CARMA LARGE AREA STAR FORMATION SURVEY: STRUCTURE AND KINEMATICS OF DENSE GAS IN SERPENS MAIN

The star formation process spans a wide range of spatial scales: from molecular clouds on parsec scales, to envelopes around young stellar objects on few thousand AU scales, to circumstellar disks on 1–100 AU scales. Low-density gas (∼10² cm⁻³) in the interstellar medium forms denser structures in molecular clouds (∼10³ cm⁻³), which evolve to higher density structures (∼10⁵ cm⁻³) at small scales to enable the formation of stars and clusters. This general picture represents the broad path from low density gas to star formation; however, a comprehensive understanding of the roles of turbulence, magnetic fields, and gravity at all spatial scales in driving this evolution is still needed. While several theoretical scenarios have been proposed to address this need (Mouschovias & Spitzer 1976; Basu & Mouschovias 1995; Mac Low & Klessen 2004; McKee & Ostriker 2007), observational tests have been insufficient to directly probe the conditions for star formation from few thousand AUs to parsecs to produce an integrated picture. Previous surveys of nearby star forming regions have been carried out with the Herschel Gould Belt Survey (e.g., André et al. 2010), the Spitzer Legacy c2d project (e.g., Evans et al. 2003; Harvey et al. 2006; Evans et al. 2009), and the JCMT Legacy Survey (e.g., Buckle et al. 2010). These surveys have provided important insights into star formation from infrared to submillimeter regimes. However, there has been a lack of large-area mapping (at parsec-scales) of the molecular gas with high angular resolution (few thousands of AU scales) and sensitivity (see Busquet et al. 2013) to probe the gas structure and density in detail.

The CARMA Large Area Star Formation Survey (CLASSy), a survey toward five star-forming regions in the nearby Gould Belt, addresses this gap. By combining the interferometric and single-dish data with the full CARMA 23 antennas, CLASSy observed the emission from three high density gas tracer molecules in target regions over a broad range of spatial scales (from few parsecs to few thousand AUs): N₂H⁺(1–0), HCO⁺(1–0), and HCN(1–0). The primary goals of the survey are to: (1) characterize the internal structure and dynamics of star-forming cores, (2) investigate the relationship between dense cores and their natal molecular clouds, and (3) test theoretical scenarios for star formation. The target regions, NGC 1333, Barnard 1, and L1451 in Perseus, and Serpens Main and Serpens South, present a wide range of star formation activities from relatively quiescent regions to active star-forming clusters. Storm et al. (2014; hereafter Paper I) presents a detailed description on the CLASSy project and the structures of dense gas in Barnard 1. In this paper, we present results of the Serpens Main region. We focus on the global structure of dust and gas, including the properties of dust and gas condensations, gas structures and kinematics, and filamentary structures.

Serpens Main is a young cluster active in star formation (see Eiroa et al. 2008, and references therein). The dust and gas in Serpens Main are mainly concentrated in two subclusters, the NW and SE subclusters (Loren et al. 1979; Casali et al. 1993; Davis et al. 1999; McMullin et al. 2000; Kaas et al. 2004). Figure 1 shows Serpens Main and the two subclusters at 250 μm from Herschel observations (André et al. 2010). The gas mass estimated in the Serpens Main region is about 97 M_☉ in the NW subcluster and about 144 M_☉ in the SE subcluster using a distance of 415 pc (Olmi & Testi 2002).

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A few hundred YSOs were identified in Serpens Main based on infrared observations including the Spitzer IRAC and MIPS bands (Harvey et al. 2006; Evans et al. 2009), and ISOCAM (Kaas et al. 2004). Previous studies have shown a high fraction of protostars to stars with disks in Serpens Main (Kaas et al. 2004). For example, Winston et al. (2007) discovered a high ratio of 48% between protostars (22 Class 0/I sources, 16 flat-spectrum sources) and pre-main-sequence stars with disks (62 Class II sources, 17 transition disks) in Serpens Main. The younger sources (Class 0/I and flat-spectrum sources) are mostly found in the central NW and SE subclusters, while more evolved sources (Class II/III) are dispersed over the larger region (e.g., Harvey et al. 2007). The star formation activities have been suggested to have undergone multiple phases (Kaas et al. 2004; Casali et al. 1993): Class II and Class III sources were formed and dispersed 2 × 10⁶ yr ago, and the current burst of Class 0 and I sources started ∼10⁵ yr ago. The SE subcluster is suggested to be more evolved than the NW subcluster due to its higher fraction of Class II/III YSOs (Winston et al. 2007).

Submillimeter to millimeter-wavelength observations have revealed a number of embedded sources as well. Davis et al. (1999) observed the Serpens Main region at 450 μm and 850 μm with the JCMT SCUBA array and identified 11 submillimeter sources. Sadavoy et al. (2010) found four starless cores in the field. Enoch et al. (2007) identified 12 continuum sources at 1 mm with Bolocam. Interferometric observations with high angular resolutions at 3 mm (Testi & Sargent 1998; Williams & Myers 2000) found continuum sources coincident with the submillimeter cores. These sources are concentrated in the two subclusters, and infall motions have been suggested toward several of these sources (Gregersen et al. 1997; Williams & Myers 2000; Olmi & Testi 2002). A number of outflows have been observed to be associated with these young sources (Eiroa et al. 1992; White et al. 1995; Wolf-Chase et al. 1998; Davis et al. 1999; Testi et al. 2000; Graves et al. 2010).

Despite some similarities in the dust emission in the two subclusters, the gas kinematics and temperatures are distinct (Testi et al. 2000; Duarte-Cabral et al. 2010). The NW subcluster has a more uniform velocity field, while the SE subcluster has a large-scale velocity gradient in the E–W direction (Graves et al. 2010). The velocity gradient was interpreted as rotation (Olmi & Testi 2002), but it has also been suggested to be the result of a cloud–cloud collision (Duarte-Cabral et al. 2011).

