AN AMMONIA SPECTRAL MAP OF THE L1495-B218 FILAMENTS IN THE TAURUS MOLECULAR CLOUD. I. PHYSICAL PROPERTIES OF FILAMENTS AND DENSE CORES

We observed the L1495-B218 filaments in the Taurus cloud using the 100 m Robert C. Byrd Green Bank Telescope (GBT12A295).¹¹ Observations were carried out from 2012 April to 2013 February in 13 shifts totaling 66 hr. We used the K-band focal plane array (KFPA), which has seven beams each with dual polarization in a hexagonal arrangement (for technical properties of the KFPA, see https://science.nrao.edu/facilities/gbt/observing/GBTog.pdf). We used the 7+1 mode of the KFPA, which allows the center beam to observe two frequencies simultaneously while the other six beams observe only a single frequency. The bandwidth of each frequency window is 50 MHz. For seven beams, we set the rest frequency to be 23.702 GHz, which is between the strongest hyperfine component of NH₃(1, 1) (23.6944955 GHz; Lovas & Dragoset 2003) and NH₃(2, 2) (23.7226333 GHz; Lovas & Dragoset 2003). For the central beam we selected a second frequency to include the CCS N_J = 2₁ $\to$ 1₀ transition (22.344033 GHz; Yamamoto et al. 1990); these results will be reported in a separate paper. The spectrometer is configured to have 16,384 channels across 50 MHz, yielding a resolution of 3.05 KHz (0.0386 km s⁻¹ at 23.705 GHz). Since the typical thermal broadening of starless cores is $\lt 0.2$ km s⁻¹ (e.g., Jijina et al. 1999; Caselli et al. 2002; Rosolowsky et al. 2008), the line profiles of NH₃ are well resolved in this setup.

We observed the L1495-B218 filaments in 20 rectangular regions that are arranged to cover high-extinction regions (Schmalzl et al. 2010) while minimizing the total observation time. Each rectangular region is 20' by 6' or 6' by 20' oriented in Galactic coordinates. Data for each rectangular region are obtained by on-the-fly mapping of 25 rows 20' long with a row spacing of 1512. The integration time per row is 150 s. The resulting integration time for a direction observed with all seven beams is ∼30 s; the total observation time for each rectangular region is 1 hr and 20 minutes. The reference OFF positions are picked to be where the extinction is low enough to suggest that they would have negligible NH₃ emission, and close to each rectangular region. The average of two observations of the OFF position made before and after mapping each rectangular region is subtracted from each on-source observation. We also carried out "daisy" pattern observations to improve the S/N toward 29 bright NH₃ regions that we found from the mapping of rectangular regions. Each daisy pattern observation was made with a radius of 28 and 22 cycles following a rose curve. The daisy pattern observation completely covers the inner 28 radius with all seven beams for an average integration time of 38 s. The total integration time for each daisy pattern is 20 minutes. We updated the pointing of the telescope using the quasar 0403+2600 between every mapping of a rectangular region or every three daisy patterns. The pointing corrections were usually less than 10'', compared to the beam size of the GBT at 23 GHz of 31''.

Data reduction was performed using the GBT KFPA pipeline. The data are regridded into regularly spaced pixels using AIPS, and the gain of the seven beams is calibrated through observing Venus and Jupiter in every observing shift. As a double-check on the absolute flux calibration, we also observed the peak dust continuum position of the L1489PPC starless core (α = 04:04:47.6, δ = +26:19:17.9, J2000.0) every observing shift (Young et al. 2004; Ford & Shirley 2011). The calibrations using Venus and Jupiter and the calibration using L1489PPC agreed within 25%.

