COLLIDING FILAMENTS AND A MASSIVE DENSE CORE IN THE CYGNUS OB 7 MOLECULAR CLOUD

The Cyg OB 7 molecular cloud is a giant molecular cloud (GMC) located at a distance of 800 pc (Humphreys 1978) in the direction of the Cygnus region (e.g., Falgarone & Perault 1987). The cloud has an apparent size of ∼4° × 7° centered at ℓ ∼ 92° and b ∼ 4°, and it has a total molecular mass of ∼1 × 10⁵ M_☉ (Dobashi et al. 1994, 1996).

Figure 1(a) shows the entire extent of the cloud. There are two well-known star-forming sites in the cloud. One is the region known as LDN 988 (Lynds 1962), where a number of pre-main-sequence stars are forming (e.g., Herbig & Dahm 2006; Allen et al. 2008), and the other is a massive dense core known as the Northern Coal Sack (NCS) producing a massive Class 0 object (Bernard et al. 1999). Except for these two regions, star formation is much less active in this cloud than in other GMCs with a similar mass (e.g., Orion A; Nagahama et al. 1998), and there is no extended HII regions associated with the cloud. The Cyg OB 7 molecular cloud is also characterized by its low temperature (∼10 K) and large turbulence (ΔV ∼ 4 km s⁻¹ in ¹³CO; Dobashi et al. 1994), and it has been regarded as a GMC in an early stage of cloud evolution prior to an active massive star formation.

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In the all-sky visual (VIS) and near-infrared (NIR) extinction maps derived from the Digitized Sky Survey (DSS; Dobashi et al. 2005) and the Two Micron All Sky Survey (2MASS; Dobashi 2011; Dobashi et al. 2013), we found a massive dense core in the northern part of the Cyg OB 7 molecular cloud. In the DSS-based extinction map, the core is cataloged as TGUH 541P1 by Dobashi et al. (2005), which corresponds to the eastern end of the dark nebula LDN 1004 (Lynds 1962). In the optically thinner 2MASS-based extinction map, it splits into several smaller condensations, such as the one numbered No. 2996 in the catalog compiled by Dobashi (2011). Hereafter, we shall refer to this core as L1004E in this paper.

In Figure 1(b), we show the location of L1004E in the $A_{K_{\rm S}}$ map produced by Dobashi (2011). As seen in the figure, the core is very large and is the densest in the entire Cyg OB 7 cloud with a maximum $A_{K_{\rm S}}$ of ∼3 mag. Based on the $A_{K_{\rm S}}$ map, we estimate its total mass to be at least ∼5 × 10³ M_☉. In spite of its huge mass, L1004E is not accompanied by any HII regions or bright infrared sources representing massive young stellar objects (YSOs), indicating that L1004E is a core in an initial stage of massive star formation or cluster formation. L1004E should provide us with a precious opportunity to investigate the initial conditions of such massive cores because the initial conditions can be easily destroyed by the strong stellar wind and UV radiation from OB stars soon after they are formed in the cores.

The angular resolutions of the 2MASS- and DSS-based extinction maps (∼3'–6') that we used to find L1004E are not sufficient to resolve the structure of the core. We therefore carried out molecular line observations at a high angular resolution using the 45 m telescope (HPBW ≃ 15'' at 115 GHz) at Nobeyama Radio Observatory (NRO), which should also provide us with information on the velocity field of the core.

The purpose of the present paper is to report the results of the observations with the 45 m telescope. We observed the core in various molecular lines such as C¹⁸O. The observational procedures are described in Section 2. Based mainly on the C¹⁸O data, we analyzed the spatial and velocity structure of the core, and we also searched for candidate YSOs associated with the core using some infrared point-source catalogs (PSCs) open to the public. We found that the core has a huge total mass of ∼1.1 × 10⁴ M_☉ and consists of a number of massive filaments and core-like structures with a mass of 10²–10³ M_☉, which appears similar to the filamentary structures recently evidenced in other molecular clouds (e.g., André et al. 2010). To our surprise, some of the filaments are apparently colliding with one another, and some candidate YSOs are located around the intersections of the filaments as if they were induced by the collisions of the filaments. We present these observational results in Section 3. In order to understand how the colliding filaments were formed in the core, we performed numerical simulations of core evolution assuming a model core with an initial mass and size similar to those of L1004E. In Section 4, we describe the method and results of the simulations and discuss what initial conditions are needed for the formation of such colliding filaments, which should play an important role in massive star formation and cluster formation in massive cores. The conclusions of this paper are summarized in Section 5.

Observations were carried out with the 45 m telescope at NRO. We observed 13 molecular lines in total: ¹²CO(J = 1–0), ¹³CO(J = 1–0), C¹⁸O(J = 1–0), CS(J = 2–1), C³⁴S(J = 2–1), HCO⁺(J = 1–0), H¹³CO⁺(J = 1–0), HC₃N(J = 5–4), CCS(J_N = 4₃–3₂), NH₃(J, K = 1, 1), NH₃(J, K = 2, 2), NH₃(J, K = 3, 3), and NH₃(J, K = 4, 4). The ¹³CO(J = 1–0) emission line was observed for four days in 2010 January, and the other lines were observed for 22 days in the period between 2009 February and 2009 May.

Our observations can be divided into two modes. One is the mapping observations to reveal the entire molecular distribution of L1004E, and the other is one-point observations made only toward the protostellar candidate IRAS 21025+5221 found in the core.

The mapping observations were carried out with six molecular lines, as summarized in Table 1. We used the 25 Beam Array Receiver System (BEARS) to observe the emission lines of CO and its isotopes. We also used an SIS receiver named S40 to observe the HC₃N and CCS lines at 45 GHz as well as a cooled HEMT receiver named H22 to observe the NH₃(J, K) = (1, 1) line at 24 GHz. Spectrometers were autocorrelators (AC) covering a bandwidth of either 32 MHz or 16 MHz with 1,024 channels with a frequency resolution of 38 kHz or 19 kHz, respectively. We mapped an area of ∼20' × 30' around the core using the on-the-fly (OTF) technique (Sawada et al. 2008) and calibrated the spectral data with the standard chopper-wheel method (Kutner & Ulich 1981). Reference positions (i.e., the emission-free OFF positions) were (α_J2000, δ_J2000) = (20^h38^m339, 51°47'02''), (20^h49^m345, 51°48'00''), (20^h58^m370, 51°36'59''), and (21^h04^m065, 52°33'47'') for the ¹²CO, C¹⁸O, NH₃, and other emission lines, respectively. We used the reduction software package NOSTAR available at NRO to subtract a linear baseline from the raw data and to resample the spectral data onto a 10'' or 30'' grid along the equatorial coordinates. We then applied a correction for the main beam efficiencies, which vary in the range η_mb = 31%–84%, depending on the frequencies, to the baseline-subtracted data, in order to scale them to units of T_mb. Further corrections for the sideband ratio were applied for the data obtained by BEARS, because it is a double-sideband (DSB) receiver. Velocity channels are resampled onto a 0.1 km s⁻¹ or 0.2 km s⁻¹ velocity grid, which resulted in a velocity resolution of 0.14–0.34 km s⁻¹. The noise levels of the resulting data are ΔT_mb = 0.08–1.25 K at these velocity resolutions, as summarized in Table 1.