There are various estimates in the literature for the gas temperature in Serpens Main. Gas temperature in the two subclusters has been estimated between 12 K and 19 K based on NH₃ (Ungerechts & Guesten 1984; Curiel et al. 1996; Levshakov et al. 2013). Earlier works reported 25–27 K based on CO observations (Loren et al. 1979), and 22–35 K based on dust emission at infrared (McMullin et al. 1994; Hurt et al. 1996). Based on C¹⁷O(1–0) and C¹⁸O(1–0) observations, Duarte-Cabral et al. (2010) concluded that the NW subcluster presents a homogeneous 10 K gas temperature, while the gas temperature in the SE subcluster is higher between 10 K and 20 K. In this paper, we assume a mean gas temperature of 20 K for the overall cloud (McMullin et al. 2000), and 13 K for regions that do not show active star formation activities (Levshakov et al. 2013).

The distance to the Serpens region has been under debate (see the discussion in Eiroa et al. 2008; Winston et al. 2010). Several studies adopted 260 ± 10 pc from Straižys et al. (1996) based on the spectral and luminosity class of the observed stars. Recently, a new estimate of 415 ± 5 pc was found based on trigonometric parallax with VLBI observations with the young stellar object EC 95 in the SE subcluster of Serpens Main (Dzib et al. 2010). Given the accuracy of the VLBI observations, we adopt a distance of 415 pc in this paper.

Figure 2 shows the integrated intensity map from the strongest hyperfine line in the N₂H⁺(1–0) observations. There are two main features shown in the map. First, the peaks in the integrated intensity map are concentrated on the NW and SE subclusters. The N₂H⁺(1–0) gas peaks are distributed over the extent of the NW subcluster, while in the SE subcluster the emission peaks are more concentrated in the central region. Second, prominent filamentary structures are observed in the regions that were not well resolved by previous observations, especially in the SE subcluster. In particular, the southern filament, which was not well resolved previously (e.g., Davis et al. 1999; André et al. 2010), has been resolved into two narrower filaments for the first time.

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The region in the northwest corner of Figure 2 (centering at α_J2000 = 18^h29^m318, δ_J2000 = 01°18'445) shows N₂H⁺(1–0) gas emission which peaks at ∼2 Jy beam⁻¹ in the strongest hyperfine line, about 50% of the typical N₂H⁺(1–0) gas peaks (∼4 Jy beam⁻¹) in the central regions of the NW and SE subclusters. The HCO⁺(1–0) emission in this region only shows in 3 channels with a weak peak of ∼1 Jy beam⁻¹, 20% of a typical peak of ∼5 Jy beam⁻¹ in the central regions of the two subclusters. The peak intensity in the strongest HCN(1–0) hyperfine line at this region is about 1.2 Jy beam⁻¹, 40% of the typical HCN(1–0) emission (∼3 Jy beam⁻¹) in the two subclusters. In general, this region shows weak emission compared to the central regions in the two subclusters for all the three molecules. This paper will mainly focus on the two subclusters in the following sections.

Figure 3 shows the HCO⁺(1–0) and HCN(1–0) integrated intensity maps of the two subclusters. The two molecular lines exhibit similar emission distributions, which are more extended than the N₂H⁺(1–0) emission; however, the filamentary structures are not prominent. In particular, the long southern filament is not obvious in the integrated intensity maps but weak narrow lines are present along some parts of the filament. The strongest HCO⁺(1–0) and HCN(1–0) emission peaks are associated with a few of the eleven submillimeter cores (SMM1–SMM11) identified by Davis et al. (1999). The N₂H⁺(1–0) emission peaks are also associated with several submillimeter cores (see discussions in Section 4.1).

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The observed differences in the emission distributions of N₂H⁺(1–0), HCO⁺(1–0), and HCN(1–0) are likely dominated by differences in their abundance distributions due to chemical effects. N₂H⁺(1–0) favors cold dense gas where CO becomes depleted because chemical reaction with CO is a major destroyer of N₂H⁺(1–0) (Bergin et al. 2001, 2002). HCO⁺(1–0) favors environments with significant ionization fraction, which tends to be warm gas (Godard et al. 2010). HCN(1–0) is prominent in warm gas and depletes with CO in cold dense gas (Tafalla et al. 2006). All three molecular transitions have critical densities around few times 10⁵ cm⁻³ (Evans 1999), so their emissivity peaks in dense gas. However, all three are resonance transitions (the lower level is the ground state), so lower density gas can emit and absorb in these J = 1 → 0 lines. For HCO⁺(1–0) and HCN(1–0), the fact that their abundance remains high or increases in the lower density gas means that their emission can trace gas from density 10⁴ to >10⁶ cm⁻³, and the lower density gas can absorb away emission from high density gas. The chemical selectivity of N₂H⁺(1–0) favors dense gas which minimizes the contributions from, and impact of, lower density gas. The focus of the analysis in this paper will be on the N₂H⁺(1–0) emission because, of the three lines observed, it is the best dense gas tracer.

HCO⁺(1–0) and HCN(1–0) have been considerably used in detecting outflow activity (e.g., Fernández-López et al. 2013). Several sources including SMM1, SMM2, SMM3, SMM4, SMM8, and SMM9 have been suggested to be associated with outflows from observations of CO and its isotopes (White et al. 1995; Graves et al. 2010). We show an example of outflow associated with SMM11 in Figure 4. The left panel shows the integrated intensity map of the HCO⁺(1–0) redshifted emission from SMM11 (the star symbol), and the right panel shows the integrated intensity map of the HCN(1–0) redshifted and blueshifted emission. For HCN(1–0), the outflow is identified based on the main component of the three hyperfine lines. HCN(1–0) clearly traces a collimated outflow powered by SMM11 in the center. The outflow is in a northeast–southwest direction with a P.A. of about 75°. This direction is nearly perpendicular to the southern filament. The red lobe has extended emission to the north; a similar morphology in the red lobe is also seen in the HCO⁺(1–0) map. However, the blue lobe is not detected with HCO⁺(1–0). An N₂H⁺(1–0) peak shown in the gray-scale image is very close to SMM11. The relation between the N₂H⁺(1–0) emission peak and SMM11 is not clear since the emission enhancement in N₂H⁺(1–0) might be due to the two overlapping filaments (Section 3.2). Also, the small offset between the N₂H⁺(1–0) emission peak and the source may be due to chemical effects from the central heating of the source (e.g., Busquet et al. 2011; Lippok et al. 2013).