3.1.1. Integrated Intensity of NH₃ (1, 1) and (2, 2) and Definition of Subregions

Figure 1 presents the integrated intensity of NH₃ (1, 1) emission. The NH₃ (1, 1) map clearly reveals dense cores associated with the L1495-B218 filaments. On the other hand, the filamentary structures between dense cores are barely detected, while those regions are very clearly visible in an extinction map (Schmalzl et al. 2010) and ¹³CO (Goldsmith et al. 2008; Pineda et al. 2010b). This suggests that the density of filamentary structures between dense cores may not be high enough to form NH₃ efficiently (n$_{{{{\rm H}}_{2}}}\lt 10$³ cm⁻³; Flower et al. 2006), or that ammonia molecules exist but excitation conditions are insufficient to observe the (1, 1) emission at our average rms level of 120 mK (Figure 2). The NH₃ (2, 2) emission is detected only from dense cores and is much weaker than (1, 1) emission, which implies that the kinetic temperature may be too low to excite to the J = 2, K = 2 state except in dense gas of n$_{{{{\rm H}}_{2}}}$ >10⁴ cm⁻³ (Ho & Townes 1983; Danby et al. 1988; Maret et al. 2009).

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We compare our NH₃ (1, 1) emissions with 500 μm dust continuum emission seen by the SPIRE instrument of the Herschel Space Observatory in Figure 1 (Palmeirim et al. 2013; Marsh et al. 2014). The 500 μm dust continuum emission is thermal emission from dust grains and traces the column density structure of the filaments. The bright regions of 500 μm and NH₃ (1, 1) emission show good agreement with each other. The 500 μm emission is more spatially extended than the NH₃ (1, 1) emission. The lowest 500 μm intensity levels at which NH₃ (1, 1) and (2, 2) are detected are 25 MJy sr⁻¹ (${{N}_{{{{\rm H}}_{2}}}}$ = 5.6 × 10²¹ cm⁻² at 10 K) and 177 MJy sr⁻¹ (${{N}_{{{{\rm H}}_{2}}}}$ = 3.9 × 10²² cm⁻² at 10 K), respectively. This shows that NH₃ is a good tracer with which to identify intermediate to dense regions within filaments.

In Figure 3, we zoom into each region and show the location of protostars identified using IRAS and Spitzer (Rebull et al. 2011, 2010; Kryukova et al. 2012). We divide the map into subregions based on Barnard's identification (Barnard et al. 1927). We discuss each region and determine if it is more evolved (having a Class I/flat spectra protostar associated with NH₃ emission) or less evolved below.

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B7/L1495 contains multiple Class II and III protostars, two flat spectra protostars, and one Class I protostar, none of which are embedded within the NH₃ core, but there are nearby NH₃ cores. The three dense cores seen in NH₃ are most commonly referred to as L1495A-S, L1495A-N, and L1495B (Lee et al. 2001). In B213 (also referred to as L1521D; Codella et al. 1997), there are two Class I protostars embedded in NH₃ cores in the eastern part of the region and another three Class I protostars in the western part of the region. Therefore, B7 and B213 are the most evolved regions in the L1495-B218 filaments, and B7 is likely to be more evolved than B213 (see Hacar et al. 2013).

B218 has only one flat spectrum protostar embedded within an NH₃ core. Thus, we classify B218 as an evolved region with star formation, although the NH₃ emission is dominated by two bright starless cores. This region is also sometimes confusingly referred to as B217 (Benson & Myers 1989). We use the notation B218 in this paper since it is closer to the original Barnard catalog position of B218 (Kenyon et al. 2008).

B10 also has only one protostar, which is Class II. In this work, we assume that B10 is a less evolved region because there is no other protostar except the one Class II protostar that is not directly associated with any dense cores in the region.

In contrast to the other regions, B211 and B216 show weak NH₃ (1, 1) emission and do not possess any known protostars. Thus, both regions are less evolved. The B216 region is also named L1521B (Lee et al. 2001) and contains starless cores with large abundances of carbon chain molecules (Hirota et al. 2004).

Hacar & Tafalla (2013) have also determined the relative ages of subregions using N₂H⁺ 1–0 emission and the locations of protostars. Their estimates of relative age of subregions agree well with ours except for B216. In their observation of N₂H⁺ 1–0, they did not detect emission in B216. B216 has weaker NH₃ (1, 1) emission and stronger CCS emission than B211 (Y. M. Seo et al. 2015, in preparation), suggesting that B216 is a younger region. Thus, B211 and B216 are both relatively young and inactive parts of the L1495-B218 filaments, with B216 likely being the most newly condensed part of the filaments.