One-point observations toward IRAS 21025+5221 were made with molecular lines, as summarized in Table 2. For these observations, we used waveguide-type dual-polarization sideband-separating SIS receivers called T100H/V (Nakajima et al. 2008) to observe the CS, C³⁴S, HCO⁺, and H¹³CO⁺ lines, and we also used the H22 receiver to observe the four NH₃ lines of (J, K) = (1, 1)–(4, 4) transitions. Spectrometers were acousto-optical spectrometers (AOSs) with a bandwidth of 40 MHz and a frequency resolution of 37 kHz, corresponding to a velocity resolution of 0.11–0.47 km s⁻¹. The baseline removal was done by using the reduction package NEWSTAR. The data were scaled up to units of T_mb in the same way as for the mapping data.

The system noise temperatures T_SYS were in the range 140–430 K, depending on the receivers, including the atmosphere. Pointing accuracy was better than ∼10'': it was checked by observing the SiO maser T-Cep at 43 GHz every two hours during the observations.

3.1. Overall Molecular Distributions

Figure 2 shows the integrated intensity distributions of the observed emission lines listed in Table 1. As seen in the figure, the C¹⁸O map in panel (a) reveals the filamentary structure of the core. In contrast, the ¹³CO map in panel (b) shows a rather flat distribution because the line is heavily saturated. The ¹²CO emission line (not shown) extends all over the mapped area, and it appears much flatter. The other molecular emission lines, HC₃N, CSS, and NH₃ in panels (c)–(e), show clumpy distributions, and they are concentrated especially around IRAS 21025+5221.

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In Figure 3, we show the 12 μm image taken by the WISE satellite. It is noteworthy that the C¹⁸O map in Figure 2(a) is very similar to the dust distribution revealed by WISE, indicating that the molecular line is a good tracer of the total molecular column density N(H₂). In order to estimate the mass of L1004E, we therefore derived N(H₂) at each observed position by analyzing the C¹⁸O data using a standard method assuming the local thermodynamic equilibrium (LTE; e.g., see Shimoikura et al. 2012). For this, we first estimated the excitation temperature of C¹⁸O from the ¹²CO spectra at each observed position, assuming that the ¹²CO emission line is optically very thick. We then calculated τ(C¹⁸O), the optical depth of the C¹⁸O emission line, and its column density N(C¹⁸O), and we converted N(C¹⁸O) to N(H₂) using an empirical conversion relation found by Frerking et al. (1982). We summarize the method in the Appendix.

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The analyses of the C¹⁸O and ¹²CO data infer that L1004E has a huge mass of ∼1.1 × 10⁴ M_☉ within the region mapped in C¹⁸O (Figure 2(a)). This mass is much higher than those of other single dense cores found in low-mass star-forming regions such as Taurus (1–80 M_☉, Onishi et al. 1998) or in massive star-forming regions found in the vicinity of some HII regions (10²–10³ M_☉, Tachihara et al. 2002; Saito et al. 2007; Shimoikura et al. 2013), suggesting that L1004E may comprise a number of distinct smaller cores. Actually, as shown in Section 3.4, L1004E very likely consists of several massive filaments having a mass of 10²–10³ M_☉.

It is also noteworthy that the C¹⁸O column density of L1004E is very high compared with cores in other star-forming regions. In fact, we found that the C¹⁸O emission line, which is often optically thin (τ < 1) in molecular clouds, has a high optical depth of τ = 2–3 at the peak intensity positions in Figure 2(a). Figure 4 shows the frequency distributions of N(C¹⁸O) in L1004E compared with those of HLC 2 and LDN 1551 observed by the same NRO 45 m telescope (the data for these regions are open to the public at the NRO website⁵). As seen in the figure, L1004E exhibits much higher N(C¹⁸O) than the others. On the basis of statistical studies of dense cores in Taurus, Onishi et al. (1998) showed that all of the cores with column density greater than N(H₂) =8 × 10²¹ cm⁻² are accompanied by YSOs selected from IRAS sources, and they suggested that the cores start to form stars immediately as soon as the column density exceeds this value. This critical value of N(H₂) corresponds to N(C¹⁸O) ∼8 × 10¹⁴ cm⁻² (see Equation (A4) in the Appendix). As shown in the next subsection, there are only two IRAS sources that are promising candidates for protostars in this massive core, suggesting that the core may be in a stage prior to active star formation or may have just initiated forming stars.

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L1004E is also characterized by its low temperature. Within the observed region, the excitation temperature derived from the ¹²CO emission line varies in the range 8 K ≲ T_ex ≲ 12 K with a mean value of ∼9 K, which is lower than those in other GMCs with a similar size (e.g., 10–70 K; Nagahama et al. 1998), but it is close to those in smaller dark clouds, such as the one in Taurus (e.g., ∼10 K; Onishi et al. 1998). In addition, there is a clear tendency that T_ex is lower in the central part of the core than in the outskirts, by a few Kelvin. Similarly, the observed line width measured by applying a single Gaussian fitting to the C¹⁸O emission line varies in the range 1 km s⁻¹ ≲ ΔV(C¹⁸O) ≲ 3 km s⁻¹ with a mean value of ∼2 km s⁻¹ in the region surrounded by the lowest contour in Figure 2(a), and it tends to be smaller where the C¹⁸O intensity is higher, suggesting dissipation of turbulence in the central part of the core. We summarize the global properties of L1004E found through the above ¹²CO and C¹⁸O analyses in Table 3.

Table 3. Physical Properties of L1004E

Quantities	Values
Mass	1.1 × 104 M☉
Tex	8–12 K
ΔV(C18O)	1–3 km s−1
τ(C18O)	2–3
Size	∼2 × 5 pc2
SFE	≲ 1%

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Finally, we show the velocity distributions of molecular gas in a series of channel maps in Figures 5–7. Molecular emission lines, especially the ¹²CO line (not shown), are spread over a wide velocity range of −20 km s⁻¹ ≲ V_LSR ≲ 10 km s⁻¹, but the other emission lines concentrate in a rather limited range around V_LSR ≃ −2 km s⁻¹ (see Figure 5 displaying the ¹³CO distributions). Figures 6 and 7 show channel maps of ¹³CO and C¹⁸O, respectively, produced at a higher velocity resolution of 0.5 km s⁻¹. These figures show that the denser parts of the core exhibit an elongated structure, and the core apparently consists of a number of filaments having slightly different velocities. The filaments are clearer in the C¹⁸O channel maps in Figure 7. We will attempt to identify the individual filaments and further analyze their stability and interactions in Section 3.4.

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3.2. Young Stellar Objects

In order to search for YSOs in the observed region, we selected candidate YSOs in the IRAS PSC using the criteria suggested by Onishi et al. (1998) in a search for YSOs in the Taurus cloud complex. We selected sources detected in at least three bands among the four IRAS bands, including 25 μm and 60 μm, satisfying the conditions log(F12/F25) < 0.0 and log(F25/F60) < 0.3, where F12 means a flux density at 12 μm, and so on. As a result, we found only two IRAS sources in the observed region. They are IRAS 21005+5217 and 21025+5221, the properties of which are listed in Table 4. Both of the IRAS sources have cold far-infrared (FIR) spectra typical of YSOs (e.g., Fukui et al. 1989; Shimoikura & Dobashi 2011), having a total FIR luminosity of L_IRAS ≃ 22 and ∼36 L_☉. Note that these are the bolometric luminosities detected only in the four IRAS bands (including the correction for wavelengths longer than 100 μm; Myers et al. 1987), and the flux in the wavelengths shorter than 12 μm is not included.

