{({{\rm{C}}}^{18}{\rm{O}})}$ is the mean molecular weight of C¹⁸O (=30). The three-dimensional velocity dispersion of turbulence at each position can be estimated as ${\sigma }_{3{\rm{D}}}=\sqrt{3}{\sigma }_{\mathrm{NT}}$ . The mean values of ${\sigma }_{\mathrm{obs}({{\rm{C}}}^{18}{\rm{O}})}$ , σ_therm, and σ_3D for each clump averaged within the clump surface S are listed in Table 5.

Table 5. Derived Velocity Dispersion

Clump	${\sigma }_{\mathrm{obs}({{\rm{C}}}^{18}{\rm{O}})}$	σ_therm	σ_3D
	(km s⁻¹)	(km s⁻¹)	(km s⁻¹)
3645a	1.16	0.10	1.96
3645b	0.77	0.10	1.32
3890a	0.91	0.10	1.55
3890b	0.82	0.10	1.42
3890c	0.48	0.10	0.84
3921	0.78	0.12	1.33
3923	0.66	0.11	1.14
3935	0.36	0.09	0.60
3937	0.36	0.09	0.60
4054	0.31	0.09	0.51
4059	0.59	0.08	1.00
4398	0.27	0.10	0.44
4417a	0.87	0.12	1.49
4417b	0.70	0.12	1.10
4417c	0.86	0.12	1.53
4423a	1.02	0.11	1.75
4423b	0.62	0.12	1.06
4565a	0.63	0.13	1.07
4565b	0.61	0.10	1.04
4565c	0.59	0.10	1.00
4678	0.45	0.10	0.81
4753a	1.19	0.12	2.05
4753b	1.35	0.12	2.33
4974	1.21	0.13	2.07

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3.3. Search for Outflows

We investigated the presence of molecular outflows associated with the clumps by searching for high velocity wings in the ¹²CO spectra. The procedure is explained in Appendix B. We also searched for molecular outflows associated with the clumps in the literatures (e.g., Wu et al. 2004). As a result, we found nine outflows in the 24 clumps in total, and two of the outflows that are associated with clumps 4417a and 4417c are newly identified by this study. We show the locations of the nine outflows in Figure 8, and summarize their properties in Table 6.

**Figure 8.** The ¹²CO intensity maps for the blue and/or red lobes of the molecular outflows found around the clumps are shown in panel (a). The red scale denotes the star density distributions. The red contours denote the red lobes, and the blue contours denote the blue lobes. The contours start from the 3σ noise level. Sample spectra obtained at the intensity peaks of the blue lobes and the red lobes are shown in panels (b) and (c), respectively. The equatorial coordinates are given in each panel. The vertical broken line in the spectra marks the systemic velocity.
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Table 6. Derived Parameters of the Outflows

Clump	Wing	$\overline{{T}_{\mathrm{ex}}}$	V_sys	V_char	V_range	S_lobe	R_lobe	$\int \int {T}_{\mathrm{mb}}\,{dVdS}$	t_d	τ_max	M_lobe^a	P_lobe^a	${\dot{P}}_{\mathrm{lobe}}$ ^a
		(K)	(km s⁻¹)	(km s⁻¹)	(km s⁻¹)	(arcsec²)	(pc)	(K km s⁻¹ arcmin²)	(10⁴ year)		(M_☉)	(M_☉ km s⁻¹)	(10⁻⁴ M_☉ km s⁻¹yr⁻¹)
3890a	blue	35.5	−48.5	9.2	(−59, −53.5)	2981	0.30	8.8	3.2	1.7	1.3–2.7	13.3–27.4	4.5–9.4
	red	35.3		8.0	(−44, −40)	2756	0.29	7.0	3.5	2.4	1.1–2.8	8.8–23.3	2.6–6.9
3890c	blue	29.3	−51.5	5.4	(−59, −53)	4838	0.38	17.8	7.0	1.5	2.5–4.8	14.8–28.8	2.4–4.6
	red	30.0		6.2	(−49, −44)	3544	0.33	9.2	5.1	6.7	1.3–8.6	7.3–48.9	1.3–8.7
3921	blue	47.6	−38.1	7.3	(−46, −41)	10744	0.60	33.7	8.0	6.4	7.7–49.6	69.9–450.2	10.8–69.9
	red	44.3		6.4	(−36, −30)	33019	1.05	166.6	16.0	9.9	36.4–361.1	271.0–2685.5	19.7–195.0
4417a	blue	58.1	−20.3	7.7	(−28, −24)	5738	0.32	20.2	4.1	3.4	3.0–10.4	22.5–79.2	5.4–19.0
4417c	blue	55.6		7.0	(−28, −24)	2925	0.23	8.9	3.2	5.6	1.2–6.8	7.9–44.3	2.3–12.7
4423a	blue	53.2	−16.9	7.7	(−24, −20)	3319	0.24	15.5	3.1	2.5	2.1–5.7	17.3–47.8	6.0–16.6
4753a	blue	44.9	5.3	11.3	(−9, 1)	13219	0.23	81.9	2.0	2.8	2.1–6.3	25.0–75.5	13.2–39.8
4753b	blue	53.6	7.9	12.0	(−6, 2)	787	<0.1	3.2	<0.5	3.7	<0.1–0.2	0.4–1.6	<0.1–3.1
	red	52.8		11.3	(13, 20)	7031	0.17	53.3	1.5	3.8	1.5–6.0	16.5–63.8	10.5–40.8
4974	blue	65.0	10.4	10.7	(0, 5.5)	24413	0.38	156.6	3.5	8.1	8.1–65.5	82.4–670.4	22.5–183.1
	red	55.4		11.6	(16.5, 22)	40894	0.50	377.8	4.2	8.4	16.9–141.7	198.1–1665.4	48.0–403.8

Note.

^aMinimum and maximum estimates for parameters of the outflows, which are estimated using τ = 0 and τ = τ_max, respectively (see Appendix B).

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For clump 4753a (NGC 2264D), Buckle et al. (2012) identified multiple blue and redshifted lobes through ¹²CO (J = 3–2) observations. Our map for this clump does not cover the full extent of the red outflow lobe, and only the blue lobe is seen in Figure 8. We therefore list properties of only the blue lobe for this clump in Table 6.

For clump 3921 (AFGL4029), Snell et al. (1988) found the total outflow lobe mass (the sum of the masses of the red and blue lobes) to be 9.7 M_☉ using ¹²CO. Their outflow mass differs significantly from our value of 44.1 M_☉ (the lower limit), which is likely to be explained mainly by their different assumed value of T_ex (= 25 K).

We compared the distributions of the molecular outflows with the locations of the IR clusters, and found that some of the outflows coincide well with the IR clusters (see Figure 8). Although the identified outflow lobes of clumps 3890a and 4417a are likely to be unrelated to the corresponding clusters, outflow lobes in the other clumps (i.e., clumps 4423a and 4974) coincide well with the positions of the clusters. In the maps of Dierickx et al. (2015) produced from their SMA observations, clump 4974 (Mon R2) shows the presence of 11 CO outflows in the innermost ∼1' region around the cluster. Though only one pair of red and blue lobes is seen in our map, it is likely that our maps trace the entirety of the high velocity flow originating from the cluster.