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Since the N₂H⁺(1–0) gas emission is less contaminated by lower density gas and by outflows like HCO⁺(1–0) and HCN(1–0) (Section 3.1), we use N₂H⁺(1–0) as the main probe for studying dense gas kinematics. We obtained the centroid velocities (V_lsr) and velocity dispersions (σ) of N₂H⁺(1–0) by fitting all the seven hyperfine lines simultaneously using Gaussian profiles on a pixel-by-pixel basis. The fitting method and the detailed algorithm are described in Paper I. We have incorporated the pixels with (1) a peak signal-to-noise ratio larger than 5 in the spectrum, and (2) a signal-to-noise ratio larger than 4 in the integrated intensity map. Pixels below the threshold are blanked in the centroid velocity and velocity dispersion maps. The left panel in Figure 5 shows a typical N₂H⁺(1–0) line profile with the seven hyperfine components and fitted centroid velocities.

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Multiple velocity components are observed along several lines of sight in both subclusters; it is most evident in the isolated component in the hyperfine structure. We performed two-component line fitting in the locations with two velocity components along the line of sight with the inclusion of a second set of hyperfine lines. The stronger component in the peak intensity with the two-component fitting was chosen as the primary component shown in the kinematic maps. The most obvious example of two velocity components is at the location of SMM11. The right panel in Figure 5 shows the spectrum at that location; the V_lsr of the two components are 7.14 km s⁻¹ and 8.66 km s⁻¹. We do not see a correlation between the locations of two-velocity components and those of YSOs or filaments.

The left panel in Figure 6 shows the centroid velocity map from the fitting of the N₂H⁺(1–0) data. As seen in the centroid velocity map, the velocity fields in the two subclusters are distinct. The NW subcluster presents relatively uniform velocity fields, while the SE subcluster has a more complicated velocity pattern. Most of the gas in the NW subcluster has centroid velocities between 8.0 and 8.5 km s⁻¹. Most of the SE subcluster shows more blueshifted centroid velocities compared to the NW subcluster. The gas kinematics near SMM11 (shown as the star symbol in the centroid velocity map) reveal two filamentary structures with different velocities (V_lsr ∼ 7.14 and 8.66 km ⁻¹, respectively), suggesting that these two filaments are distinct and overlapped along the line of sight at the position of SMM11. The northwest corner in Figure 2 has centroid velocities around 8.5 km s⁻¹ as shown in the subplot.

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The center of the SE subcluster has three main regions with different velocities: the blueshifted area in the southeast, the redshifted area in the southwest, and the area in the north with intermediate velocities. The two crossing filaments in the south appear to have blueshifted and redshifted velocities similar to the southeast blueshifted and southwest redshifted areas, respectively, suggesting that the southeast area may be connected to the blueshifted filament, and the southwest area possibly connects to the redshifted filament.

The right panel in Figure 6 shows the velocity dispersion map, also obtained from the N₂H⁺(1–0) fitting. The velocity dispersions have a median value of 0.24 km s⁻¹ and a mean value of 0.30 km s⁻¹. Assuming a gas temperature of 20 K for the overall cloud (McMullin et al. 2000), which suggests an isothermal sound speed of ∼0.27 km s⁻¹, about 60% of the region display a subsonic to sonic level velocity distribution along the line of sight. In the SE subcluster, the central region appears to have larger velocity dispersions (typically >0.5 km s⁻¹) than the surrounding filaments (typically <0.2 km s⁻¹). The southern filaments are especially quiescent with velocity dispersions ∼0.1 km s⁻¹. The northwest corner in Figure 2 has subsonic velocity dispersions as shown in the subplot.

We identified 18 continuum sources at 3 mm (S1–S18: Table 3) as shown in Figure 7 (left panel). The sources were identified based on two criteria: (1) peak brightness ⩾5σ or (2) peak brightness ⩾3σ and an association with an emission peak in at least one of the following bands: Spitzer 8, 24, 70  μm, Herschel 160, 250, 350, 500  μm, where the peak must be within half of the largest beam among the bands showing detections. The sources are mostly concentrated in the NW and SE subclusters, consistent with previous results (e.g., Davis et al. 1999; Williams & Myers 2000). S1 and S2 are in more isolated positions. There are 8 sources in the NW subcluster, and 8 sources in the SE subcluster. Testi & Sargent (1998) reported 32 continuum sources above 4.0 mJy beam⁻¹ with a sensitivity of 0.9 mJy beam⁻¹. All of our sources are detected by Testi & Sargent (1998) except S1 and S2 (outside their mapping area). However, we could not confirm most of their sources with peaks of ∼4.0 mJy beam⁻¹, which corresponds to 2.5–3σ levels in our map.

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The positions, major and minor axes, aspect ratios, peak brightness, and total flux densities of these sources are given in Table 3. For sources with >5σ detections, the quantities were determined by Gaussian fits to the emission. For <5σ sources, we report the peak brightness and omit major, minor axes and total flux densities. S7 (in the NW subcluster) has the highest brightness among all the sources and S11 (in the SE subcluster) has the second highest brightness. The geometric sizes range from ∼1700 AU to ∼6300 AU with a mean value of 2700 AU. S4 is particularly extended and may be multiple sources. The aspect ratios range from 1.1 to 4.2 with an averaged value of 2.0, suggesting that the sources are elongated and not spherical.

The right panel in Figure 7 shows a comparison of continuum sources from previous observations at multiple wavelengths including the SCUBA 850 μm submillimeter sources from Davis et al. (1999), the Bolocam 1 mm sources from Enoch et al. (2007), and the Spitzer YSOs from Evans et al. (2009). Davis et al. (1999) identified 11 submillimeter sources (SMM1–SMM11) and three "sub-clumps" (a, b, and c) associated with SMM9 (S68N), which were resolved by high angular resolution observations carried out by Williams & Myers (2000) using BIMA at 3 mm (S68Na–S68Nd). All of the submillimeter sources have correspondences to 3 mm sources, except for S68Nd. The majority of these submillimeter sources are associated with Class 0/I objects (Winston et al. 2007; Sadavoy et al. 2010) with outflow activities (e.g., Davis et al. 1999; Graves et al. 2010). Despite the good correlation between the submillimeter and 3 mm sources, not all the submillimeter sources are associated with the 1 mm sources; this is possibly due to the limitations from the sensitivity and the angular resolution (30'') in the Bolocam observations. Only three sources (S7, S14, and S15) have all the counterparts in Spitzer YSOs, the submillimeter cores, the 1 mm cores, and the 3 mm cores.