Table 4. IRAS Point Sources

	Coordinates			Flux Density
IRAS No.	αJ2000	δJ2000		F12	F25	F60	F100	Quality	C. C.	LIRAS
				(Jy)	(Jy)	(Jy)	(Jy)			(L☉)
21005 + 5217	21h02m055	52°28'54''		0.9932(6)	2.580(5)	7.521(9)	<10.97(...)	3331	AAAB	21.8
21025 + 5221	21h04m065	52°33'47''		0.3691(11)	1.907(28)	8.101(10)	39.96(17)	3333	CAAA	35.9

Notes. Numbers in parentheses in the columns for F12–F100 are the uncertainties in units of percent. L_IRAS is the bolometric luminosity integrated over the four IRAS bands by the method of Myers et al. (1987).

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We further searched for YSOs in the WISE PSC using the selection criteria suggested by Koenig et al. (2012), which are to select candidates of Class I and Class II sources (Lada 1987; Greene et al. 1994) from the WISE PSC. The criteria require detection in the WISE 3.4 μm, 4.6 μm, and 12 μm bands with rather complex limitations in magnitudes and colors in the three bands, to exclude non-YSO objects such as galaxies, active galactic nuclei (AGNs), unresolved knots of shock emission due to outflows, and so on (for details, see the Appendix of Koenig et al. 2012). As a result, we found a score of candidates for Class I or Class II sources in the observed region, but they are mostly located outside of the denser parts of the core, suggesting that many of them are sources either in the foreground or background, not having a physical association with the core.

We should note, however, that there may be more faint YSOs in the WISE PSC, which were excluded by the tight selection criteria of Koenig et al. (2012). As they state in their paper, it is difficult in general to establish definite criteria to select YSOs perfectly. Their criteria have a strong restriction especially on the magnitudes of the sources in order to exclude AGNs, i.e., the apparent magnitudes at 3.4 μm and 4.6 μm have to be brighter than 14.0 and 13.5 mag, respectively (see their Section A.1). If we disregard these restrictions that exclude AGNs, we would find more candidates for faint YSOs. Actually, we found a score of such faint sources lying along the filaments of the core, which are likely to be YSOs forming therein. In the original WISE PSC, however, it seems that there is a certain fraction of false detections, probably caused by the algorithm to extract point sources from the WISE images. In order to avoid such false detections, we visually checked the locations of the point sources on the WISE images, and we selected only those having an apparent counterpart in at least one of the four band images of WISE (i.e., 3.4, 4.6, 12, and 22 μm). As a result, we found 83 candidate YSOs (i.e., 50 Class I sources and 33 Class II sources) within the area mapped in C¹⁸O, including the above faint sources and without the restrictions to exclude AGNs. The two IRAS sources are also included in these numbers because they have a counterpart in the selected WISE sources. We show the locations of these sources in Figure 8, and we shall regard them as YSOs forming in L1004E.

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Here we attempt to estimate the star-formation efficiency (SFE) of L1004E. A certain fraction of the 83 sources should be AGNs or YSOs unrelated to the core, but for simplicity we shall assume that all of them are YSOs forming in the core.

We also assume that their average mass is ∼1 M_☉, which is the mean value of stars following the Salpeter mass function (dN/dm∝m^−2.35, Salpeter 1955) over the range 0.4–10 M_☉. These assumptions yield an estimate for the SFE of only ≲ 1% because the total molecular mass of the core is 1.1 × 10⁴ M_☉ (see Table 3). This value of SFE is much lower than for other massive cores forming clusters (e.g., SFE ∼30% on average; Shimoikura et al. 2013). Note that this is the maximum estimate for the SFE because a certain fraction of the WISE sources should be unrelated to L1004E. In an extreme case, if we take only the two IRAS sources and several bright WISE sources, which are located where the C¹⁸O emission is strong, as promising YSOs forming in L1004E, a very low SFE of only ∼0.1% would be inferred, which should be the minimum estimate for the SFE in L1004E.

We found that the two IRAS sources selected as candidate YSOs have a counterpart not only in the WISE PSC but also in the 2MASS PSC, as summarized in Table 5. IRAS 21025+5221 is probably a younger YSO than IRAS 21005+5217 because it is not detected in the J and H bands of 2MASS, whereas IRAS 21005+5217 is not detected in the IRAS 100 μm band. In order to better access the stellar properties of these sources, such as the ages, masses, and luminosities, we employed a recent stellar model developed by Robitaille et al. (Robitaille et al. 2007; Robitaille 2008). The model was first developed by Robitaille et al. (2006), and it comprises several parameters for the central star, circumstellar disk, and envelope to calculate the spectral energy distributions (SEDs) for a wide range of wavelengths that can be compared with the observations. Tools for the model fitting are available on their website (http://caravan.astro.wisc.edu/), which provides us with 10,000 sets of model parameters to fit the observational data, sorted according to the resulting χ². We utilized their tools on online to fit the SEDs of the two IRAS sources using the observed parameters listed in Tables 4 and 5. The resulting SEDs of the model best fitting the data are shown in Figure 9, and some of the best model parameters with the minimum χ² are summarized in Table 6. The A_V values in the first column of the table are the fitted total extinctions along the line of sight to the stellar envelope, which is consistent with what we would expect from the observed column density of C¹⁸O. The other parameters (age, mass, and luminosity) are the best-fitting parameters for the central star. Looking into the 10 best sets of the model parameters with the smallest χ², these parameters summarized in the table seem to be well determined, with small variations in the case of IRAS 21005+5217, and the parameters are rather ambiguous in the case of IRAS 21025+5221, varying in the range 1 × 10³–8 × 10⁴ yr, 0.2–5 M_☉, and 12–65 L_☉, which is mostly due to the lack of data points in the J and H bands (there are only the upper limits for these data points). In any case, IRAS 21025+5221 is obviously younger than the other source.

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Table 5. Counterparts of the IRAS Sources

	WISE					2MASS
IRAS No.	W1	W2	W3	W4		J	H	KS
	(mag)	(mag)	(mag)	(mag)		(mag)	(mag)	(mag)
21005 + 5217	9.165 ± 0.021	7.207 ± 0.020	3.601 ± 0.015	1.095 ± 0.010		13.457 ± 0.024	11.701 ± 0.021	10.519 ± 0.015
21025 + 5221	10.160 ± 0.025	7.621 ± 0.020	5.297 ± 0.014	2.039 ± 0.015		>18.296	>15.779	13.846 ± 0.074

Note. Counterparts of IRAS 21005+5217 and 21025+5221 are J210205.43+522854.2 and J210407.18+523350.0 in the WISE PSC, and 717809903 and 717897656 in the 2MASS PSC, respectively.

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Table 6. Parameters of YSOs

IRAS No.	AV	Age	Mstar	Ltotal
	(mag)	(yr)	(M☉)	(L☉)
21005 + 5217	13.68	1.61 × 106	3.63	2.06 × 102
21025 + 5221	27.06	5.99 × 104	2.44	5.35 × 101

Note. The values are the best-fitting parameters for a model developed by Robitaille et al. (2007).