3.4. Search for IR Clusters Based on the 2MASS Data and Estimation of the Physical Properties

The 2MASS PSC was used to systematically search for IR clusters associated with all of the 24 observed clumps. We selected a 15' × 15' region around each clump, except for the clump 4974,⁷ and produced star density maps of the regions to identify clusters using stars that are not recorded as "minor planets" in the 2MASS PSC. We will explain the reason we selected the stars in this way in Appendix C.

The star density map of each cluster was constructed by counting the number of stars in a 0 farcm 4 radius from each 7 farcs 5 grid set along the equatorial coordinates. The obtained star density maps still contained contributions from the background sources. To estimate the properties of the clusters, we obtained final star density maps free from the background using the 3σ clipping procedure described in detail by Shimoikura et al. (2013). The resulting 1σ noise level of the star density maps is in the range of 3–5 stars arcmin⁻².

We searched for pixels in the star density maps with a density greater than the 4σ noise level for each region, and regarded them as IR clusters. We then defined the extents of the clusters by the contour drawn at the 30% level of the peaks. As a result, we identified 23 IR clusters within the 24 clumps. Twenty of the IR clusters have been previously identified in other studies. In addition to these, we newly identified three IR clusters associated with the dust condensations Nos. 3890 and 4753. Distribution of the identified IR clusters in the area observed with the 45 m telescope is shown in the last panel of Figures 2–7, in which the WISE 3.4 μm image (Wright et al. 2010) is overlaid to see the extended emission associated with the clumps or the IR clusters. In each panel, the IR clusters are labeled 3645cl, 3890cl1, 3890cl2, and so on. In summary, the observed regions contain 24 molecular clumps, and 16 of them are associated with at least one IR cluster, whereas the other eight clumps are associated with no apparent IR cluster. Among the 23 clusters identified, six are not associated with any particular clumps.

To derive the properties of the IR clusters, we first defined their radius as ${R}_{\star }=\sqrt{{S}_{\star }/\pi }$ , where S_⋆ is the surface area of the clusters defined at the 30% contour level. We then investigated the cumulative number of stars for each cluster, N_⋆(r), as a function of distance r from the cluster center. An example of the results is shown in Figure 9. We found that N_⋆(r) increases rapidly with r and becomes rather flat at r ≃ 2 R_⋆ – 4 R_⋆, and then diverges at a larger r due to counting uncertainty, which is the same tendency that we already found in other cluster-forming regions (Shimoikura et al. 2013).

**Figure 9.** Cumulative number of stars as a function of radius for the cluster 3645cl. The number of stars was measured with the background-subtracted star density map. The number of stars of the cluster N_⋆ (indicated by the green line) was defined as the mean number of stars at r = 2R_⋆ and 3R_⋆, where R_⋆ is the cluster radius (see text).
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We defined the total number of stars contained in an IR cluster, N_⋆, as the average value of N_⋆(r) in the flattened part of the N_⋆(r) versus r diagram. For most of the clusters, we defined N_⋆ as the average value in the range 2R_⋆ < r < 3R_⋆. For clusters 3923cl and 4974cl, we decided to define N_⋆ in the range 4R_⋆ < r < 5R_⋆. We found that N_⋆ varies in the range of 12 to 380, and R_⋆ varies from 0.12 to 0.76 pc. These parameters are summarized in Table 7.

Table 7. Physical Properties of the IR Clusters

IR Cluster	α(J2000)	δ(J2000)	R_⋆	N_⋆	Peak Density	Dmin/Dmaj^a
	(^{h m s})	(° ' '')	(pc)		(stars arcmin⁻²)
3645cl	00:15:29.2	61:14:25	0.64	63	34	0.5
3890cl1	02:28:16.1	61:31:10	0.76	172	47	0.4
3890cl2	02:28:20.7	61:28:27	0.35	48	63	0.8
3890cl3	02:28:30.4	61:27:17	0.30	29	39	0.9
3890cl4	02:28:47.7	61:33:27	0.35	43	43	0.5
3890cl5	02:29:04.1	61:33:24	0.44	69	59	0.7
3921cl1	03:01:19.3	60:29:28	0.49	59	35	0.8
3921cl2	03:01:33.8	60:29:13	0.45	57	49	0.5
3923cl	03:03:15.3	60:27:58	0.40	63	44	0.8
4054cl	03:51:33.3	51:29:59	0.13	18	24	0.6
4417cl1	05:41:06.9	35:49:24	0.28	33	33	0.5
4417cl2	05:41:10.0	35:50:09	0.27	23	23	0.5
4417cl3	05:41:23.9	35:52:09	0.34	27	25	0.6
4417cl4	05:41:30.8	35:49:53	0.40	47	23	0.4
4423cl1	05:40:54.9	35:44:14	0.35	40	27	0.8
4423cl2	05:40:53.1	35:42:14	0.40	135	65	0.6
4423cl3	05:40:55.5	35:40:07	0.43	80	33	0.6
4423cl4	05:40:52.4	35:38:22	0.25	12	21	0.9
4565cl	06:18:38.1	23:19:18	0.47	94	35	0.6
4753cl1	06:41:04.2	09:35:45	0.19	36	22	0.5
4753cl2	06:41:06.7	09:34:07	0.12	15	16	0.7
4753cl3	06:41:09.7	09:29:37	0.13	34	40	0.6
4974cl	06:07:46.0	−06:22:55	0.28	380	86	0.7

Note.

^aRatio of the minor axis to the major axis of the cluster surface area fitted with the 2D Gaussian function.

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The largest N_⋆ (=380) in our sample is found in 4974cl, which is a rich IR cluster in the Mon R2 region. The cluster has already been studied with the 2MASS data by Carpenter (2000), who estimated the total number of stars to be N_⋆ = 371 in an effective radius of ∼1.85 pc based on the Wainscoat model (Wainscoat et al. 1992). We found that their value for N_⋆ is found to be quite close to ours.

Several studies have used NIR data to derive the structural parameters of clusters by fitting the star density profiles with the model proposed by King (1962). Although we attempted to fit the star density of the identified IR clusters with the King model, most of the clusters could not be fitted well, owing to their complex morphologies. The 23 clusters studied here have a wide variety of structures, and some of them show multiple peaks. Camargo et al. (2011) studied eight IR clusters among those we study here (clusters 4417cl1–cl4 and 4423cl1–cl4) using the 2MASS PSC and the King model, but they could successfully fit only two of them (4417cl1 and 4417cl3, which they call "Sh2-235 Cluster" and "Sh2-235 East2," respectively).