We calculate the masses of the continuum sources with the relation:

$$\begin{equation} M=\frac{d^{2}F_{\nu }}{B(T_{d})\kappa _{\nu }}, \end{equation} \tag{ 1 }$$

where F_ν, d, κ_ν, and B_ν(T_d), are respectively the total observed flux density, distance, grain opacity, and blackbody intensity at dust temperature, T_d. We adopt T_d = 20 K; the filament temperatures (Section 6) are 12–14 K, so we assume the average dust temperature near the protostar is slightly higher. We estimate κ_ν at observed wavelength using κ_ν = 0.1(ν/10³ GHz)^β cm² g⁻¹ (Beckwith et al. 1990) with an assumed dust-to-gas ratio of 100. Assuming β ∼ 1.5, we obtain κ_ν = 0.0027 cm²g⁻¹ at 3.3 mm. The masses of the sources <5σ are calculated from the peak brightness and represent lower limits. The resulting masses are summarized in Table 3. Most of the sources have masses ranging from 0.3 to 3.5 M_☉. The two brightest sources, S7 and S11, have masses of 11.3 M_☉ and 5.9 M_☉, respectively. Uncertainties in κ_ν, dust temperature, β, and distance imply that the masses have systematic uncertainties at the factor of two level.

Figure 8 shows the resulting tree from the nonbinary dendrogram analysis. The tree structure beginning at branch 59 and extending upward represents the SE subcluster, while the structure beginning at branch 60 represents the NW subcluster. To better compare the intensities of the leaves and their properties, we differentiate stronger leaves from weaker leaves using a contrast criterion: "high-contrast" leaves have peak intensities at least 6σ in intensity above the level of their nearest branch, while "low-contrast" leaves have peak intensities below 6σ (contrast values are listed in Table 4). There are 12 high-contrast leaves and 33 low-contrast leaves. We further define "sprouts" as the leaves directly growing out from the base tree (colored as gray in Figure 8). All the sprouts are low-contrast leaves in Serpens Main. Figure 9 illustrates the two-dimensional footprints of leaves (integrated from their three-dimensional structures) overlaid on the integrated intensity map of N₂H⁺(1–0). The NW subcluster has a similar number in high-contrast and low-contrast leaves, while the number of high-contrast leaves is noticeably less than that of the low-contrast leaves in the SE subcluster. The sprouts are mostly distributed in the outskirts of the two subclusters.

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Table 4. N₂H⁺(1–0) Dendrogram Leaf and Branch Properties