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3.3. Dense Gas around IRAS 21025+5221

We found that IRAS 21025+5221 is accompanied by a small and well-defined molecular condensation, which should be the direct parental core of the IRAS source, but the other IRAS source is not accompanied by such a very evident condensation. Figure 10 displays the close-up view of the condensation traced by some molecular emission lines, and Figure 11 shows the spectra of various molecular lines observed toward the IRAS source.

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As seen in Figure 10, the condensation is evident especially in HC₃N, CCS, and NH₃. The ratio of the NH₃ (J, K) = (1, 1) and (2, 2) emission lines implies a gas temperature for the condensation of ∼12 K (e.g., Ho & Townes 1983; Danby et al. 1988), which is close to the excitation temperature T_ex ≃ 10 K derived from the ¹²CO emission line.

As shown in Section 3.4, we estimate the total mass, radius, and mean molecule density of the condensation to be M_LTE ≃ 170 M_☉, R ≃ 0.33 pc, and n(H₂) ≃ 1.9 × 10⁴ cm⁻³ (see No. 1 in Table 7), respectively, based on the C¹⁸O data in the same way as described in Section 3.1. Note that the condensation is accompanied by IRAS 21025+5221 and many other faint YSOs selected from the WISE PSC, indicating that the condensation is probably a young dense core that has just initiated formation of a star cluster.

Table 7. Properties of Filaments and Subcores

No.	Vrange	αJ2000	δJ2000	N(H2)	ΔV	MLTE	$\Delta {\overline{V}}$	S	R	Mvir	Ellipticity	Mcr	MLTE/L
	(km s−1)			(1022 cm−2)	(km s−1)	(M☉)	(km s−1)	(pc2)	(pc)	(M☉)	α	(M☉ pc−1)	(M☉ pc−1)
1	(−3.5, −0.3)	21h04m032	52°34'06''	3.1	1.58	170	1.70	0.34	0.33	199	1.00	1158	259
2	(−4.0, −2.0)	21h03m577	52°28'36''	2.1	0.44	230	1.52	0.52	0.41	196	0.91	90	277
3	(−2.2, −0.9)	21h03m555	52°36'46''	1.9	0.63	177	1.08	0.45	0.38	91	0.17	186	96
4	(−2.2, −0.9)	21h03m380	52°36'16''	2.1	0.77	326	1.04	0.64	0.45	102	0.37	277	221
5	(−2.2, −0.9)	21h03m347	52°32'16''	2.1	1.20	420	1.39	0.76	0.49	200	0.20	668	192
6	(−4.4, −2.5)	21h03m161	52°31'36''	1.9	0.73	590	1.88	1.30	0.64	478	0.42	249	295
7	(−3.0, −0.3)	21h02m225	52°28'24''	4.5	1.78	793	1.78	1.04	0.57	380	0.50	1471	488
8	(−4.6, −1.0)	21h02m207	52°18'44''	3.0	1.48	212	1.89	0.22	0.27	197	0.63	1021	314
9	(−3.6, 0.0)	21h02m000	52°19'42''	3.0	2.54	165	2.94	0.32	0.32	579	0.77	2994	223
10	(−1.7, 0.0)	21h01m42s4	52°22'31''	1.9	0.42	107	1.26	0.35	0.33	110	0.43	82	106
11	(−3.6, −1.7)	21h01m34s7	52°22'30''	2.1	1.09	415	2.42	0.95	0.55	670	0.48	551	261
12	(−3.6, −1.8)	21h01m25s7	52°27'50''	2.1	1.45	491	1.51	0.81	0.51	240	0.28	983	255

Notes. Rather round filaments (Nos. 1, 2, 8, and 9) with a high ellipticity of α > 0.5 are called "subcores" in Section 3.4. Values in the table are measured based on the C¹⁸O data (see Section 3.4.1). Some filaments and subcores (Nos. 2, 3, 5, 6, 9, 10, and 11) are partially contaminated by another filament at different velocities, and we derived ΔV (the FWHM line width at the peak positions) and $\Delta {\overline{V}}$ (the line width averaged over the surface S) by applying a Gaussian fitting with two components.

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The idea that the condensation is very young can also be supported by the CCS and HC₃N data. It is known that these molecules are abundant in the early stage of chemical evolution of dense cores (∼10⁵ yr), and they rapidly disappear along with the core evolution (≳ 10⁶ yr; Suzuki et al. 1992; Hirota et al. 2009). Based on the CCS and HC₃N spectra shown in Figure 11, we calculated the fractional abundances of these molecules, i.e., f(X) = N(X)/N(H₂) where X =CCS or HC₃N, using the same method as Shimoikura et al. (2012, see their Section 3.2), and we found log f(CCS) = −9.09 and log f(HC₃N) = −9.45. We compare the results with those measured in dense cores in other star-forming regions as well as with a model calculation performed by Suzuki et al. (1992) in Figure 12, which is quoted from Figure 9 of Shimoikura et al. (2012), who studied starless cores in the Polaris cirrus (see their Table 9 for data points of the other cores). There is an apparent tendency in the figure that data points for dense cores not associated with YSOs (represented by the open circles) are located in the upper-right side of the diagram having higher f(CCS) and f(HC₃N), and those associated with YSOs (filled circles) are instead more widely distributed in the bottom-left side. It is interesting to note that the condensation associated with IRAS 21025+5221 (the open square labeled L1004E) is located between the two distributions, suggesting that this condensation is a young core that has just started star formation.

Finally, we should note that there are some noticeable features in a series of spectra shown in Figure 11. Most of the spectra have a peak radial velocity of V_LSR ∼ −2 km s⁻¹, which should represent the systemic velocity of gas around IRAS 21025+5221. However, the HCO⁺ and CS emission lines exhibit a double-peaked profile with a greater blue-shifted velocity component. Such a profile is often seen around protostars in optically thick emission lines like HCO⁺, and it is considered to be a sign of collapsing motion of dense cores (e.g., Zhou et al. 1993). It is also noteworthy that the ¹²CO emission exhibits a very broad line width, extending over the velocity range −20 km s⁻¹ < V_LSR < 10 km s⁻¹. This could be due to a molecular outflow possibly associated with IRAS 21025+5221, although it is difficult to confirm its red- and blue-shifted wings because the ¹²CO line around the IRAS source is heavily contaminated by the emission from the diffuse ambient gas over a wide velocity range (especially at −20 km s⁻¹ < V_LSR < −10 km s⁻¹). The wing-like features are also seen in the spectra of HCO⁺ and CS, which should be more free from such contamination, but we have only limited data for these lines. Observations of these molecular lines at a higher angular resolution using interferometers such as SMA and BIMA would be needed to confirm and resolve the outflow as well as the collapsing motion of the condensation.

3.4. Giant Filaments

3.4.1. Identification of the Filaments and Their Gravitational Stability

As seen in the C¹⁸O total intensity map in Figure 2(a), L1004E has an elongated morphology consisting of several filaments and core-like structures. In order to characterize the filaments, we attempted to identify the individual filaments based on the C¹⁸O data. We first tried to find a systematic way to define the filaments, but we found that it is very difficult to find a numerical definition to separate the filaments reliably. After some trials, we finally decided to pick relatively large filaments by visual inspection of an isotemperature map of C¹⁸O in three dimensions (Figure 13). We then determined the velocity range where the identified filaments are detected, and we produced a C¹⁸O intensity map integrated over the velocity range for each of the filaments in order to measure their physical properties, such as mass, size, and line width. Although our method to define the filaments is tentative, we will analyze the filaments identified in this manner, because our main purpose is not to compile a complete list of the filaments but to investigate their typical properties, gravitational stabilities, and velocity structures.