Lada & Lada (2003) suggested that there are two morphological types of cluster structures, hierarchical and concentrated, and that these structures may reflect the physical processes responsible for cluster formation. We found that most of our identified clusters are not spherical, except for six clusters not associated with any particular clumps. For example, cluster 3890cl2, which is located in a cavity of C¹⁸O gas, has a spherical morphology (see Figure 3). By contrast, cluster 4423cl2 is elliptical and matches well with its associated clump (see Figure 5). We measured the ratio of the minor and major axis with the 2D Gaussian fit for each cluster, as shown in the last column of Table 7, and found that clusters associated with less molecular gas tend to be more spherical, with a ratio of minor to major axis of >0.8, possibly suggesting that the more spherical clusters are older.

3.5. Relationships between Clumps and IR Clusters

By comparing the distributions of the clumps with those of the associated IR clusters (Figures 2–7), we found that their spatial coincidences vary from clump to clump. For example, in some cases, there are two clumps within the extent of one cluster (e.g., clusters 3645cl and 4565cl), while there are sometimes two IR clusters within the extent of one clump (e.g., clump 4753a). We also note that the IR clusters in clump 3921 can be resolved by eye into two IR clusters, 3921cl1 and 3921cl2, and the former cluster is not associated with any molecular emission.

There have been some studies to investigate the evolution of cluster-forming clumps—for example, by Ridge et al. (2003), Kawamura et al. (2009), Higuchi et al. (2009), and Shimoikura et al. (2013). In their studies, clumps are classified by eye inspection, mainly according to the presence of the associated clusters and their morphological relations. To examine the relationship between the clumps and the IR clusters and to classify their morphological types more quantitatively, we investigated the spatial correlations between N(C¹⁸O) and the star densities (SD) of the associated clusters for the 16 clumps. To do this, we re-gridded and smoothed the data sets to the same angular resolution (48'') and performed a linear least-square fit to quantify the N(H₂) versus SD relation. The results are shown in Figure 10. Correlation coefficients of the fit, r, range from 0.1 to 0.8.

**Figure 10.** Correlation between N(H₂) and the star density of the 16 clumps with IR clusters. The blue lines denote the linear least-square fit. The intercepts i and correlation coefficients r for the relations are denoted in the panels.
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To characterize the identified clumps and clusters in terms of the cluster formation, we classified them into four types according to the following correlation relationship:

1.
We classify clumps associated with no apparent IR cluster as Type 1.
2.
We classify clumps that are well-correlated with IR clusters with a correlation coefficient of ≳0.5 as Type 2. Such clumps have morphologies that are similar to the clusters.
3.
We classify clumps not well-correlated with IR clusters with a correlation coefficient of <0.5 as Type 3. In such clumps, the peaks of the star density of the IR clusters do not match with those of the clumps.
4.
Finally, we classify clusters not associated with any clumps as Type 4.

Among the 24 clumps, a total of eight, seven, and nine clumps are classified as Type 1, 2, and 3, respectively. In addition, six IR clusters are classified as Type 4. The classification of the clumps and IR clusters is summarized in Table 8.

Table 8. Clumps and IR Clusters

Dust Condensation No.	Clump	IR Cluster^a	Type	Outflow^a	IRAS^b	L(L_☉)^c
3645	3645a	3645cl (1)	3	N	⋯	⋯
	3645b	3645cl (1)	3	N	00127+6058	4.0 × 10³
3890	3890a	N	1	Y (5)	⋯	⋯
	3890b	N	1	N	⋯	⋯
	⋯	3890cl1 (1)	4	N	⋯	⋯
	⋯	3890cl2 (2)	4	N	02245+6115	1.0 × 10⁴
	⋯	3890cl3^d	4	N	⋯	⋯
	⋯	3890cl4^d	4	N	⋯	⋯
	3890c	3890cl5 (1)	3	Y (6)	⋯	⋯
3921	⋯	3921cl1 (2)	4	N	⋯	⋯
	3921	3921cl2 (2)	2	Y (6)	02575+6017	1.3 × 10⁴
3923	3923	3923cl (2)	3	N	02593+6016	1.7 × 10⁴
3935	3935	N	1	N	⋯	⋯
3937	3937	N	1	N	⋯	⋯
4054	4054	4054cl (1)	3	N	⋯	⋯
4059	4059	N	1	N	⋯	⋯
4398	4398	N	1	N	⋯	⋯
4417	4417a	4417cl1 (2), cl2 (3)	3	Y^d	⋯	⋯
	4417b	4417cl3 (4)	2	N	05379+3550	3.6 × 10³
	4417c	4417cl4 (4)	2	Y^d	05382+3547	2.0 × 10³
4423	⋯	4423cl1 (1)	4	N	⋯	⋯
	4423a	4423cl2 (2)	2	Y (6), (7)	05375+3540	1.3 × 10⁴
	⋯	4423cl3 (1)	4	N	⋯	⋯
	4423b	4423cl4 (1)	3	N	05375+3536	8.9 × 10³
4565	4565a	4565cl (2)	3	N	06155+2319A	5.0 × 10³
	4565b	4565cl (2)	3	N	⋯	⋯
	4565c	N	1	N	⋯	⋯
4678	4678	N	1	N	⋯	⋯
4753	4753a	4753cl1 (2), cl2^d	2	Y (6), (8)	06382+0939	4.7 × 10²
	4753b	4753cl3 (2)	2	Y (6), (8)	06384+0932	2.5 × 10³
4974	4974	4974cl (2)	2	Y (6)	06053-0622	4.2 × 10⁴

Notes.

^a"Y" indicates detection and "N" indicates no detection. ^bSelected IRAS point source using the selection criteria proposed by Dobashi et al. (1994). ^cThe bolometric luminosity calculated following the method of Myers et al. (1987). ^dThe IR clusters or outflows identified by this work.

References. (1) Bica et al. (2003a), (2) Bica et al. (2003b), (3) Camargo et al. (2011), (4) Kirsanova et al. (2008), (5) Nakano et al. (2017), (6) Wu et al. (2004), (7) Nakano and Yoshida (1986), (8) Buckle et al. (2012).

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3.6. Physical Properties of the Clumps

We investigated the correlations between the physical properties of the clumps using the derived parameters listed in Tables 3, 5, and 6.

Figure 11 shows the relations among M_vir, M_LTE, R, and ΔV for the clumps of Types 1, 2, and 3, which are shown in different colors. We also plotted the same relations for clumps identified in the S252, S247, and BFS52 regions using C¹⁸O data presented by Shimoikura et al. (2013), which were also obtained with the NRO 45 m telescope. We classified these clumps into the three types (Types 1–3) in the same way as explained above.