No.	R.A.a	Decl.a	Maj. Axisa	Min. Axisa	P.A.a	Axisb	Fillingc	Sized	〈Vlsr〉e	ΔVlsrf	〈σ〉g	Δσh	Pk. Int. i	Contrastj	Levelk
	(J2000)	(J2000)	('')	('')	($\deg$)	Ratio	Factor	(pc)	(km s−1)	(km s−1)	(km s−1)	(km s−1)	(Jy beam−1)	(σ)
Leaves
0	18:30:03.2	+01:14:36.5	37.3	14.7	146.9	0.39	0.76	0.047	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.56	2.7	0
1	18:29:44.6	+01:17:04.4	29.6	25.8	61.3	0.87	0.61	0.056	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.58	2.8	0
2	18:29:57.0	+01:13:09.4	20.5	7.8	40.4	0.38	0.86	0.025	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	1.54	3.8	5
3	18:30:02.0	+01:11:37.1	32.1	9.2	74.8	0.29	0.74	0.035	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.51	2.2	0
4	18:29:43.7	+01:16:42.5	40.0	21.4	61.6	0.53	0.60	0.059	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.54	2.4	0
5	18:29:30.8	+01:18:58.4	70.5	38.4	148.5	0.54	0.79	0.105	8.83(2)	0.12(1)	0.12(0)	0.03(0)	1.95	14.0	1
6	18:29:59.3	+01:10:09.8	77.5	18.0	10.0	0.23	0.67	0.075	8.61(0)	0.04(0)	0.11(0)	0.02(0)	1.48	6.2	4
7	18:30:00.4	+01:11:26.7	76.9	11.6	0.7	0.15	0.79	0.060	8.48(1)	0.05(1)	0.19(1)	0.03(0)	1.27	4.3	4
8	18:30:04.8	+01:14:49.8	29.0	16.7	35.2	0.58	0.68	0.044	7.95(9)	0.21(8)	0.28(7)	0.16(6)	0.60	2.2	1
9	18:29:49.6	+01:15:18.3	39.0	22.2	145.3	0.57	0.75	0.059	8.52(3)	0.11(2)	0.35(3)	0.12(2)	2.85	12.8	4
10	18:29:52.0	+01:15:59.8	42.5	9.1	11.1	0.22	0.73	0.040	8.52(1)	0.04(1)	0.19(0)	0.02(0)	1.71	3.3	5
11	18:30:02.1	+01:08:44.0	94.7	28.3	28.7	0.30	0.74	0.104	8.44(1)	0.04(0)	0.10(0)	0.02(0)	0.95	5.3	1
12	18:30:00.6	+01:10:21.2	41.2	14.5	3.6	0.35	0.85	0.049	8.36(1)	0.04(1)	0.11(0)	0.02(0)	1.44	5.8	4
13	18:29:48.7	+01:14:31.9	41.4	29.3	133.4	0.71	0.56	0.070	8.41(8)	0.17(7)	0.48(7)	0.16(6)	0.62	3.2	0
14	18:29:49.4	+01:15:40.2	23.6	18.0	105.5	0.76	0.77	0.041	8.17(3)	0.06(2)	0.25(1)	0.03(1)	1.82	3.3	4
15	18:29:44.5	+01:16:00.7	28.6	15.8	95.8	0.55	0.74	0.043	8.42(3)	0.07(2)	0.28(1)	0.04(1)	0.71	3.2	1
16	18:29:50.6	+01:16:50.0	84.4	22.6	27.7	0.27	0.58	0.088	8.53(2)	0.12(1)	0.21(1)	0.05(0)	2.05	6.5	5
17	18:29:48.4	+01:16:39.3	42.7	30.3	128.5	0.71	0.76	0.072	8.58(3)	0.15(2)	0.30(2)	0.13(2)	2.22	9.0	4
18	18:29:51.5	+01:17:42.8	47.5	18.1	29.9	0.38	0.64	0.059	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.54	2.5	0
19	18:29:28.4	+01:18:31.0	26.4	18.2	59.7	0.69	0.68	0.044	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.79	3.4	1
20	18:29:56.4	+01:13:08.2	26.9	12.3	76.9	0.46	0.89	0.037	8.12(4)	0.10(3)	0.37(4)	0.09(3)	1.99	7.9	5
21	18:30:00.1	+01:13:10.2	13.3	10.8	40.9	0.81	0.88	0.024	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.87	2.6	3
22	18:30:09.3	+01:13:23.8	22.2	15.0	39.1	0.68	0.78	0.037	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.82	4.1	1
23	18:29:56.7	+01:13:41.3	22.5	8.2	24.6	0.36	0.82	0.027	8.00(2)	0.04(2)	0.22(2)	0.05(2)	1.51	2.5	8
24	18:29:48.6	+01:13:38.4	24.0	16.5	125.6	0.69	0.85	0.040	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.53	2.3	0
25	18:29:53.3	+01:13:59.9	79.3	29.3	77.8	0.37	0.65	0.097	8.13(1)	0.10(1)	0.18(0)	0.03(0)	1.48	6.2	5
26	18:29:52.2	+01:15:24.3	45.6	20.5	43.3	0.45	0.89	0.061	7.99(3)	0.12(2)	0.20(1)	0.06(1)	2.55	12.0	4
27	18:29:57.1	+01:15:18.5	35.6	18.2	74.7	0.51	0.75	0.051	8.31(4)	0.13(3)	0.18(1)	0.05(1)	1.10	5.7	2
28	18:29:59.7	+01:15:20.9	57.6	10.3	135.3	0.18	0.65	0.049	7.98(4)	0.11(3)	0.21(1)	0.04(1)	1.44	4.8	6
29	18:29:49.2	+01:16:14.3	26.5	20.0	135.4	0.76	0.73	0.046	8.18(2)	0.05(1)	0.20(1)	0.04(1)	1.65	4.8	3
30	18:29:50.5	+01:18:24.3	42.3	20.5	113.3	0.48	0.67	0.059	8.03(3)	0.06(3)	0.13(2)	0.05(2)	0.66	3.5	0
31	18:29:56.0	+01:12:22.5	25.7	19.1	53.9	0.74	0.64	0.045	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.51	2.2	0
32	18:30:13.6	+01:13:46.4	55.1	16.1	143.6	0.29	0.68	0.060	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.90	5.8	0
33	18:29:58.6	+01:14:03.9	67.3	39.9	170.5	0.59	0.80	0.104	7.66(2)	0.13(1)	0.26(0)	0.06(0)	3.86	24.0	8
34	18:30:11.3	+01:15:59.3	34.6	21.1	131.0	0.61	0.87	0.054	7.83(2)	0.06(1)	0.09(0)	0.01(0)	0.89	5.0	1
35	18:30:13.2	+01:16:12.5	21.0	12.2	155.5	0.58	0.80	0.032	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.63	2.6	1
36	18:30:03.0	+01:11:41.4	18.1	12.3	94.7	0.68	0.91	0.030	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.91	4.0	2
37	18:30:02.5	+01:12:15.6	22.6	8.7	99.0	0.39	0.81	0.028	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.96	3.4	3
38	18:30:01.3	+01:12:08.3	34.6	10.3	2.5	0.30	0.85	0.038	7.32(2)	0.05(2)	0.15(2)	0.04(1)	1.27	3.3	6
39	18:29:49.8	+01:14:17.3	15.1	11.9	67.6	0.78	0.95	0.027	7.50(3)	0.06(2)	0.30(4)	0.09(4)	0.76	2.6	2
40	18:29:47.2	+01:14:48.0	26.9	8.3	38.4	0.31	0.79	0.030	7.71(5)	0.10(4)	0.24(6)	0.11(5)	0.71	2.1	2
41	18:30:00.1	+01:11:34.3	46.7	13.3	125.5	0.29	0.89	0.050	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	2.11	11.0	6
42	18:29:59.5	+01:12:43.2	23.3	12.6	14.7	0.54	0.93	0.034	7.02(3)	0.09(3)	0.26(2)	0.05(2)	1.74	5.6	8
43	18:29:58.9	+01:13:20.8	31.8	11.4	3.1	0.36	0.91	0.038	7.25(5)	0.12(5)	0.23(3)	0.07(2)	2.18	8.7	8
44	18:30:00.7	+01:12:59.9	40.0	27.4	7.3	0.69	0.78	0.067	6.95(5)	0.22(4)	0.28(2)	0.08(1)	3.11	18.2	8
Branches
45	18:29:49.5	+01:15:25.6	58.7	34.8	7.3	0.59	0.78	0.091	8.31(4)	0.16(3)	0.28(2)	0.10(1)	1.46	⋅⋅⋅	3
46	18:29:50.9	+01:16:38.9	124.2	24.4	25.2	0.20	0.55	0.111	8.59(5)	0.17(4)	0.19(1)	0.05(1)	1.35	⋅⋅⋅	4
47	18:29:50.4	+01:16:24.3	165.2	65.0	28.1	0.39	0.51	0.208	8.52(6)	0.23(4)	0.23(2)	0.09(1)	1.24	⋅⋅⋅	3
48	18:29:58.5	+01:13:59.5	103.9	57.2	179.7	0.55	0.52	0.155	8.00(6)	0.29(5)	0.25(1)	0.08(1)	1.24	⋅⋅⋅	7
49	18:29:50.1	+01:16:08.1	176.9	110.6	19.3	0.63	0.75	0.281	8.34(2)	0.28(1)	0.21(0)	0.11(0)	1.13	⋅⋅⋅	2
50	18:30:00.5	+01:12:56.3	53.4	35.8	146.0	0.67	0.74	0.088	7.05(8)	0.19(7)	0.25(5)	0.12(4)	1.13	⋅⋅⋅	7
51	18:29:56.7	+01:13:09.4	49.9	31.2	78.0	0.62	0.74	0.079	8.27(5)	0.20(4)	0.36(4)	0.19(3)	1.13	⋅⋅⋅	4
52	18:29:59.2	+01:13:39.6	156.2	66.3	19.6	0.42	0.54	0.205	7.84(8)	0.37(6)	0.21(2)	0.10(1)	1.02	⋅⋅⋅	6
53	18:30:00.6	+01:11:47.5	85.6	24.4	149.3	0.29	0.57	0.092	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.91	⋅⋅⋅	5
54	18:29:59.4	+01:13:53.7	201.0	93.2	0.9	0.46	0.43	0.275	7.91(6)	0.34(4)	0.23(1)	0.08(1)	0.91	⋅⋅⋅	5
55	18:30:00.0	+01:10:48.0	193.6	36.3	175.3	0.19	0.60	0.169	8.49(2)	0.10(1)	0.14(1)	0.07(1)	0.80	⋅⋅⋅	3
56	18:29:58.6	+01:13:43.4	242.4	163.2	12.3	0.67	0.34	0.400	7.92(6)	0.37(4)	0.20(1)	0.08(1)	0.80	⋅⋅⋅	4
57	18:29:58.7	+01:13:40.3	233.2	173.3	10.8	0.74	0.41	0.404	7.82(4)	0.39(3)	0.20(1)	0.09(0)	0.69	⋅⋅⋅	3
58	18:29:59.2	+01:13:10.1	351.4	185.1	5.0	0.53	0.39	0.513	7.90(4)	0.43(3)	0.20(1)	0.11(0)	0.58	⋅⋅⋅	2
59	18:29:59.4	+01:13:14.9	359.7	207.0	5.1	0.58	0.44	0.549	7.83(4)	0.44(3)	0.19(1)	0.11(0)	0.47	⋅⋅⋅	1
60	18:29:50.2	+01:16:05.0	180.1	129.2	16.3	0.72	0.75	0.307	8.16(4)	0.27(3)	0.16(1)	0.09(1)	0.47	⋅⋅⋅	1
61	18:29:30.3	+01:18:55.2	100.6	50.2	138.6	0.50	0.65	0.143	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.42	⋅⋅⋅	0
62	18:29:56.9	+01:14:02.0	553.7	260.4	28.4	0.47	0.47	0.764	8.07(4)	0.42(3)	0.20(1)	0.11(0)	0.37	⋅⋅⋅	0
63	18:30:11.8	+01:16:02.5	61.9	21.8	118.5	0.35	0.68	0.074	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.35	⋅⋅⋅	0