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In total, we picked 12 filaments, as labeled in Figure 13. The condensation associated with IRAS 21025+5221 shown in Section 3.3 corresponds to the one labeled No. 1. Some of the filaments including the condensation have a round shape, and it may be more appropriate to call them "cores" or "subcores" rather than "filaments." In order to see how much the filaments are round or elongated, we fitted the C¹⁸O intensity distribution of the individual filaments with an elliptical two-dimensional Gaussian function and derived their major and minor radii (R_maj and R_min) to determine their ellipticities α (=R_min/R_maj), which can be a measure of their elongated shapes (e.g., α = 1 is for a spherical shape). In this subsection, we call filaments with α ⩽ 0.5 "filaments" and call the others with α > 0.5 "subcores." Four of the 12 filaments we identified (Nos. 1, 2, 8, and 9 in Figure 13) can be classified as subcores.

Other than the ellipticities, we measured some properties of the filaments and subcores, which are summarized in Table 7. In the table, the parameter V_range is the velocity range that we used to define the filaments and subcores, and α_J2000 and δ_J2000 are their peak positions in the C¹⁸O intensity maps integrated over V_range. N(H₂) and ΔV are the molecular column density and the line width (defined at FWHM) measured at the peak positions, respectively, and M_LTE is the mass derived from the C¹⁸O intensity in the same way as described in Section 3.1. We defined the surface area of the filaments and subcores S at the half maximum of the peak C¹⁸O intensity integrated over V_range, and we defined their radii as $R=\sqrt{S/\pi }$. We also derived C¹⁸O spectra averaged over S and fitted them with Gaussian functions to measure the mean line width $\Delta {\overline{V}}$. In order to check the gravitational stability of the filaments and subcores, we also calculated their virial mass in a standard way (e.g., Kawamura et al. 1998), as

$$\begin{equation} {M_{\rm vir}} = 209\left({\frac{R}{{\rm pc}}} \right){\left({\frac{{\Delta {\overline{V}}}}{{\rm km\,{s^{ - 1}}}}} \right)^2} M_\odot. \end{equation} \tag{ 1 }$$

As summarized in the table, we found that the identified filaments and subcores have a mass, line width, and column density of M_LTE = 107–793 M_☉, $\Delta {\overline{V}}=1.0\hbox{--}2.9$ km s⁻¹, and N(H₂) = 1.9–4.5 × 10²² cm⁻², with mean values of 341 M_☉, 1.7 km s⁻¹, and 2.5 × 10²² cm⁻², respectively. These quantities are comparable to those of cores forming massive stars (e.g., Tachihara et al. 2002; Saito et al. 2007) or star clusters (e.g., Higuchi et al. 2010; Shimoikura et al. 2013).

We also found that the masses of the filaments and subcores M_LTE are roughly consistent with M_vir as shown in Figure 14(a), indicating that they are likely to be in virial equilibrium. However, dispersion in the M_vir versus M_LTE diagram is large, probably because M_vir in Equation (1) is for an ideal sphere, but many of the filaments and subcores have an elongated shape. Actually, the difference between M_LTE and M_vir tends to be larger for the filaments and subcores with lower ellipticities, e.g., M_LTE is a few times higher than M_vir for many of the filaments with α ⩽ 0.5.

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In order to better investigate the gravitational stability of highly elongated filaments, we employed a simple model of isothermal cylindrical gas with infinite length (e.g., Stodólkiewicz 1963; Ostriker 1964; Inutsuka & Miyama 1992). The cylindrical gas can be gravitationally stable when the mass density ρ as a function of radius r from its axis follows the equation

$$\begin{equation} \rho (r) = {\rho _c}{\left[ {1 + {{\left({\frac{r}{{{H_0}}}} \right)}^2}} \right]^{ - 2}}, \end{equation} \tag{ 2 }$$

where H₀ is an effective radius written as

$$\begin{equation} {H_0} = \sqrt{\frac{2}{{\pi G{\rho _c}}}} c_s, \end{equation} \tag{ 3 }$$

and G, c_s, and ρ_c are the gravitational constant, the speed of sound, and the density at r = 0, respectively. Integration of Equation (2) from r = 0 to infinity yields M_cr, the mass per unit length of the gravitationally stable filaments, which can be expressed as

$$\begin{equation} M_{\rm cr} =\pi H_0^2 \rho _c= \frac{2c_s^2}{G}. \end{equation} \tag{ 4 }$$

If we assume that c_s is equal to the observed line width ΔV because the internal motion of the observed filaments is apparently dominated by turbulence rather than thermal motion, M_cr can be written in the following useful form:

$$\begin{equation} M_{\rm cr} = 465{\left({\frac{{\Delta V}}{{\rm km\,{s^{ - 1}}}}} \right)^2} M_\odot \, {\rm pc^{-1}}. \end{equation} \tag{ 5 }$$

Using the above equation, we calculated M_cr of the filaments by inserting ΔV in Table 7, assuming that we are observing the filaments orthogonally to their elongation. We also calculated the observed gas mass per unit length of the filaments as M_LTE/L, where L is the length of the filaments, estimated as $L=2R/\sqrt{\alpha }$, which can be compared with M_cr. We summarize these values in the last columns of Table 7 and compare M_cr and M_LTE/L in Figure 14(b). As seen in the figure, M_cr and M_LTE/L do not match for the subcores with high ellipticities (α > 0.5, shown by open circles) because M_cr is almost meaningless for the subcores. About half of the elongated filaments (α ⩽ 0.5, filled circles) have M_LTE/L close to M_cr, indicating that they can be gravitationally stable. The other half of the elongated filaments (such as No. 12) have M_cr a few times higher than M_LTE/L, suggesting that they might be gravitationally unbound and are dispersed into the interstellar medium.

However, we should note that the C¹⁸O spectra of such filaments with M_cr > M_LTE/L are often contaminated by a faint emission from other filaments at different velocities. It is difficult to separate them reliably to measure ΔV precisely at the present sensitivity of our C¹⁸O data. Such contamination can easily cause an overestimation of M_cr by a factor of a few. In fact, the difference between M_cr and M_LTE/L is larger for filaments with larger ΔV. A more sensitive C¹⁸O data set with a much better signal-to-noise ratio is needed to verify the gravitational stability of the filaments, especially for those appearing to be gravitationally unbound.

3.4.2. Velocity Distributions and Collisions of the Filaments

As can be seen in the C¹⁸O channel map in Figure 7, the filaments and subcores often have slightly different radial velocities. It is noteworthy that some of them show an apparent anticorrelation with one another in the channel map, i.e., a ridge of a filament corresponds to a valley or hole of another filament. A typical example of the anticorrelation is shown in Figure 15. Filaments labeled 4 and 5 (Table 7) in panel (b) of the figure correspond to a hole between subcore 2 and filament 6 in panel (a). Similarly, another filament labeled 7 in panel (b) corresponds to a hole in the fainter C¹⁸O intensity distribution in panel (a). We suggest that some of these anticorrelations represent collisions between the filaments and subcores.