**Figure 11.** Relation between (a) M_vir and M_LTE, (b) M_LTE and R, and (c) $\overline{{\rm{\Delta }}V}$ (C¹⁸O) and R for the 24 clumps. Blue, red, and pink circles represent the clumps of the different types. Plus signs denote the clumps associated with a molecular outflow. We also show data points of other clumps presented by Shimoikura et al. (2013).
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As shown in Figure 11(a), many of the clumps have a mass of the same order as their virial masses, suggesting that they may be in the virial equilibrium. However, there is a tendency that masses of the massive clumps (M_LTE ≳ 10³ M_☉) are significantly higher than the virial masses. These clumps can collapse if they are not supported by the clump-supporting forces such as the magnetic field. In fact, as we will show in Section 4.2, some of the Type 2 clumps are actually collapsing.

The relationship between M_LTE and R in Figure 11(b) reveals that the clumps have a molecular number density in the range 10⁴ < n(H₂) < 10⁵ cm⁻³, which is consistent with the results of previous studies of cluster-forming clumps (e.g., Saito et al. 2007; Shimoikura et al. 2013).

In Figure 11(c), it is apparent that the clumps with clusters, particularly Type 2 clumps, have larger line widths than those without clusters. We also found that the clumps having large line widths are associated with outflows, suggesting that the outflows are supplying turbulence to the clumps.

It has been long suggested that outflows are an important source of turbulence of natal clumps (e.g., Snell et al. 1988; Nakamura & Li 2011). In order to see how much the outflows can contribute to the observed turbulence, we estimated the dissipation rates of turbulence of the clumps as ${\dot{P}}_{\mathrm{turb}}\,=-0.21\,{M}_{\mathrm{LTE}}\,{\sigma }_{3{\rm{D}}}^{2}/R$ (Nakamura & Li 2014; see their Equations (4) and (5)) using the parameters listed in Tables 3 and 5, and compared them with ${\dot{P}}_{\mathrm{flow}}$ , the ejection rates of momentum of the outflows in Table 6. Results are shown in Figure 12. For ${\dot{P}}_{\mathrm{flow}}$ , we plotted the geometrical mean values with error bars representing the minimum and maximum estimates (see Appendix B). As seen in the figure, ${\dot{P}}_{\mathrm{flow}}$ is comparable to or larger than ${\dot{P}}_{\mathrm{turb}}$ for all of the Type 2 and 3 clumps within the errors, suggesting that the observed turbulence can be maintained by the outflows for these clumps. For the Type 1 clump (3890a), however, ${\dot{P}}_{\mathrm{flow}}$ is significantly smaller than ${\dot{P}}_{\mathrm{turb}}$ , and thus the observed turbulence of this clump should dissipate on a scale of crossing time (R/σ_3D ≃ 3.8 × 10⁵ year), if the clump does not form additional outflows in the future.

**Figure 12.** ${\dot{P}}_{\mathrm{flow}}$ vs. ${\dot{P}}_{\mathrm{turb}}$ relation for the clumps associated with outflows. For ${\dot{P}}_{\mathrm{flow}}$ , we plot the geometrical mean values with error bars (green line) representing the minimum and maximum estimates (see Appendix B).
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**Figure 12.** ${\dot{P}}_{\mathrm{flow}}$ vs. ${\dot{P}}_{\mathrm{turb}}$ relation for the clumps associated with outflows. For ${\dot{P}}_{\mathrm{flow}}$ , we plot the geometrical mean values with error bars (green line) representing the minimum and maximum estimates (see Appendix B).
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Figure 11 suggests that all of the Type 2 clumps have similar properties, with a typical mass and radius of ∼10³M_☉ and 0.5 pc, respectively. By contrast, the properties of the other types of clumps are widely distributed in the diagrams. Two Type 1 clumps, 3890a and 3890b, have a very large mass of ∼4000 M_☉, and they are lying in a locus similar to that of the Type 2 clumps in Figure 11, suggesting that they are potential sites of cluster formation in the future. However, as we will show in Section 4.1, the Type 1 clumps exhibit puzzling chemical compositions. We will discuss the origin of the Type 1 clumps in Section 4.3.

4. Discussion

At a glance, we would expect that the clump + cluster systems should evolve from Type 1 to Type 4 successively, but this needs a careful inspection of the obtained data set. In the following, we will examine the chemical compositions of the clumps, which can be used as a measure of their ages in terms of chemical reaction. We will then inspect the velocity structures as well, and will discuss how the clump + cluster systems should evolve.

4.1. Chemical Compositions of the Clumps

To date, the CCS emission has been detected mostly toward dense regions in low-mass star-forming regions, but not in active cluster-forming regions such as DR21, W3, or W40 (e.g., Lai & Crutcher 2000; Shimoikura et al. 2015). In this study, we detected the CCS emission for the first time in active cluster-forming clumps (i.e., toward the three Type 2 clumps 4753a, 4753b, and 4974). The CCS emission was also detected in one non-cluster-forming Type 1 clump (3890a), which was already reported by Sakai et al. (2006).

The relationships between the clumps and the IR clusters suggest that the clumps classified as Types 1–3 are in different stages of evolution. To investigate this in terms of chemical reactions, we compared f(CCS) and f(HC₃N) for the nine clumps in which HC₃N was detected. The relation is shown in Figure 13. As explained in Section 3.1, we estimated the upper and lower limits of the fractional abundances for different assumptions of T_ex. We plotted their geometrical mean values with error bars representing the two limits. In the figure, we also show the results of calculations based on a chemical model by Suzuki et al. (1992). They carried out single-dish survey observations toward 49 dark cloud cores in low-mass star-forming regions, and also performed the model calculations to find that CCS and HC₃N are more abundant in an early stage of chemical evolution. Their results were also confirmed by Hirota et al. (2009). The fractional abundances of CCS and HC₃N can therefore be regarded as a good measure of chemical reaction time in dense cores just before/after the formation of stars therein.

In Figure 13, we also show the f(CCS) and f(HC₃N) data points for dark cloud cores for comparison, which we reported earlier (Shimoikura et al. 2012). We note that the plots for the Type 2 and Type 3 clumps in the figure are likely to be shifted from the global trend of the dark cloud cores, though the ambiguity is large. Although we do not clearly understand the reason for the shift at the moment, it may reflect a significant difference in chemical reactions in massive clumps with IR clusters and small dark cloud cores.

To better establish the evolutionary stages of the Type 1–3 clumps, we compared in Figure 14 $\overline{f}$ (CS), the average fractional abundance of CS, and $\overline{f}$ (SO), that of SO within the clump surface S for the 24 clumps. We also plot the same relation for the clumps in our earlier paper (Shimoikura et al. 2013). It is also known that CS and SO can be used as a chemical clock (e.g., Bergin & Langer 1997), and it is expected that CS should appear in an early stages of chemical reactions in molecular clumps, while SO should appear in a later stage. We also show a theoretical model calculated by Bergin & Langer (1997) in the figure. According to the calculations based on their "model 1," f(CS) and f(SO) start to decrease monotonically at ∼2 × 10⁵ year and ∼2 × 10⁶ year, respectively.