Notes. ^aThe coordinate (R.A. and decl.), major axis, minor axis, and position angle are derived from the task regionprops in MATLAB. ^bThe axis ratio is calculated as minor axis divided by major axis. ^cThe filling factor is calculated as the ratio between the area of the object enclosed by the fitted ellipse and the area of the fitted ellipse. ^dThe size is the geometric mean of the major and minor axis, calculated as $\sqrt{{\rm (Major \ axis)} \times {\rm (Minor \ axis)}}$. ^eThe mean V_lsr (〈V_lsr〉) is the mean of fitted V_lsr in an object weighted by the statistical uncertainty from V_lsr fitting. The uncertainty in the weighted mean V_lsr (shown in parentheses) is computed as $\Delta V_{{\rm lsr}} / \sqrt{N}$, where N is the number of independent beams. The uncertainty is reported in the last digit. ^fThe V_lsr variation (ΔV_lsr) is calculated as the standard deviation of V_lsr in an object. The uncertainty in ΔV_lsr (shown in parentheses) is calculated as $\Delta V_{{\rm lsr}} / \sqrt{2(N-1)}$. The uncertainty is reported in the last digit. ^gThe mean velocity dispersion (〈σ〉) is calculated as the mean of fitted velocity dispersions in an object weighted by the statistical uncertainty from σ fitting. The uncertainty in the weighted mean σ (shown in parentheses) is computed as $\Delta \sigma / \sqrt{N}$, where N is the number of independent beams. The uncertainty is reported in the last digit. ^hThe σ variation (Δσ) is calculated as the standard deviation of σ in an object. The error in σ (shown in parentheses) is calculated as $\Delta \sigma / \sqrt{2(N-1)}$. The error is reported to the last digit. ⁱFor a leaf, the peak intensity in a single channel from our binned data cube. For a branch, the intensity level where the structures directly above it merge together. ^jThe contrast is calculated as the difference between the peak intensity and the merging level of an object. Contrasts are only computed for leaves, divided by the 1σ sensitivity of the data. ^kThe branching level in the dendrogram. For example, level 0 means that the object grows from the base level; level 1 means that the object grows from a branch one level above the base level.

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The northwest corner in Figure 2 showing weak N₂H⁺(1–0) emission is associated with a high-contrast leaf (leaf 5), a low-contrast leaf (leaf 19), and a 3 mm source (S1). Dust emission is detected in this region at 250  μm, 350  μm, and 500  μm with Herschel (see Figure 1 for the 250  μm image). McMullin et al. (2000) also showed a C¹⁸O(1–0) peak near the N₂H⁺(1–0) peak. This is likely a new location for star formation.

The broad outline of the branching structure and the complexity of the tree can be captured in a few statistical measures (Houlahan & Scalo 1992). A branching level is defined as the number of branching steps between the object and the tree base. For example, leaf 3 has a branching level of zero because it grows directly from the tree base. Leaf 36 has a branching level of two since it goes through branch 59 and 62 before reaching the base branch. The branching levels for each structure are summarized in Table 4. The maximum branching level is eight in the SE subcluster, and five in the NW subcluster. The mean branching level of the entire tree is 3.1, while the mean branching level of the SE and NW subcluster is 5.0 and 3.7, respectively.