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In order to find evidence for such collisions, we made position–velocity (PV) diagrams along the cuts labeled A–B, C–D, and E–F in panel (a) of Figure 15. The resulting diagrams are displayed in panels (c)–(e) of the figure. As seen in panel (c), filaments 4 and 5 have a similar velocity, and filament 6 is located in between, having a slightly shifted peak velocity by ∼0.5 km s⁻¹, and the three filaments appear physically connected to each other with fainter C¹⁸O emission. Another PV diagram in panel (d) for the cut C–D shows a similar feature. These features seen in the PV diagrams can be naturally accounted for if we assume that the filaments 4 and 5 used to be one continuous filament and the subcore 2 and filament 6 used to be another continuous filament, and they collided and passed through each other. The filaments 4 and 5 in panel (b) are shifted by ∼05 (= 0.12 pc) from the corresponding hole in panel (a). If we take the relative velocity of the filaments to be 0.5–1 km s⁻¹, as seen in panels (c) and (d), their collision may have occurred 0.1–0.2 Myr ago.

As described in Section 4, we have performed numerical simulations to investigate the formation and evolution of the filaments in a very massive core having the same total mass as L1004E (∼1 × 10⁴ M_☉). The simulations can reproduce filaments inside of the model core, and some of them collide with one another to form stars. It is noteworthy that the PV diagrams taken around such colliding filaments in the simulations (e.g., see Figure 19(c)) often appear very similar to those actually observed, as displayed in Figures 15(c) and (d), strongly suggesting that the anticorrelations seen in the C¹⁸O channel map (Figure 7) represent collisions of the filaments.

In the case of the anticorrelation seen around filament 7 in Figures 15(a) and (b), however, there is no abrupt jump in velocity in the PV diagram (see panel (c)). Although such a PV map can also be seen in our simulations for a filament drifting in the shear or for distinct filaments colliding with a small relative velocity, it is difficult to judge whether the anticorrelations in the channel maps are due to collisions of the filaments or are merely trace velocity gradients along a single filament without collisions.

We will further investigate the velocity structure of the filaments and subcores around the two IRAS sources. As shown in Section 3.3, IRAS 21025+5221 is a promising candidate YSO that is forming in subcore 1. There are ∼20 WISE sources in the vicinity (Figure 10), suggesting that the subcore has just started to form a small star cluster. A careful inspection of the C¹⁸O data and the WISE 12 μm image indicates that the subcore is part of a small filament extending in the northeast direction. We delineate it with the white dashed line in Figure 16(a) (labeled 1' in the circle). In addition, the small filament is crossed by another filament, which is an extension of filament 3 to the northwest of the IRAS source. As can be seen in the channel maps and the PV diagrams shown in panels (b)–(e) of Figure 16, these filaments (1' and 3) have different velocities that can be divided at V_LSR ≃ −1.8 km s⁻¹, and subcore 1 is located at their intersection where the two velocity components are merged. These pictures imply that the small filament 1' collided with filament 3 in the past, and they were merged at the intersection to form subcore 1. We suggest that the collision induced the formation of the subcore and then the small star cluster.

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In the case of the other IRAS source (21005+5217), filaments showing such apparent collisions are difficult to identify. Several YSOs including the IRAS source are located between filaments 7 and 12, as shown in Figure 17. Filament 7 has a branch labeled 7' in the figure that has the same radial velocity as the main body of the filament and extends to the west close to the boundary of filament 12. As seen in panel (e) of the figure, the branch and filament 12 have slightly different radial velocities by ∼0.5 km s⁻¹, and their interface exhibits a rather complex velocity field, which might reflect the interaction between the branch of filament 7 and filament 12. However, it is difficult to confirm the possible interaction and its influence on the formation of YSOs with only the present data set.

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To summarize, subcore 1 is very likely to have collided with a part of filament 3, which may have influenced the formation of IRAS 21025+5221 and the other ∼20 YSOs. In the case of IRAS 21005+5217, there are two filaments (7 and 12) showing complex velocity fields in the vicinity, although it is difficult to confirm their possible collision and its influence on star formation.

A clear evidence of collisions between molecular clouds was first found in Sgr B (Hasegawa et al. 1994; Sato et al. 2000), and since then, similar collisions as well as star formation induced by the collisions have been evidenced in some star-forming regions (e.g., Torii et al. 2011; Nakamura et al. 2014). However, these are collisions between clouds or clumps on much larger scales. Note that what we suggest in this paper is collisions between filaments inside a single massive dense core, which may be a direct trigger for the formation of massive stars or star clusters. We will discuss the origin of the colliding filaments in Section 4.

To summarize the results of our observations, L1004E has a huge mass of ∼1.1 × 10⁴ M_☉, and it consists of a number of filaments having a mass of 10²–10³ M_☉. Some of the filaments are apparently colliding with one another, and it is likely that some YSOs are forming around the regions where the filaments are colliding (e.g., around IRAS 21025+5221 in Figure 16).

It is probably natural to assume that such collisions induce star formation in the filaments. Actually, according to recent numerical simulations (Kitsionas & Whitworth 2007), collisions of spherical clumps can yield high SFEs of 10%–30%, which is a typical value for IR clusters (Lada & Lada 2003), but head-on collisions are needed for the high SFEs. Note that collisions of filaments can be partially regarded as equivalent to the head-on collisions of spherical clumps, and the formation and collisions of giant filaments in a massive core like L1004E may play a key role in cluster formation.

There is a problem, however, in understanding the collisions of the filaments. There have been a number of numerical simulations on the evolution of dense cores (e.g., Nakamura & Li 2005; Machida et al. 2006; Matsumoto & Hanawa 2011). In general, the simulations show that filaments can form easily in the cores, but they scarcely collide with one another. The core studied here might have extraordinary parameters (e.g., too high mass or density), or there might be an unknown mechanism causing their collisions that was not taken into account in the earlier simulations.

In order to find what physical conditions are needed for the collision of filaments, we performed self-gravitational hydrodynamics simulations using the adaptive mesh refinement technique (AMR) developed by Matsumoto (2007). For the initial conditions, we assumed a uniform core with a huge mass (1 × 10⁴ M_☉) and size (5 × 5 × 5 pc³) corresponding to an average density of n₀(H₂) ≃ 1.3 × 10³ cm⁻³, which are similar to those found in L1004E. Turbulence typically of an order of Mach 10 (∼1.9 km s⁻¹) is imposed in the initial core (see for detail Matsumoto & Hanawa 2011). The initial velocity field is incompressible with a power spectrum of P(k)∝k⁻⁴, generated following Dubinski et al. (1995), where k is the wave number. This power spectrum results in a velocity dispersion of σ(λ)∝λ^1/2, in agreement with the Larson scaling relations (Larson 1981). We calculated decaying turbulence with the self-gravity, and we did not consider a driving force of turbulence during the evolution (cf. Federrath et al. 2010). The gas was assumed to be isothermal with a temperature of 10 K. The evolution of the core was followed from t = 0 Myr to ∼1 Myr, and we observed the formation and evolution of the resulting filaments in two-dimensional velocity channel maps and three-dimensional isodensity maps that are equivalent to those in Figures 7 and 13.