As seen in Figure 14, the distribution of the clumps can be well separated according to their types. The figure shows that $\overline{f}$ (CS) and $\overline{f}$ (SO) are decreasing in the order of Type 2 , Type 3, and Type 1. In general, differences in the chemical composition can be caused not only by the ages but also by the density of the clumps. However, the latter may not be an important cause for the clumps studied here, because most of them have similar densities in the range 10⁴–10⁵ cm⁻³ (Figure 11).

We further compared the f(CCS) versus f(HC₃N) and $\overline{f}$ (CS) versus $\overline{f}$ (SO) relations with known cluster ages. The ages of the clusters associated with the clumps 4753a and 4753b are estimated to be ∼3 Myr (for NGC 2264; e.g., Sung et al. 2004) and those of clump 4974 are estimated to be ∼1–4 Myr (for Mon R2; e.g., Maaskant et al. 2011). As seen in Figures 13 and 14, it is interesting to note that the ages of the clusters associated with the Type 2 clumps (∼1–4 Myr) are consistent with the model calculations by Suzuki et al. (1992) and Bergin & Langer (1997). However, we should note that the models assume the gas temperature of only 10 K for dark clouds and do not take into account the feedback of star formation, and thus we cannot directly compare the ages of the clusters with the chemical reaction time of the models. Though it is difficult to take into account the feedback of star formation, recent chemical model calculations for much warmer clumps (up to 200 K; e.g., Chapman et al. 2009; Hassel et al. 2011) show that fractional abundances of carbon-chain species such as CCS and HC₃N generally decrease in the time range, roughly from ∼1 × 10⁵ year to ∼1 × 10⁶ year, in the same way as for cold dark clouds (10 K) but with shorter reaction time for higher gas temperatures. Because the observed clumps are warmer in the order of the Type 2, Type 3, and Type 1 clumps (see Tables 3 and 4), the loci of the Types 1–3 clumps in Figures 13 and 14 indicate that the Type 2 clumps are the youngest and the Type 1 clumps are the oldest among the three types in terms of chemical compositions.

In summary, the differences in the fractional abundances of CCS, HC₃N, CS, and SO among the three types of clumps are likely to reflect the different evolutionary stages of the clump types: The Type 1 clumps are seen in the lower-left side of the diagram in Figure 14, suggesting that they may be rather old in terms of chemical compositions. The Type 2 clumps are in an early stage of cluster formation, in which the associated clusters are still embedded in an amount of gas and dust. The Type 3 clumps are in a more evolved stage than the Type 2 clumps, with much less molecular gas. The Type 4 clusters with no or very little gas should be in the final stage of cluster formation. We suggest that the massive clumps should evolve in the order of Type 2, 3, and 4 successively.

The Type 1 clumps are puzzling, because we would expect that they are the clumps just before the onset of cluster formation in a stage prior to the Type 2 clumps, but their chemical compositions indicate that they are older than the Type 2 clumps. We will discuss the nature and origin of the Type 1 clumps in Section 4.3.

4.2. Velocity Structures of the Clumps

The results shown in Figures 11–12 suggest that there are interesting systematic differences among the types of clumps. In the following, we further investigate the velocity structures of the Types 1–3 clumps.

Figure 15 shows the distribution of the velocity dispersion σ_obs measured with the ¹³CO and C¹⁸O emission lines for the 24 clumps as a function of the projected distance from the cluster center (for Type 2 and Type 3 clumps) or from the clump peak (for Type 1 clumps). Values of σ_obs measured with the two emission lines are shown by dots with different colors—gray and pink for the ¹³CO and C¹⁸O emission lines. We found that σ_obs at the center of the clumps differs depending on the types of the clumps; the σ_obs values of Type 1 (except for clumps 3890a and 3890b), Type 2 (except for 4417b), and Type 3 are mostly ≲0.5 km s⁻¹, ≳1.0 km s⁻¹, and ≳0.5 km s⁻¹, respectively. This suggests that the large velocity dispersion at the clump center is a typical feature of cluster-forming Type 2 and Type 3 clumps. The velocity dispersion is particularly large in the Type 2 clumps, indicating that there must be a lot of motions around the clump center in the beginning of cluster formation.

We also investigated the C¹⁸O distributions based on the position–velocity (PV) diagrams for all of the clumps. In Figure 16, we show examples of the PV diagrams measured along the major and minor axes of the clumps, which are displayed in panels (b) and (c) of the figure. As denoted by the white broken circles in panels (b), we found that the PV diagrams of some Type 2 clumps measured along the major axis show double peaks separated by ∼1 km s⁻¹, and they are symmetrically located with respect to the clump centers. This feature is seen only in three of the seven Type 2 clumps (4417c, 4423a, and 4753b), but not in Type 1 or Type 3 clumps.

A possible interpretation for the double-peaked feature of the Type 2 clumps could be a collision of two smaller clumps (e.g., Higuchi et al. 2009), but in that case, we would expect that the velocity difference of the two peaks should largely vary, because the collision velocity is a free parameter and can basically take any values. However, the velocity differences seen in the PV diagrams for clumps 4417c, 4423a, and 4753b are rather small, at consistently only ≲1 km s⁻¹, suggesting that the double-peaked feature in the PV diagrams is unlikely to be caused by the clump collisions.

To understand the velocity structure of these Type 2 clumps, we analyzed the C¹⁸O data of clump 4423a (S235AB) in our previous paper (Shimoikura et al. 2016), which shows the double-peaked feature most clearly among the three Type 2 clumps, and concluded that the observed feature around the clump center should be caused by the infalling motion with rotation of the entire clump, not by the collisions of smaller clumps. Note that the double-peaked feature in the PV diagram is very similar to those observed around dense cores forming a single low-mass YSO, which was successfully interpreted by Ohashi et al. (1997) as an infalling core with rotation. As we described in detail in the previous paper (Shimoikura et al. 2016), we made a simple model of a massive cluster-forming clump (∼1000 M_☉) with analog to the model suggested by Ohashi et al. (1997) for a small core forming a single YSO (see their Figure 8 and Appendix), and we confirmed that the model can reproduce well the PV diagrams observed toward clump 4423a. Obviously, the other Type 2 clumps shown in Figure 16 (4417c and 4753b) also exhibit the double peaks in the PV diagram, indicating that these clumps should also be infalling, although they are too complex to fit nicely with our simple model. Actually, the collapsing motion of clump 4753b was also suggested by Peretto et al. (2006), who found the two velocity components through molecular line observations using the IRAM 30 m telescope.

The above findings imply that, in the beginning of cluster formation, the massive cluster-forming clumps (∼1000 M_☉) have a simple structure similar to a small dense core forming a single low-mass star, and we would expect that the dense massive core and therefore the most massive star(s) in the cluster should form at the center of the clump. Such a scenario is supported by recent numerical simulations (Smith et al. 2009; Wang et al. 2010). In the case of the three Type 2 clumps shown in Figure 16 (4417c, 4423a, 4753b), some observational evidences for the formation of massive cores and YSOs at the clump center can also be found in the literature (Felli et al. 2004; Peretto et al. 2006; Dewangan & Anandarao 2011).