A path length is defined as the number of branching steps between a leaf and the tree base, similar to the definition of a branching level. Different from a branching level, a path length is considered only for leaves and not considered for branches. The mean path length of the tree, defined as the mean of path lengths from the leaves, can then better reflect the hierarchy in the tree since branching levels from branches would not be double counted. Larger mean path length corresponds a larger degree of hierarchical structure in the tree. The mean path length of the entire tree is 3.0, while the mean path length of the SE and NW subcluster is 5.1 and 4.1, respectively. This suggests that the SE subcluster is more hierarchical than the NW subcluster.

The branching ratio is defined as the number of substructures which merge at a branch level. For example, branch 55 has a branching ratio of three since it joins leaf 6, 7, and 12. Branch 60 has a branching ratio of two since it fragments to leaf 40 and branch 49. A larger branching ratio corresponds to a higher degree of fragmentation. The mean branching ratio in Serpens Main is 3.2 (2.6 in the SE subcluster and 2.4 in the NW subcluster), smaller than the mean branching ratio of 3.9 in Barnard 1 (Paper I).

Overall, these tree statistics indicate that the SE subcluster exhibits more complex hierarchical structure compared to the NW subcluster. There are ∼40 YSOs in the SE subcluster and ∼12 YSOs in the NW subcluster (Evans et al. 2009), suggesting that the complexity of hierarchical structure is associated with star formation activity. The Serpens Main dendrogram also has more complex structure compared to the Barnard 1 dendrogram presented in Paper I; that dendrogram has a maximum branching level of 4, a mean path length of 1.2, and a mean branching ratio of 3.9. Since Serpens Main has more star formation activity than Barnard 1, these results suggest that the hierarchical nature of the dense gas in molecular clouds is linked with the star formation activity of those regions.

The comparison in the distribution between the leaves and 3 mm sources (Section 3.3) is shown in Figure 9. The 3 mm continuum sources are indicated by star symbols (including yellow and red stars); the red stars represent the sources coincident with the SMM cores. A majority of the SMM cores are better associated with the high-contrast leaves than the low-contrast leaves, suggesting that the high-contrast leaves may be associated with formation of dense cores.

Table 4 shows the morphological properties of the leaves and branches. We derived the morphological properties using the two-dimensional footprint (as shown in Figure 9) of inherently three-dimensional structures. R.A., decl., major axis, minor axis, and position angle were calculated with the task "regionprops" in MATLAB. For all the objects including leaves and branches, we include all the emission from the leaves/branches within it when performing the region props fitting. Axis ratios are minor axes divided by major axes, and the sizes are the geometric mean of the two axes. We define a "filling factor" to quantify the regularity of an object compared to its fitted shape. The filling factor is calculated as the area of the object enclosed by the fitted ellipse divided by the area of the fitted ellipse; smaller values correspond to more irregular shapes.

Figure 10 presents the histograms of the size, filling factor, and axis ratio of the leaves and branches. The leaves have sizes ranging from 0.024 pc (∼1.7 beam size) to 0.105 pc with a mean of 0.053 pc from all the leaves, and the branches have larger sizes with a mean value of 0.26 pc. The high-contrast leaves have a moderately larger mean size of 0.071 pc than the low-contrast leaves with a mean size of 0.046 pc. The histogram of filling factor for leaves displays an increase in number toward regular shapes (value close to 1); branches show an opposite trend. The flat distribution in axis ratio shows that the objects are rarely described by spherical shapes (axis ratio = 1), and a number of objects have elongated structures. In particular, the southern filament shows several high-contrast and low-contrast leaves with their branches in filamentary morphologies (Figure 9).

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Table 4 and Figure 10 also show the kinematic properties of the leaves and branches including 〈V_lsr〉, ΔV_lsr, 〈σ〉, and Δσ. All of these quantities are derived using the results of the N₂H⁺(1–0) spectral line fitting described in Section 3.2. 〈V_lsr〉 and 〈σ〉 are the mean centroid velocities (V_lsr) and the mean velocity dispersion (σ) in an object; the calculated means are weighted by the statistical uncertainties from the spectral line fitting. ΔV_lsr, the V_lsr variation, is the standard deviation of V_lsr to the mean value (〈V_lsr〉). Similarly, Δσ is the standard deviation of velocity dispersions to the mean value (〈σ〉).

In determining the object kinematic properties, the calculation was based on the spatial footprint of a leaf; for a branch, it was based on the area in the "onion layer," which is the area between the branch and the structures directly above it in the tree. The regions with two-velocity components (Section 3.2) were not used in this analysis due to the overlapping spatial footprints. We also excluded objects that had less than three beam areas of kinematic pixels.

The mean V_lsr (〈V_lsr〉) ranges from 6.9 to 8.8 km s⁻¹ without a significant difference in distribution between leaves and branches (Figure 10). Leaves and branches in the NW subcluster have 〈V_lsr〉 distributed between 8.0 and 8.5 km s⁻¹, and the objects in the SE subcluster are more blueshifted except for the southern filaments. In the ΔV_lsr distribution (V_lsr variation calculated as the standard deviation of V_lsr inside an object), the branches clearly show larger ΔV_lsr than the leaves. Branches and leaves have a mean ΔV_lsr of 0.28 km s⁻¹ and 0.09 km s⁻¹, respectively. This is expected since branches incorporate larger spatial scales and may reflect large-scale motions. The high-contrast leaves have larger ΔV_lsr peaking at ∼0.13 km s⁻¹ than the low-contrast leaves peaking at ∼0.06 km s⁻¹. Similarly, this difference is possibly due to larger sizes for the high-contrast leaves which incorporate more turbulent power across the plane of the sky (see Section 5), and/or due to local star formation activities.

For 〈σ〉, there is no clear difference in the distribution between leaves and branches, and there is also no clear difference in the distribution between the high-contrast and low-contrast leaves. Most of the leaves and branches show velocity dispersions below the sonic level, 0.27 km s⁻¹ assuming 20 K gas temperature. The mean velocity dispersion including leaves and branches is 0.2 km s⁻¹. A few high-contrast leaves have supersonic velocity dispersions (leaf 9, 20, 33, 44). Among these leaves, leaf 9, 33, and 44 have the highest intensities in the tree. Leaf 20, 33, 44 are located in the central region of the SE subcluster and are associated with SMM cores; leaf 9 is associated with SMM1 in the NW subcluster. The close correlation between the four leaves and the SMM cores suggest that the large velocity dispersions may be due to local star formation activity. Most of the leaves have 〈σ〉 2–3 times larger than ΔV_lsr.