3.1.2. Spectral Line Fitting

3.1.3. Gas Kinetic Temperature and Excitation Temperature

Maps of the gas kinetic temperature deduced from NH₃ (1, 1) and (2, 2) emission are presented in Figure 4. The gas kinetic temperature ranges from 8 to 15 K in most of the region mapped. At the bright NH₃ peaks indicated by red arrows, the kinetic temperature decreases toward the core center. The drop in the kinetic temperature is about −1 to −3 K, or about 10%–30% of the average kinetic temperature of surroundings. This temperature drop may ultimately break the dynamical stability of these dense cores and lead them to collapse (see Khesali et al. 2013).

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Figure 5 presents histograms of physical quantities to investigate statistical differences between subregions. In the first panel of Figure 5, we show histograms of the gas kinetic temperature. Medians of the gas kinetic temperature in subregions are all around 9.5 K with less than 1 K deviation (60% of all spectra have kinetic temperature within ±1 K of 9.5 K). The two less evolved regions, B10 and B216, have lower kinetic temperature than the other more evolved regions (we exclude B211 from discussion because it has multiple velocity components and our NH₃ fitting model works only for a single velocity component). The histograms of the gas kinetic temperature demonstrate the tendency that a less evolved region is cooler than a more evolved region and that a denser region is cooler than a diffuse region if there are no embedded protostars; however, the gas kinetic temperature differences are subtle.

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Histograms of NH₃ excitation temperature are shown in the second panel of Figure 5. Median values of the excitation temperature are mostly around 5 K, which is only half of the median values of the kinetic temperature. This demonstrates that NH₃ in all regions is subthermally excited.

3.1.4. LSR Velocity

NH₃ lines at 39 NH₃ integrated intensity peaks in the L1495-B218 filaments are shown in Figures 6 and 7 (for peak locations, see Section 3.2.1). The range of NH₃ v_lsr is from 5.0 to 7.2 km s⁻¹, which is the same range seen in the C¹⁸O J = 1–0 spectra of Hacar et al. (2013). NH₃ structures are confined to a single velocity component except in B211. Comparing NH₃ to C¹⁸O (Hacar et al. 2013) and ¹³CO (Goldsmith et al. 2008), we found that all NH₃ peaks have corresponding velocity components in ¹³CO, while only 28 out of 39 NH₃ peaks are directly associated with the same velocity components in C¹⁸O. Some NH₃ peaks where NH₃ integrated intensity is relatively high ($\geqslant$ 40 K km s⁻¹, i.e., four core-like structures neighboring in a row in B213) do not have corresponding velocity components in C¹⁸O and ¹³CO emission. We also found a few NH₃ peaks with both NH₃ and C¹⁸O emission but discrepancies in their LSR velocities, which may be a sign of chemical differentiation.

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The LSR velocity structure of the L1495-B218 filaments was extensively studied by Hacar et al. (2013) using C¹⁸O J = 1–0. They identified 35 filaments using a "friend of friends" algorithm (FIVe; Hacar et al. 2013), and for each filament they deduced physical properties, including mass, dispersion of v_lsr, nonthermal motion, and mean kinetic temperature (see Table 3 in Hacar et al. 2013). Using dense cores identified from their N₂H⁺ J = 1–0 observations, they suggested that only 7 out of 35 filaments are "fertile," meaning that they contain an N₂H⁺-bright dense core. However, N₂H⁺ traces gas with density higher than 10⁴ cm⁻³, which is the central density of relatively evolved dense cores (Lada et al. 2008). It is likely that dense cores at early stages are not fully revealed by N₂H⁺. Ammonia molecules have an intermediate effective excitation density that is between C¹⁸O J = 1–0 and N₂H⁺ J = 1–0; therefore, our ammonia map may probe the velocity structure of both developing dense cores and later stages.