The fact that at least three of the seven Type 2 clumps exhibit the double-peaked feature indicates that the infalling motion with rotation of the entire massive clumps is a common phenomenon in the Type 2 clumps. We note that all of the Type 2 clumps showing the highest f(CS) and f(SO) are the ones exhibiting the double-peaked feature in the PV diagrams, indicating that the dynamical infall with rotation occurs in the beginning of cluster formation.

For the rest of Type 2 clumps (3921, 4417b, 4753a, 4974), the double-peaked feature is not seen in our data set, but it can be due to rather poor angular resolution of the observations (22''). In fact, the clumps show large velocity gradient along their major axes, similar to those observed toward the three clumps with the double-peaked feature, suggesting that they are collapsing but the double-peaked features are not resolved by the current observations.

4.3. Nature of the Observed Massive Type 1 Clumps and the Possible Evolutionary Scenario of the Cluster Formation

As discussed in Section 4.1, the observed Type 1 clumps are generally older than the Type 2 clumps in terms of chemical compositions. Some of the small Type 1 clumps (∼100 M_☉) can be remnants of the Type 3 clumps, or they might be too small to produce clusters and have survived for a long time without collapsing for some reason—for example, by maintaining turbulence by outflows driven by one or a few low-mass YSOs forming there (Snell 1987; Dobashi et al. 1993; Nakamura & Li 2011), or by the support of the magnetic field, like what has been suggested for small clouds in the Ophiuchus north region (Nozawa et al. 1991; Hirota et al. 2009). However, the massive Type 1 clumps, namely 3890a and 3890b with a mass of ∼4000 M_☉, are rather mysterious, because, except for their puzzling chemical compositions, they appear to be the very initial clumps that should evolve to Type 2 clumps in terms of the mass and velocity structures. Here we focus on the nature of these massive Type 1 clumps.

As indicated in Figure 11, these clumps lie in the same loci as Type 2 clumps in the figures, and they appear to be potential sites of cluster formation in the future. The Type 1 clumps are associated with several Class I sources (Jose et al. 2016), and 3890a is associated with a molecular outflow (in Figure 8), and thus sporadic star formation should be taking place there. However, the clumps are not associated with any apparent clusters, nor they do not show the double-peaked features in the PV diagrams, suggesting that they are not collapsing but should be gravitationally stable on the clump-scale. Based on the calculations denoted in Section 3.6, we found that the turbulence of the Type 1 clumps is not large enough to support the clumps by itself (i.e., M_vir < M_LTE), and therefore additional clump-supporting force is needed. An easy solution for the additional force is the magnetic field. The clumps would be gravitationally stable if they are supported by a rather strong magnetic field of an order of ∼1 mG. In other words, the clumps may be magnetically sub-critical (Nakano 1985; Shu et al. 1987)—that is, their collapsing motions by the self-gravity are prevented by the magnetic field. Observational data compiled by Crutcher et al. (2010) show that the magnetic field of this strength (∼1 mG) is possible at the density of the clumps (∼10⁵ cm⁻³). We therefore suggest that the massive Type 1 clumps (3890a and 3890b) have been stable for a long time due to the strong magnetic field, which may be the reason why they are chemically older than the Type 2 clumps. The clumps have a potential to collapse and evolve into the Type 2 clumps in the future, whenever the support by the magnetic field is weakened.

Type 2 clumps such as 4423a and 4753b forming clusters must have evolved from Type 1 clumps that used to be younger in terms of chemical compositions being located in earlier stages in Figures 13 and 14 than the observed Type 2 clumps. It is likely that such Type 1 clumps are not found in our sample. The reason why we do not find them in our sample is probably their short lifetime. The Type 1 clumps have a typical density of ∼1 × 10⁵ cm⁻³ (Figure 11), corresponding to the free-fall time of only τ_ff ≃ 10⁵ year, and thus they should contract as soon as they lose the internal supporting forces such as the turbulence and the magnetic field. Beside the Type 1 clumps, ages of the clusters forming in the Type 2 clumps are >1 × 10⁶ year, and therefore the probability to find such Type 1 clumps should be less than 1/10 of that for the Type 2 clumps. This should be the reason why it is difficult to find such Type 1 clumps.

All of the above imply how the clumps of different types should evolve. When massive and dense Type 1 clumps (∼1000 M_☉, ∼ 10⁵ cm⁻³) are formed, they are initially stable, being supported by the turbulence and magnetic field. They start collapsing and evolve into Type 2 clumps as soon as they lose the clump-supporting forces, or they remain as Type 1 clumps without collapsing if they maintain the clump-supporting forces (e.g., the magnetic field of an order of ∼1 mG). The Type 2 clumps collapse on the clump-scale, and form clusters at the clump center. Along with the growth of the clusters, the clumps disperse by the feedback of cluster formation (e.g., powerful outflows and stellar wind), which corresponds to our Type 3 category. In the end, only clusters remain (Type 4). In Figure 17, we schematically summarize this evolutionary scenario of the cluster-forming clumps.

**Figure 17.** Proposed evolutionary scenario of cluster formation.
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5. Conclusions

To study cluster formation processes systematically, we carried out observations of 15 dust condensations selected from a catalog compiled by Dobashi (2011) in various molecular lines using the NRO 45 m telescope. The main results of the observations can be summarized as follows:

1.
The observations resolved the 15 dust condensations into 24 molecular clumps in the C¹⁸O data whose masses vary from 5 to 4397 M_☉. We also analyzed the 2MASS PSC to investigate the star density distributions of the associated clusters, and identified 23 clusters in the observed regions. Among the 24 clumps, 16 are associated with one or more IR clusters, whereas the other eight are not associated with apparent IR clusters. We also detected nine outflow sources in the 24 clumps, and two of the outflows are newly identified by this study.
2.
To assess the relationship between the clumps and IR clusters, we investigated the spatial correlations between N(H₂) and the star densities, and classified the clumps and IR clusters into four types: eight clumps having no associated IR clusters are classified as Type 1, seven clumps showing good correlations with IR clusters are classified as Type 2, nine clumps showing poor correlations with IR clusters are classified as Type 3, and six IR clusters with no associated clumps are classified as Type 4.
3.
Type 2 clumps have a typical mass of ∼1 × 10³M_☉, a radius of ∼0.5 pc, and a density of ∼1 × 10⁵ cm⁻³, and the distributions of the associated clusters coincide well with the C¹⁸O distributions, indicating that the clusters are forming around the center of the clumps. The velocity dispersion in the Type 2 clumps tends to be larger (>0.5 km s⁻¹) at the cluster center. We found that such Type 2 clumps are accompanied by two velocity components that differ by ∼1 km s⁻¹, which can be recognized as the two peaks in the position–velocity diagram. On the other hand, neither Type 1 nor Type 3 clumps exhibit such velocity structures. In our previous paper, we presented evidence that the clump 4423a (Type 2) showing the two velocity components is infalling with rotation on the clump-scale. In this paper, we found at least two similar cases (4417c and 4753b) in the other Type 2 clumps, which indicates that the infalling motion with rotation is a common phenomenon among the Type 2 clumps.
4.
We suggest that the clump + IR cluster systems should evolve from Type 1 to Type 4. The Type 1 clumps are stable in the beginning and evolve into Type 2 clumps as soon as they lose the clump-supporting forces, and the Type 2 clumps are collapsing on the clump-scale to form clusters at the clump center. The Type 3 clumps are in a more advanced stage, with much less molecular gas, and the Type 4 clusters are more evolved, and their natal clumps have already dispersed. All of the clumps classified to Type 1 in this study are older than the Type 2 clumps in terms of chemical compositions. We suggest that they are the Type 1 clumps being gravitationally stable without collapsing for a long time due to the strong magnetic field, or that they are the remnants of Type 3 clumps. Type 1 clumps that are younger than the observed Type 2 clumps in terms of chemical composition should be rare to find, due to their short lifetime.