The details of the simulations will be presented in a subsequent publication (T. Matsumoto et al. 2014, in preparation). In this paper, we provide a summary in the following points (1)–(3), and we show some snapshots of the evolution of the column densities observed from two different directions (X and Y) at some different epochs in Figures 18(a)–(f):

• 1.  
  Filaments are formed in the core at t ≃ 0.2 Myr, and stars are formed in the filaments spontaneously at t ≃ 0.6 Myr. In total, 209 stars are formed at the end of the simulations (t ≃ 1 Myr).
• 2.  
  Apparent collisions of the filaments are not observed throughout the calculation time.
• 3.  
  In the velocity channel maps, we sometimes observe a hole and bump showing anticorrelations at different velocities, which appears similar to those seen in Figures 7 and 15(a) and (b). The anticorrelations observed in the simulations, however, represent relatively large-scale transient structures drifting in the shear, but they are not well-defined filaments forming stars.We repeated the simulations for several sets of different initial parameters, but the results were essentially the same as described above. The holes and bumps on a rather large scale described in point (3) may account for a part of the observations, but we could not reproduce the well-defined colliding filaments forming stars with the above simulations, and we concluded that a simple increase of mass and size of the initial core does not result in collisions of the filaments. An additional condition is apparently needed to account for the collisions.After some trials, we finally found that the filaments can collide when there is a large velocity gradient across the initial core, in a sense compressing it. In other words, we have to force the filaments to collide by adding the velocity gradient. An example of the simulations incorporating the velocity gradient can be summarized as in the following point (4).
• 4.  
  If we assume a velocity gradient of dV/dX ≃ 2 km s⁻¹ pc⁻¹ in one direction across the initial core, which is provided by a sinusoidal flow with an amplitude of Mach 10,⁶ the filaments are formed at t ≃ 0.2 Myr in the same way as described in point (1), and some of them start to collide with one another (or across each other) to form stars at t ≃ 0.4 Myr. Stars are often formed at the intersections of the filaments, but they are also formed spontaneously along the ridge of dense filaments without collisions. Roughly 25% ± 5% of the stars are formed directly by collisions. In total, 479 stars are formed at the end of the simulation, which is ∼2.5 times larger than in the case of no initial velocity gradient.

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Some snapshots of the above simulations are displayed in Figures 18(g)–(l). Some characteristic features observed in the C¹⁸O data, i.e., the anticorrelations in the channel maps and the velocity jumps in the PV diagrams (Figures 15 and 16), are often seen in the simulated data. In Figure 19, we provide an example of such features as seen in the simulations. Panel (a) of the figure displays the column density distributions in different velocity ranges (colored in red and blue) exhibiting anticorrelations at some places. As shown in panel (b), the first star observed in the simulation (indicated by the star symbol) was formed in one of the blue filaments ∼0.1 Myr after another red filament (indicated by the ellipse with the dashed line) collided and passed through it. We can see a clear velocity jump in the PV diagram in panel (c) measured along the filaments. Panels (d) and (e) display the column density distributions in the two different velocity ranges in panel (a) separately, but the data are smoothed to a lower resolution (0.1 pc ≃ 25'' at 800 pc) similar to that of the C¹⁸O data. Some noticeable anticorrelations, including the one around the first star mentioned above, are indicated by boxes, and they appear similar to those seen in the C¹⁸O data in Figure 15.

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It is noteworthy that some elongated condensations in panels (d) and (e) of Figure 19 that would be regarded as one filament actually consist of a bunch of thinner filaments that can be seen at a higher spatial resolution (∼0.02 pc) in panel (a). Filaments observed in the C¹⁸O data probably have similar substructures, which would be resolved by interferometer observations with higher angular resolutions of a few arcseconds. Actually, such thin filaments were recently evidenced in the Taurus region by Hacar et al. (2013), who found bundles of small and gravitationally stable filaments with a typical length of ∼0.5 pc, which may correspond to the thin filaments observed in our simulations.

As we can see in Figure 18(k), the point of the simulations is that the velocity gradient generates a layer of high-density gas containing a number of filaments in the middle of the initial core. In such a layer, star formation should occur more frequently, not only because the free-fall time should be shorter because of the gas compression but also because the collision rate of the filaments should be higher. Though it is not easy to separate clearly the contributions of the two effects to star formation, roughly 25% ± 5% of the stars are formed directly by collisions of the filaments. This is consistent with the fact that there are 83 candidate YSOs selected in L1004E (see Section 3.2), and ∼20 of them are located where collisions of the filaments are inferred (Figures 16 and 17).

In the above simulations, the layer has a thickness of ∼0.5–1 pc, and its edge-on view appears to be similar to the C¹⁸O intensity map in Figure 2(a). We suggest that this is the case for L1004E. To be more precise, L1004E may not be a complete edge-on view of the layer, but it may be an oblique view. In fact, the ¹³CO channel maps (Figure 6) show that there is a velocity gradient of dV/dX ≃ 2 km s⁻¹pc⁻¹ in the direction orthogonal to the elongation of L1004E (i.e., from the southeast to northwest; see the panels for −4 km s⁻¹ < V_LSR < 0 km s⁻¹ in the figure).

For now, it is not yet very clear how large an initial velocity gradient is needed to cause the collisions of the resultant filaments, but it should be greater than that necessary to make the crossing time τ_cross shorter than the free-fall time τ_ff = 1.05(n/10³ cm⁻³)^−1/2 Myr of the initial core. In the case of L1004E, τ_ff ∼ 1 Myr for the average density n(H₂) ≃ 1.3 × 10³ cm⁻³, and τ_cross ∼ 0.5 Myr if we take τ_cross as the reciprocal of the observed velocity gradient dV/dX (≃ 2 km s⁻¹pc⁻¹).

It is not clear either how the initial velocity gradients influence the final SFEs of the cores because we only have results for the two cases with (dV/dX ≃ 2 km s⁻¹pc⁻¹) and without (dV/dX = 0 km s⁻¹pc⁻¹) the velocity gradients at the moment. We would expect higher SFEs for larger velocity gradients because the initial cores can be compressed more sufficiently, but this should be clarified by additional simulations.

The velocity gradient necessary for collisions of the resultant filaments can be caused by an external effect, e.g., shock fronts of supernova remnants (SNRs) or HII regions, compressing the initial core. Actually, there have been a number of studies on such molecular clouds influenced by SNRs (e.g., Tatematsu et al. 1987, 1990; Moriguchi et al. 2001) or HII regions (e.g., Dobashi et al. 2001; Toujima et al. 2011; Shimoikura et al. 2013; Chibueze et al. 2013). It is noteworthy that the Cyg OB 7 molecular cloud has been suggested to be interacting with the nearby SNR HB 21 (cataloged as G89.0+4.7 by Green 1998) by Tatematsu et al. (1990). In addition, there are some other SNRs (i.e., DA 530, DA 551, and 3C434.1) in the vicinity of the Cyg OB 7 cloud (Dobashi et al. 1994, see their Figure 11). Although the distances to these SNRs have not been determined well (e.g., Mavromatakis et al. 2007), it is very possible that they have influenced the initial velocity fields of L1004E. Other than the influence of the SNRs and HII regions, stellar winds from nearby OB stars can also provide a similar effect on the velocity field of the initial cores. Note that several young OB stars have been found located 5–10 pc away from L1004E (Reipurth & Schneider 2008).

In Figure 20, we summarize the suggested scenario for the formation of the colliding filaments. The collision of the filaments in massive cloud cores may be essential for cluster formation. The ubiquitousness of the scenario, however, has to be confirmed, especially by observing other massive star-forming regions or cluster-forming regions such as M 17 and Ori KL, because, at the moment, L1004E is probably the only core where such collisions of giant filaments are found.