Matching the LSR velocity of NH₃ (1, 1) and (2, 2) structures to 35 filaments of Hacar et al. (2013), we found NH₃ (1, 1) emission in filaments 6, 8, 10, 11, 15, 20, 28, and 32 (Table 3 of Hacar et al. 2013). Hacar et al. (2013) suggested that filaments 6, 10, 11, 15, 20, 32, and 34 are fertile (i.e., having dense cores in their N₂H⁺ observation). Filament 34 is not within the field of view of our observation, so it is excluded in this study. Our NH₃ observation reveals that two more filaments, 8 and 28, also have NH₃ emission. Hacar et al. (2013) argued that a filament tends to be sterile when the line density of the filament is less than 15 ${{M}_{\odot }}$ pc⁻¹, which is the critical density for an isothermal cylinder at 10 K (Stodólkiewicz 1963; Ostriker 1964). Filament 28 has a line density of 24.1 ${{M}_{\odot }}$ pc⁻¹ (Hacar et al. 2013), but there was no detection of dense cores in N₂H⁺ J = 1–0. With our NH₃ observations, we found that there are at least two dense cores in filament 28. On the other hand, filament 8 has a line density of 9.3 ${{M}_{\odot }}$ pc⁻¹ (Hacar et al. 2013), which is lower than the critical line density, but we see that there is a relatively bright NH₃ core. Since Hacar et al. (2013) estimated the masses of filaments from C¹⁸O J = 1–0, it may be possible that they underestimated the mass due to CO depletion. The filament mass estimated from dust continuum may be larger than mass estimated from C¹⁸O J = 1–0, but the filaments cannot be distinguished along the line of sight, which will result in an overestimation of filament masses. From the fact that filament 8 is relatively bright in NH₃ (1, 1), it is likely that the line density of 9.3 ${{M}_{\odot }}$ pc⁻¹ is the minimum line density of filament 8, and the true line density may be higher than the critical value.

3.1.5. Velocity Dispersion

Velocity dispersions range from 0.05 to 0.25 km s⁻¹ except in B211 (B211 has multiple velocity components that are not pursued in this study). Overall, we found that velocity dispersions, which include both thermal and nonthermal components, tend to be wider in the less evolved regions than those in the more evolved regions. Histograms of the velocity dispersions (Figure 5) show this trend clearly. The median value of velocity dispersions for the least evolved region, B216, is 0.118⁻¹, while the most evolved region, B7, has a median dispersion equal to 0.104 km s⁻¹ (the thermal velocity dispersion of NH₃ at 10 K is 0.069 km s⁻¹).

Using accurate gas kinetic temperatures deduced from NH₃ (1, 1) and (2, 2), we estimate the velocity dispersions of nonthermal kinetic motions ${{\sigma }_{{\rm nt}}}$ (Figure 8) as follows:

$$\begin{eqnarray}&&{{\sigma }_{{\rm nt}}}=\sqrt{\sigma _{v}^{2}-\frac{k{{T}_{k}}}{{{\mu }_{{\rm N}{{{\rm H}}_{3}}}}{{m}_{{\rm H}}}}},\end{eqnarray} \tag{ 1 }$$

where k is Boltzmann's constant, ${{\mu }_{{\rm N}{{{\rm H}}_{3}}}}$ is the molecular weight of ammonia (17 a.m.u.), and m_H is the mass of a hydrogen atom. We find that most regions of the filaments are supported mainly by thermal pressure (the fourth panel in Figure 5), while some edges of filaments are dominated by nonthermal support (${{\sigma }_{{\rm nt}}}\geqslant {{\sigma }_{{\rm thermal}}}$ = 0.188 km s⁻¹ at ${{T}_{k}}$ = 10 K and μ = 2.33). The median ratio of thermal support to nonthermal support (${{R}_{p}}\equiv c_{s}^{2}/\sigma _{{\rm nt}}^{2}$) is around 5. In addition, the median ratio of thermal support to nonthermal support tends to be larger for more evolved regions (median R_p = 6.3 in the more evolved region B7, while R_p = 3.7 in the less evolved region B216). This suggests that nonthermal motions are considerably dissipated in more evolved regions, making it easier to initiate star formation, which has been seen toward dense cores in other molecular clouds (e.g., Goodman et al. 1998; Pineda et al. 2010a; Tatematsu et al. 2014).