We are very grateful to the anonymous referee for providing useful comments and suggestions to improve this paper. This work was financially supported by Grant-in-Aid for Scientific Research (Nos. 17H02863, 17H01118, 26287030, 17K00963) by the Japan Society for the Promotion of Science (JSPS). The 45 m radio telescope is operated by NRO, a branch of NAOJ.

Software: NOSTAR (Sawada et al. 2008).

Appendix A: Derivation of the Column Density

The brightness temperature corrected for the main-beam efficiency T_mb of the observed emission line is given by

$\begin{eqnarray}&&{T}_{\mathrm{mb}}=[J({T}_{\mathrm{ex}})-J({T}_{\mathrm{bg}})][1-\exp (-\tau )],\end{eqnarray} \tag{ 7 }$

where τ is the optical depth, $J(T)={T}_{0}/({e}^{{T}_{0}/T}-1)$ , and T_bg = 2.7 K. T₀ is a constant calculated as T₀ = hν₀ /k, where k, h, and ν₀ are the Boltzmann constant, the Planck constant, and the rest frequency of the observed emission line, respectively. On the assumption of the LTE, column density for the optically thin lines can be obtained with the following equation (e.g., Hirahara et al. 1992):

$\begin{eqnarray}&&N=\displaystyle \frac{3h}{8{\pi }^{3}}\displaystyle \frac{Q}{{\mu }^{2}{S}_{{ij}}}\displaystyle \frac{{e}^{{Eu}/{{kT}}_{\mathrm{ex}}}}{{e}^{{T}_{0}/{T}_{\mathrm{ex}}}-1}\displaystyle \frac{1}{J({T}_{\mathrm{ex}})-J({T}_{\mathrm{bg}})}\int {\beta }^{-1}{T}_{\mathrm{mb}}{dv}.\end{eqnarray} \tag{ 8 }$

Here, Q is the partition function approximated as Q =k T_ex/h B₀, where B₀ is the rotational constant of the molecule, μ is the dipole moment, E_u is the energy of the upper level, and S_ij is the intrinsic line strength of the transition for i to j state. β is the escape probability given by $\beta =(1-{e}^{-\tau })/\tau$ , and β = 1 for τ ≪ 1. The spectral line parameters are taken from Splatalogue,⁸ a database for astronomical spectroscopy. We summarize the line parameters used in this study in Table 9.

Table 9. Molecular Constants

Molecule	Transition	S_ij	B₀	μ	E_u
			(GHz)	(Debye)	(cm⁻¹)
CCS	J_N = 4₃ – 3₂	3.972	6.477750	2.88000	3.75568
HC₃N	J = 5 – 4	5.000	4.549059	3.73172	4.55219
C³⁴S	J = 2 – 1	2.000	24.103540	1.95700	6.19802
CS	J = 2 – 1	2.000	24.495560	1.95700	4.90249
SO	J_N = 3₂ – 2₁	2.934	21.523556	1.53500	6.41219
C¹⁸O	J = 1 − 0	1.000	54.891420	0.11049	3.66194
¹³CO	J = 1 − 0	1.000	55.101010	0.11046	3.67592
¹²CO	J = 1 − 0	1.000	57.635960	0.11011	3.84503

Note. All of the constants are taken from Splatalogue.

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Appendix B: Search for Outflows and Estimation of the Outflow Parameters

In order to search for reliable candidates of outflows, we checked the ¹²CO spectra if they show blue- and/or redshifted high velocity wings around the center velocity of C¹⁸O at each pixel. We also investigated the ¹²CO distributions based on the PV diagrams, which is useful to find outflows and to determine the velocity range of the outflowing gas. In total, we found nine outflows, which are shown in Figure 8. We also show some emission lines observed toward the peak position of the high velocity emission.

In Table 6, we provide an estimate of the masses of the outflows M_lobe and their properties. We measured the peak positions of the lobes, and also defined the surface area of the lobes S_lobe at the 3σ contour level of the maps for each outflow. R_lobe is the radius of the lobes calculated as ${R}_{\mathrm{lobe}}=\sqrt{{S}_{\mathrm{lobe}}/\pi }$ , and V_sys is the systemic velocity defined as the peak velocity of the C¹⁸O spectra. The maximum velocity shift of the ¹²CO emission from the systemic velocity, which we call characteristic velocity, V_char, is defined as ${V}_{\mathrm{char}}=| {V}_{\mathrm{sys}}-{V}_{\max }|$ , where V_max is the maximum velocity of the high velocity wings detected at the 3σ noise level. We tried to measure the optical depth of ¹²CO from the ratio of the ¹²CO intensity to the ¹³CO intensity. However, there is very little detectable ¹³CO emission above the noise level within the lobes. We therefore measured the upper limit of the optical depth at the intensity peak position of the lobes, τ_max, and derived properties of the outflowing gas for the upper limits.

To estimate τ_max, we assumed that the ¹³CO is optically thin and that the [¹²CO]/[¹³CO] abundance ratio is equal to the terrestrial value (89),

$\begin{eqnarray}&&\displaystyle \frac{I{(}^{12}{\mathrm{CO}}_{\mathrm{wing}})}{I{(}^{13}{\mathrm{CO}}_{\mathrm{wing}})}=89\times \displaystyle \frac{1-{e}^{-{\tau }_{\max }}}{{\tau }_{\max }},\end{eqnarray} \tag{ 9 }$

where I(¹²CO_wing) and I(¹³CO_wing) are the integrated intensity of the ¹²CO and ¹³CO emission lines measured at the peak positions of the lobes, respectively.

As the lower limits for the properties of the outflowing gas, we assumed that wing components in the ¹²CO emission line are optically thin (τ ≪ 1).