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We have carried out millimeter-wave observations of a massive dense core L1004E in the Cyg OB 7 molecular cloud in the various molecular lines ¹²CO, ¹³CO, C¹⁸O, CCS, HC₃N, and NH₃ using the 45 m telescope at the Nobeyama Radio Observatory. The main findings of this paper are summarized below.

• 1.  
  The molecular observations revealed the total extent and velocity structures of L1004E. Based on the C¹⁸O data, we find that the core has a huge mass and size of 1.1 × 10⁴ M_☉ and ∼5 × 2 pc², respectively. The core is also characterized by the cold temperature ∼10 K as measured in the ¹²CO and NH₃ molecular lines. The maximum column density observed is N(H₂) ≃ 5 × 10²² cm⁻² at the peak position of the C¹⁸O intensity map. The turbulent motion measured from the line width varies in the range ΔV(C¹⁸O) ≃ 1–3 km s⁻¹ over the core.
• 2.  
  We searched for candidate YSOs in the IRAS PSC and found that there are only two sources that can be regarded as promising YSOs. They are IRAS 21005+5217 and 21025+5221. We employed a stellar model developed by Robitaille et al. (2007) to access the age, mass, and luminosity of the IRAS sources. We searched for YSOs also in the WISE PSC, which is much more sensitive than the IRAS PSC, by using the selection criteria proposed by Koenig et al. (2012). If we disregard one of their criteria to exclude AGNs, 83 candidates for YSOs were found in the observed region, and ∼20 of them are concentrated in a condensation around IRAS 21025+5221. Assuming that all of the WISE sources are real YSOs, we estimated the star-formation efficiency of the entire core to be SFE ≲ 1% at most.
• 3.  
  We find that the core consists of a number of filaments and some core-like structures. In the velocity channel maps of C¹⁸O, these filaments appear to be colliding with one another, and some candidate YSOs are located near the intersections of the filaments. We identified 12 major filaments and core-like condensations and estimated their masses to be 10²–10³ M_☉. We investigated their gravitational stability to find that at least half of the filaments and core-like condensations are likely to be in virial equilibrium, and the others might be gravitationally unbound.
• 4.  
  Using the adaptive mesh refinement technique (Matsumoto 2007), we performed numerical simulations to reproduce the collisions of the filaments. For the initial conditions of the core, we assumed a high mass, size, and density similar to those observed toward L1004E. The results of the simulations indicate that the filaments are formed in the core, but they never collide with one another during their evolution. After some trials, we finally found that the filaments can collide only when there is a large velocity gradient in the initial core, in a sense compressing it, which can be generated by an external energetic effect such as the shock fronts of SNRs. There are actually some SNRs in the vicinity of the Cyg OB 7 molecular cloud, including HB 21 which has been suggested to be interacting with the cloud. We suggest that L1004E was influenced by such an external effect (possibly by HB 21) to have the initial velocity gradient, which results in the formation of the colliding filaments.

This research was financially supported by Grants-in-Aid for Scientific Research (Nos. 22340040, 23540270, 23540270, 24244017, 24700866, 26287030, 26350186, 26400233, and 26610045) from the Japan Society for the Promotion of Science (JSPS) and also by the Mitsubishi Foundation. The 45 m radio telescope is operated by NRO, a branch of the National Astronomical Observatory of Japan. Numerical computations were carried out on Cray XC30 at the Center for Computational Astrophysics, National Astronomical Observatory of Japan. This research has made use of the NASA/IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. The Wide-Field Infrared Survey Explorer is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory (JPL), California Institute of Technology (Caltech), funded by the National Aeronautics and Space Administration (NASA). The Two Micron All Sky Survey is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.

We derived the total mass of the observed core as summarized in the following. The method we used assumes the LTE, and it is a standard way to derive the total molecular mass from the C¹⁸O emission line. Details of the method can be found in the literature (e.g., Shimoikura et al. 2012).

In general, the observed brightness temperature of a certain molecular line T_mb(X) (e.g., X = C¹⁸O, ¹²CO, etc.) can be expressed as

$$\begin{equation} {T_{\rm mb}}(X) = [ {J({T_{\rm ex}}) - J({T_{\rm bg}})} ] [ {1 - {{\mathop {\rm e}\nolimits } ^{ - \tau (X)}}} ], \end{equation} \tag{ A1 }$$

where J(T) = (T₀/exp (T₀/T) − 1), and T₀ is a constant(T₀ = 5.27 K for C¹⁸O and 5.53 K for ¹²CO). T_ex and T_bg are the excitation temperature and the cosmic background (2.7 K), respectively, and τ(X) is the optical depth. We first estimated T_ex at each observed position by solving the above equation for T_mb(¹²CO) measured at the peak velocity of the C¹⁸O spectra assuming τ(¹²CO)≫1. We then derived τ(C¹⁸O) and N(C¹⁸O) and converted N(C¹⁸O) to N(H₂) to estimate the total mass M_core by summing up the derived N(H₂) over the observed area. The process of the derivation can be summarized in the following equations:

$$\begin{equation} \tau ({{\rm C^{18}O}} ) = - \ln \left[ {1 - \frac{{{T_{\rm mb}}({\rm C^{18}O})}}{{J({T_{\rm ex}}) - J({T_{\rm bg}})}}} \right] \end{equation} \tag{ A2 }$$

$$\begin{equation} N({\rm C^{18}O}) = \frac{{C_0}{T_{\rm ex}}}{{1 - \exp (- \frac{{T_0}}{{{T_{ex}}}})}}\int {\tau ({\rm C^{18}O})dv} \end{equation} \tag{ A3 }$$

$$\begin{equation} N({\rm H_2}) = \left[ {\frac{{N({\rm C^{18}O})}}{{1.8 \times {{10}^{14}}}} + 3.7} \right] \times {10^{21}} \end{equation} \tag{ A4 }$$

$$\begin{equation} {M_{\rm core}} = \mu {m_{\rm H}}S_{\rm pix}\sum {N({\rm H_2})} \end{equation} \tag{ A5 }$$

where N(C¹⁸O) and N(H₂) are in units of cm⁻², and the constant C₀ is 2.52 × 10¹⁴ cm⁻² K⁻¹ (km s⁻¹)⁻¹ for the C¹⁸O(J = 1–0) emission line. μ, m_H, and S_pix in the last equation are the mean molecular weight taken to be 2.4, the hydrogen mass, and the area of the pixels of the C¹⁸O map (10'' × 10'' ≃ 1.432 × 10³⁴ cm² at the assumed distance 800 pc). A summation in the right side of Equation (A5) is made for the total area observed in C¹⁸O, as shown in Figure 2(a). Equation (A4) is derived from an empirical relationship between A_V and N(C¹⁸O) (Frerking et al. 1982) as well as between A_V and N(H₂) for R_V = 3.1 (Bohlin et al. 1978).

Note that N(H₂) calculated using Equation (A4) and then M_core calculated using Equation (A5) may be the minimum estimates for the true values because C¹⁸O is known to be depleted onto dust grains in a very dense cloud interior like L1004E (e.g., Bergin et al. 2002; Tafalla et al. 2002; Lada et al. 2007), whereas we assume the linear N(C¹⁸O)–N(H₂) conversion relation based on the results of Frerking et al. (1982), whose measurements were done in much less dense regions. However, we shall use the simple conversion relation in Equation (A4) in this paper because it is difficult at the moment to assess precisely how much the depletion of C¹⁸O is occurring in L1004E.