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3.2.1. Identifying Dense Structures in the L1495-B218 Filaments

The L1495-B218 filaments have many dense cores in different evolutionary stages of star formation, ranging from starless to protostellar cores. We use our ammonia observations to identify dense cores in the L1495-B218 filaments using the CSAR (Kirk et al. 2013), which uses both a seeded-watershed and dendrogram algorithm to find clumpy structures and their spatial relationships. We used the integrated intensity of the central hyperfine group (the strongest hyperfine group of nitrogen splitting) of NH₃ (1, 1) to identify dense structures because the central hyperfine group gives the highest S/N compared to the other four hyperfine groups. Parameters in the CSAR algorithm are set to find structures above a 7.5σ integrated intensity level in the (1, 1) transition (∼3σ in (2, 2) transition) and to identify a clump with a size larger than ${{\theta }_{{\rm mb}}}/2\sim 15^{\prime\prime}$ (fullbeam option) and a 2σ enhancement in intensity from its background. We also used the removeedge option in order not to have overextended edges for a source. In this study, we use 2σ as an intensity interval to clip intensity peaks instead of using the typical value of 3σ because with the 3σ intensity interval the CSAR algorithm tends to combine two peaks as one elongated clumpy structure. These peaks typically lie on top of nested sources that are many σ brighter than their background. The CSAR algorithm also had trouble in excluding intensity spikes at edges of maps that have a high noise level (${{\sigma }_{{{T}_{k}}}}\geqslant 0.3$ K). In order to exclude the edges of NH₃ maps, we made 12 patches and applied the CSAR algorithm to each patch.

The main reason we use NH₃ (1, 1) instead of dust continuum is because NH₃ emission acts as a volume density filter. From the excitation curve of NH₃ (1, 1), the effective excitation density varies slowly over the range of gas kinetic temperature from 7 to 15 K. The excitation temperature of dense structures identified by the CSAR algorithm is typically above 3.2 K, and the effective excitation density for the range of observed gas kinetic temperature and NH₃ abundance varies only from 7 × 10² to 1 × 10³ cm⁻³. This suggests that NH₃ (1, 1) emission naturally filters out regions with a density lower than ∼7 × 10² cm⁻³. This may make NH₃ structures appear smaller than corresponding dust continuum structures, but the NH₃ sources identified by the CSAR algorithm are true structures in volume density, whereas analysis in dust continuum sees only an enhancement in total column density.

From the integrated intensity of the central hyperfine group of NH₃ (1, 1), we found 39 leaves (a leaf: a structure containing an intensity peak) and 16 branches (a branch: a nested group of leaves). Figure 9 shows the locations of NH₃ leaves, and Figure 10 shows hierarchy among NH₃ leaves and branches in a dendrogram. The dendrogram has no lowest common branch because NH₃ (1, 1) structures are highly fragmented due to the volume density and chemical filtering. In this study we refer to "active" leaves as those that have a Class I or flat spectrum protostar within their lowest-level branches in the dendrogram (also known as root) or within a distance of three times their radius. Note that this definition means that active leaves could be either starless or protostellar. Only four leaves have embedded protostars, and 17 leaves are classified as active. Hacar et al. (2013) found 19 dense cores in N₂H⁺ 1–0, while CSAR finds 39 leaves in NH₃ (1, 1). This difference may be because NH₃ is an intermediate-density gas tracer that reveals more cores than the denser gas tracer N₂H⁺, and our NH₃ observations (${{\theta }_{{\rm mb}}}\sim 31^{\prime\prime}$) have better angular resolution than the N₂H⁺ observation (${{\theta }_{{\rm mb}}}\sim 50^{\prime\prime}$).

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For the comparison between dust and NH₃, we also identified dust cores using CSAR. From the 500 μm dust continuum data of the Herschel Space Observatory (${{\theta }_{{\rm mb}}}\sim 36^{\prime\prime}$), we found 51 dust leaves. Figure 11 shows the locations and boundaries of dust leaves. A total of 32 dust leaves coincide with 38 NH₃ leaves, while 19 dust leaves do not agree with any NH₃ leaf. Nine of the dust leaves contain at least two NH₃ leaves. This suggests that there may be multiple dense cores or fragments within a core since NH₃ is sensitive to volume density whereas the dust continuum is optically thin and depends on the total column density.