Recent observations from Herschel suggested a characteristic FWHM width of 0.09 ± 0.04 pc derived from 278 filaments in eight regions (IC 5146, Orion B, Aquila Rift, Musca, Pipe Nebula, Polaris, Taurus and Ophiuchus; Arzoumanian et al. (2013)). In Section 6, we estimated the widths of filaments identified from our N₂H⁺(1–0) data to be 0.036 pc. This N₂H⁺(1–0) width is about one-third of the characteristic width from Herschel. Indeed, the Herschel filaments appear to be more extended in width compared with the N₂H⁺(1–0) filaments in Serpens Main (Figure 12).

Fernández-López et al. (2014) reported a similar width for a few filaments in Serpens South using N₂H⁺(1–0). That study suggests that the narrower widths observed with N₂H⁺(1–0) are possibly due to a combined effect of excitation conditions and chemical reactions. At the centers of the filaments where densities are expected to be above 10⁵ cm⁻³, N₂H⁺(1–0) emission depends almost linearly on its column density at a fixed temperature, and the N₂H⁺(1–0) emission would be observed with sufficient excitation conditions in temperature and density for the transition. Toward the edges where densities drop rapidly below 10⁵ cm⁻³, the emission efficiency could drop rapidly because of insufficient increase in the N₂H⁺(1–0) column density to emit a fixed line temperature. Another possible mechanism for the narrower widths is from chemical effects (Bergin et al. 2001, 2002): at regions less than CO depletion threshold (2–6 × 10⁴ cm⁻³; Tafalla et al. 2002), CO destroys N₂H⁺(1–0), resulting in a drop in the N₂H⁺(1–0) abundance and hence a drop in the emission. However, the difference in the N₂H⁺(1–0) widths and dust widths may as well be due to the Herschel resolution not being sufficient to resolve 0.03 pc structures at the Serpens distance.

While the discussion above corresponds to dust filaments composed of single N₂H⁺(1–0) filaments, which most of the filaments in Serpens Main show, FS1 and FS2 are observed as two separate structures inside one Herschel dust filament (Figure 12). In this particular case, the width difference between the dust filament and the two molecular filaments is not likely due to excitation conditions nor chemical effects. The N₂H⁺(1–0) observations show substructures in the dust filament, resolving it into two quasi-parallel filaments with ∼0.03 pc width. This result, along with the obtained in the Serpens South filaments, suggests that filamentary structures found in some star-forming regions can be more complex than single filaments represented by Herschel, and high angular resolution observations are needed to examine the widths of filaments in star-forming regions.

A number of recent studies have performed molecular line observations and revealed kinematic properties of filamentary structures toward nearby star-forming regions (Schneider et al. 2010; Kirk et al. 2013; Palmeirim et al. 2013; Arzoumanian et al. 2013) and IRDCs (Miettinen 2012; Peretto et al. 2014). Filaments in some regions, including IRDC G14.225-0.506 and G035.39-00.33, show supersonic nonthermal velocity dispersions (Busquet et al. 2013; Henshaw et al. 2013), suggesting significant nonthermal contributions in the physical process of star formation. On the other hand, subsonic to transonic nonthermal velocity dispersions with velocity coherence have been observed in regions such as L1517 (Hacar & Tafalla 2011), B5 (Pineda et al. 2011), and B213 in Taurus (Hacar et al. 2013). Most of our identified filaments (FC1 and FN1) in Serpens Main (Section 6) show transonic velocity dispersions, while FS1 shows particularly subsonic velocity dispersions.

The properties of the filaments in the SE subcluster (Table 5) show that there are two types of filaments in this region. Examples of one type are filaments FC1 and FN1 which show large velocity gradients along their major axis (>3 km s⁻¹), small masses (4 M_☉), and nearly critical mass per unit length (M_L ≃ M_{L, crit}; see Equation (2)). In another type of filaments, we observe the opposite characteristics with small velocity gradients along the axis (<2 km s⁻¹), larger masses (∼15 M_☉), and supercritical mass per unit lengths (M_L ≃ 3.5 × M_{L, crit}), such as in filaments FS1, FS2, and FS3. Filament FC2 appears to have intermediate characteristics although its properties are closer to those of the southern filaments.

Each type of filaments appears to be spatially correlated: FN1 and FC1 are northeast of the SE subcluster and the other filaments are south or west of it. The correlations suggest that these filaments could be associated with larger structures. The observed, dense filaments are in the intersection of large-scale structures possibly originated from large-scale turbulence (e.g., Padoan et al. 2001; Mac Low & Klessen 2004; Elmegreen & Scalo 2004; McKee & Ostriker 2007; Hennebelle & Falgarone 2012).

Figure 16 shows the comparison between the N₂H⁺(1–0) gas and Spitzer YSOs from Evans et al. (2009). Younger YSOs (Class 0 and I sources) are represented by red triangles, and more evolved YSOs (Class II and III sources) are represented by blue stars. In general, younger YSOs are more closely related to the N₂H⁺(1–0) emission and are concentrated in the two subclusters, while more evolved YSOs are distributed more widely. This suggests that the N₂H⁺(1–0) gas correlates with early stages of star formation. Also, the NW subcluster contains primarily younger sources, and the SE subcluster is associated with both younger and more evolved YSOs, suggesting that the NW subcluster is younger than the SE subcluster.

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Figure 16 also shows a comparison between the N₂H⁺(1–0) filaments and YSOs. It is striking that a string of five YSOs is formed along FS1 and FS2, while no YSOs are associated with FC1, FN1, and FC2. FS1 and FS2 have supercritical mass per unit lengths (M_L = 2.6 and 3.7 × M_{L, crit}, respectively), while FC1 and FN1 have nearly critical mass per unit lengths. These results suggest that stars are formed in situ along filaments that are gravitationally unstable. Furthermore, the results could reflect that FS1 and FS2, which belong to the same type of filaments, are more evolved than FN1 and FC1 in the other type.