Using the calculated T_ex (see Section 3.1), we derived the ¹²CO column densities of the outflows N(¹²CO) from Equation (8). For the estimation of the upper and lower limits, we used $\beta =(1-{e}^{-{\tau }_{\max }})/{\tau }_{\max }$ and β = 1, respectively. The molecular column density N(H₂) was then calculated from N(¹²CO), assuming a CO fractional abundance of 1 × 10⁻⁴ (Frerking et al. 1982). Masses of the outflow lobes M_lobe were derived from Equation (2) within S_lobe.

We list in Table 6 the derived M_lobe, as well as the momentum P_lobe = M_lobeV_char, dynamical timescale t_d =R_lobe/V_char, and momentum supply rate ${\dot{P}}_{\mathrm{lobe}}={P}_{\mathrm{lobe}}/{t}_{{\rm{d}}}$ . In this study, we made no attempt to correct for the inclination angle of the outflows.

Appendix C: Criteria to Select Stars Based on the 2MASS PSC

In order to search for IR clusters in this paper, we used all of the stars in the 2MASS PSC, except for those identified as minor planets, because most of the cataloged stars are significantly detected at least in one of the 2MASS bands (JHKs). However, as pointed out by Cambrésy et al. (2002), it is known that there are a certain fraction of false stars in the 2MASS PSC around bright stars and nebulae associated with small H ii regions. In order to check how much our sample of stars can be contaminated by the false stars, we made a test by applying some tighter criteria and by checking the appearance of the selected stars on the 2MASS images.

The test was made toward the dust condensations No. 4753 (NGC 2264) and No. 4974 (Mon R2) that are known to be accompanied by IR clusters (e.g., Peretto et al. 2006; Dierickx et al. 2015). We produced star density maps covering a 15' × 15' area around No. 4753 and a 40' × 40' area around No. 4974 using stars selected under the following four different criteria:

(1)
Stars except for those with a minor planet flag.
(2)
Stars satisfying the above (1), and having a photometry quality flag of A, B, or C and a read flag of 1, 2, or 3 in all of the three JHKs bands.
(3)
Stars satisfying the above (1), and having a photometry quality flag of A, B, or C and a read flag of 1, 2, or 3 at least in one of the JHKs bands.
(4)
Stars satisfying the above (1), and having a cataloged magnitude of J < 16.0 mag, H < 15.5 mag, and Ks < 15.0 mag.

The criteria (1) are what we used in this study, the criteria (3) are to ensure the detection at least in one of the 2MASS bands, the criteria (4) are tighter than these, and the criteria (2) are the tightest.

The results are summarized in Figure 18, where the individual selected stars (blue circles) and star densities (red contours) of the two regions are shown. The 2MASS J band image is overlaid in all of the panels. We estimated N_⋆, the number of stars in the two clusters, by removing the background based on the 3σ clipping procedure in the same way as described in Section 3.4. The values of N_⋆ are given in the upper-right corner of each panel.

As seen in the figures, in the case of criteria (2), many stars apparently escaped selection because the criteria are too tight, and we cannot even realize the existence of the cluster in the case of No. 4753. In the case of criteria (3), almost the same stars are selected as in criteria (1). In the case of criteria (4), the spatial distributions of the clusters (traced by the contours for the star densities) are similar to those derived using criteria (1), though there are still some apparent real stars that escaped selection and N_⋆ decreases by ∼20% and ∼60% for Nos. 4753 and 4974, respectively.

In the lower panels of Figure 18, we also show a close-up view of the central regions. There are some stars among those selected with criteria (1) and (3), which we cannot determine if they are real stars or false detections due to the influence of nearby bright source and lumpy/filamentary structures of the nebula. However, criteria (1) allows us to select all of the apparent stars in the J band images, while criteria (2) and (4) miss many obviously real stars.

In addition to the above criteria (1)–(4), we also tried the criteria that Cambrésy et al. (2002; see their Section 3) employed to identify IR clusters in the North America and Pelican nebulae, and found that the resulting stars are similar to those selected by the above criteria (2).

We believe that there is no ideal criteria that can exclude false stars perfectly from the 2MASS PSC in all of the IR clusters, and thus we have to choose realistic criteria to better measure the cluster parameters we want to know. Because we first need to know the existence of clusters and second their distributions and extents, even roughly, we decided to use criteria (1) in this paper.

A Statistical Study of Massive Cluster-forming Clumps

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Abstract

1. Introduction

2. Observations

2.1. The Target Dust Condensations

2.2. Observations with the NRO 45 m Telescope

2.2.1. Observations of ${}^{12}{CO},{}^{13}{CO}\,{C}^{18}O,SO,CS,$ and ${C}^{34}S$

2.2.2. Observations of CCS and ${{HC}}_{3}N$

3. Results

3.1. Identification of Molecular Clumps and Estimation of Their Physical Properties

3.2. Velocity Dispersion of the Clumps

3.3. Search for Outflows

3.4. Search for IR Clusters Based on the 2MASS Data and Estimation of the Physical Properties

3.5. Relationships between Clumps and IR Clusters

3.6. Physical Properties of the Clumps

4. Discussion

4.1. Chemical Compositions of the Clumps

4.2. Velocity Structures of the Clumps

4.3. Nature of the Observed Massive Type 1 Clumps and the Possible Evolutionary Scenario of the Cluster Formation

5. Conclusions

Appendix A: Derivation of the Column Density

Appendix B: Search for Outflows and Estimation of the Outflow Parameters

Appendix C: Criteria to Select Stars Based on the 2MASS PSC

Footnotes

A Statistical Study of Massive Cluster-forming Clumps

Article metrics

Permissions

Share this article

Author e-mails

Author affiliations

ORCID iDs

Dates

Abstract

1. Introduction

2. Observations

2.1. The Target Dust Condensations

2.2. Observations with the NRO 45 m Telescope

2.2.1. Observations of {}^{12}{CO},{}^{13}{CO}\,{C}^{18}O,SO,CS, and {C}^{34}S

2.2.2. Observations of CCS and {{HC}}_{3}N

3. Results

3.1. Identification of Molecular Clumps and Estimation of Their Physical Properties

3.2. Velocity Dispersion of the Clumps

3.3. Search for Outflows

3.4. Search for IR Clusters Based on the 2MASS Data and Estimation of the Physical Properties

3.5. Relationships between Clumps and IR Clusters

3.6. Physical Properties of the Clumps

4. Discussion

4.1. Chemical Compositions of the Clumps

4.2. Velocity Structures of the Clumps

4.3. Nature of the Observed Massive Type 1 Clumps and the Possible Evolutionary Scenario of the Cluster Formation

5. Conclusions

Appendix A: Derivation of the Column Density

Appendix B: Search for Outflows and Estimation of the Outflow Parameters

Appendix C: Criteria to Select Stars Based on the 2MASS PSC

Footnotes

2.2.1. Observations of ${}^{12}{CO},{}^{13}{CO}\,{C}^{18}O,SO,CS,$ and ${C}^{34}S$

2.2.2. Observations of CCS and ${{HC}}_{3}N$