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In order to compare how well dust continuum and NH₃ agree with each other, we investigate the separation of the dust peak position and the NH₃ peak position in a dust leaf associated with an NH₃ leaf. Most of the NH₃ peak positions show agreement with corresponding dust peak positions with a median separation of 187, which is slightly larger than half the FWHM beam size. However, there are four dust leaves having a separation between dust and NH₃ peaks larger than 30'' (the maximum separation is 662), and three out of four are associated with a nearby protostar (Class I or flat spectrum). This suggests that a large separation may be due to a chemical effect produced by the radiation from a protostar. The fact that most of the NH₃ sources agree with the dust sources demonstrates that NH₃ sources identified by CSAR may represent dense structures within the L1495-B218 filaments. In the following subsections all of the analyses are done with NH₃ sources determined from our NH₃ data.

3.2.2. Size and Mass

The physical properties of NH₃ leaves and branches are summarized in Tables 1–3. The quoted kinetic temperature and velocity dispersion are the median values estimated from NH₃ fittings within NH₃ leaves and branches except for NH₃ leaf 11. This has a peak NH₃ (1, 1) line intensity weaker than 5σ except at its peak location, so we fit the NH₃ line at the peak intensity location.

Table 1.  Properties of NH₃ Sources

IDa	b	l	α	δ	Peak NH$_{3}$ b	Peak Dustc	N$_{{{{\rm H}}_{2}}}$ d	Embeddede	Area
			J2000.0	J2000.0	(K km s−1)	(MJy sr−1)	(1022 cm−2)	YSOs	(10−2 pc2)
1	+168:42:22.8	−15:28:12	4:18:33.0	+28:27:58	7.07 ± 0.09	85.9	1.69$_{-0.14}^{0.11}$	N	0.046
1.5	+168:42:22.8	−15:28:12	4:18:33.0	+28:27:58	7.07 ± 0.09	85.9	1.69$_{-0.14}^{0.11}$	⋯	1.206
2	+168:42:59.9	−15:28:42	4:18:33.1	+28:27:11	6.67 ± 0.08	91.2	2.28$_{-0.17}^{0.15}$	N	0.012
3	+168:46:43.4	−15:30:18	4:18:39.1	+28:23:29	3.60 ± 0.08	176.6	4.03$_{-0.43}^{0.53}$	N	0.526
4	+168:47:46.1	−15:29:12	4:18:45.9	+28:23:30	1.02 ± 0.13	112.4	4.30$_{-2.03}^{2.51}$	N	0.046
5	+168:41:41.8	−15:36:18	4:18:04.2	+28:22:52	2.82 ± 0.09	94.9	2.48$_{-0.29}^{0.73}$	N	0.473
6	+168:47:45.6	−15:45:18	4:17:52.8	+28:12:26	3.07 ± 0.06	75.0	2.33$_{-0.27}^{0.55}$	N	0.194
6.5	+168:50:46.4	−15:45:06	4:18:02.6	+28:10:28	3.83 ± 0.06	58.5	1.43$_{-0.16}^{0.14}$	⋯	0.507
7	+168:50:46.4	−15:45:06	4:18:02.6	+28:10:28	3.83 ± 0.06	58.5	1.43$_{-0.16}^{0.14}$	N	0.257
7.5	+168:55:25.8	−15:48:00	4:18:07.0	+28:05:13	6.41 ± 0.06	70.5	2.64$_{-0.27}^{0.17}$	⋯	2.881
8	+168:53:21.5	−15:47:06	4:18:03.7	+28:07:17	5.04 ± 0.05	57.3	1.60$_{-0.12}^{0.10}$	N	0.071
8.5	+168:55:25.8	−15:48:00	4:18:07.0	+28:05:13	6.41 ± 0.06	70.5	2.64$_{-0.27}^{0.17}$	⋯	0.768
9	+168:55:25.8	−15:48:00	4:18:07.0	+28:05:13	6.41 ± 0.06	70.5	2.64$_{-0.27}^{0.17}$	N	0.192
10	+168:45:39.7	−15:48:00	4:17:37.6	+28:12:02	1.57 ± 0.10	52.5	1.57$_{-0.41}^{0.80}$	N	0.348
11	+168:46:00.1	−15:44:12	4:17:51.2	+28:14:25	0.82 ± 0.10	39.2	1.27$_{-0.52}^{0.92}$	N	0.050
12	+168:48:46.1	−15:49:36	4:17:41.7	+28:08:46	5.34 ± 0.06	79.0	2.53$_{-0.07}^{0.19}$	N	0.226
12.5	+168:48:46.1	−15:49:36	4:17:41.7	+28:08:46	5.34 ± 0.06	79.0	2.53$_{-0.07}^{0.19}$	⋯	0.357
13	+168:49:48.1	−15:50:24	4:17:42.2	+28:07:29	2.08 ± 0.07	58.6	1.02$_{-0.21}^{0.12}$	N	0.017
13.25	+168:48:46.1	−15:49:36	4:17:41.7	+28:08:46	5.34 ± 0.06	79.0	2.53$_{-0.07}^{0.19}$	⋯	1.076
14	+168:51:02.6	−15:51:18	4:17:43.0	+28:06:00	2.19 ± 0.08	59.4	1.51$_{-0.25}^{0.52}$	N	0.070
15	+168:52:22.9	−15:53:06	4:17:41.1	+28:03:50	2.87 ± 0.06	57.4	2.14$_{-0.31}^{0.28}$	N	0.050
15.5	+168:52:16.1	−15:54:30	4:17:36.1	+28:02:57	3.43 ± 0.07	71.7	1.92$_{-0.20}^{0.37}$	⋯	0.884
16	+168:52:16.1	−15:54:30	4:17:36.1	+28:02:57	3.43 ± 0.07	71.7	1.92$_{-0.20}^{0.37}$	N	0.146
17	+168:59:50.6	−15:57:06	4:17:50.3	+27:55:52	6.17 ± 0.07	70.8	2.25$_{-0.18}^{0.23}$	N	0.655
18	+169:18:24.7	−16:07:30	4:18:11.7	+27:35:46	2.90 ± 0.07	74.7	1.87$_{-0.17}^{0.36}$	N	0.030
18.5	+169:18:37.1	−16:07:54	4:18:11.0	+27:35:21	2.86 ± 0.07	73.4	2.21$_{-0.28}^{0.28}$	⋯	0.242
19	+169:18:37.1	−16:07:54	4:18:11.0	+27:35:21	2.86 ± 0.07	73.4	2.21$_{-0.28}^{0.28}$	N	0.015
19.25	+169:18:37.1	−16:07:54	4:18:11.0	+27:35:21	2.86 ± 0.07	73.4	2.21$_{-0.28}^{0.28}$	⋯	1.161
20	+169:19:14.2	−16:09:24	4:18:07.9	+27:33:53	2.04 ± 0.09	55.9	1.74$_{-0.50}^{0.32}$	N	0.078
21	+169:45:40.7	−16:10:18	4:19:23.3	+27:14:46	2.30 ± 0.11	82.6	1.52$_{-0.31}^{0.50}$	N	0.481
21.925	+169:49:44.6	−16:08:06	4:19:42.5	+27:13:25	9.49 ± 0.07	120.0	2.05$_{-0.07}^{0.08}$	⋯	2.979
22	+169:47:27.3	−16:07:42	4:19:37.1	+27:15:18	7.40 ± 0.08	69.6	1.71$_{-0.10}^{0.15}$	N	0.610
22.85	+169:49:44.6	−16:08:06	4:19:42.5	+27:13:25	9.49 ± 0.07	120.0	2.05$_{-0.07}^{0.08}$	⋯	2.363
23	+169:49:44.6	−16:08:06	4:19:42.5	+27:13:25	9.49 ± 0.07	120.0	2.05$_{-0.07}^{0.08}$	Y	0.279
23.75	+169:49:44.6	−16:08:06	4:19:42.5	+27:13:25	9.49 ± 0.07	120.0	2.05$_{-0.07}^{0.08}$	⋯	1.687
24	+169:52:39.5	−16:08:00	4:19:51.5	+27:11:26	10.45 ± 0.06	67.0	2.24$_{-0.08}^{0.09}$	N	0.231
24.5	+169:52:39.5	−16:08:00	4:19:51.5	+27:11:26	10.45 ± 0.06	67.0	2.24$_{-0.08}^{0.09}$	⋯	0.524
25	+169:54:32.0	−16:07:48	4:19:57.6	+27:10:15	7.36 ± 0.08	74.7	1.57$_{-0.08}^{0.07}$	Y	0.075
26	+169:56:49.5	−16:06:12	4:20:09.7	+27:09:44	1.40 ± 0.08	35.4	0.83$_{-0.22}^{0.11}$	N	0.118
27	+169:59:13.1	−16:06:48	4:20:14.7	+27:07:39	1.11 ± 0.09	34.1	0.69$_{-0.07}^{0.14}$	N	0.045
27.75	+170:00:03.0	−16:08:18	4:20:12.2	+27:06:02	1.88 ± 0.10	33.6	0.60$_{-0.11}^{0.18}$	⋯	0.605
28	+170:00:03.0	−16:08:18	4:20:12.2	+27:06:02	1.88 ± 0.10	33.6	0.60$_{-0.11}^{0.18}$	N	0.133
28.5	+170:00:03.0	−16:08:18	4:20:12.2	+27:06:02	1.88 ± 0.10	33.6	0.60$_{-0.11}^{0.18}$	⋯	0.559
29	+170:01:49.1	−16:08:54	4:20:15.5	+27:04:23	1.90 ± 0.09	29.6	0.74$_{-0.18}^{0.11}$	N	0.124
30	+170:10:40.2	−16:02:30	4:21:02.5	+27:02:30	3.81 ± 0.09	53.9	1.29$_{-0.21}^{0.14}$	N	0.363
30.5	+170:09:25.2	−16:04:42	4:20:51.6	+27:01:54	2.23 ± 0.08	59.6	1.29$_{-0.17}^{0.51}$	⋯	0.927
31	+170:09:25.2	−16:04:42	4:20:51.6	+27:01:54	2.23 ± 0.08	59.6	1.29$_{-0.17}^{0.51}$	N	0.138
32	+170:08:47.8	−16:03:24	4:20:54.1	+27:03:13	1.54 ± 0.07	70.2	1.87$_{-0.37}^{0.61}$	N	0.051
33	+170:15:58.6	−16:01:24	4:21:21.7	+26:59:31	9.36 ± 0.09	73.2	2.38$_{-0.10}^{0.21}$	N	0.838
34	+170:13:16.3	−16:01:48	4:21:12.5	+27:01:09	1.41 ± 0.10	71.9	0.71$_{-0.11}^{0.38}$	Y	0.041
35	+171:02:00.7	−15:47:48	4:24:20.6	+26:36:02	2.22 ± 0.15	54.9	1.73$_{-0.36}^{1.59}$	N	0.091
36	+171:01:47.9	−15:46:12	4:24:25.3	+26:37:16	1.87 ± 0.12	44.3	1.43$_{-0.21}^{0.36}$	N	0.076
37	+171:48:05.3	−15:25:24	4:27:47.5	+26:17:58	9.33 ± 0.11	60.6	1.82$_{-0.11}^{0.15}$	N	0.639
38	+171:48:04.1	−15:22:54	4:27:55.8	+26:19:38	3.62 ± 0.11	48.6	1.96$_{-0.42}^{0.43}$	Y	0.090
39	+171:49:30.0	−15:20:06	4:28:09.2	+26:20:28	9.20 ± 0.12	89.6	2.64$_{-0.23}^{0.14}$	N	0.809

^aIDs with decimal points are NH₃ branches. ^bTotal integrated intensity of NH₃ (1, 1) emission. ^c500 μm dust continuum of Herschel Space Observatory. Typical rms is 0.4 MJy/sr. ^dStatistical uncertainty of peak column density is only due to uncertainties of the 500 μm dust continuum flux density and T_k. T_d = T_k is assumed. ^eBranches are omitted and noted as "..."

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Table 2.  Physical Properties of NH₃ Sources

IDa	Tkb	${{\sigma }_{v}}$ c	Mass from Dust	Virial Massd	Mass from NH3e
	(K)	(km s−1)	(${{M}_{\odot }}$)	(${{M}_{\odot }}$)	(${{M}_{\odot }}$)
1	10.24$_{-0.42}^{0.17}$	0.199$_{-0.005}^{0.005}$	0.18	0.45	0.36
1.5	9.92$_{-0.86}^{0.52}$	0.201$_{-0.005}^{0.011}$	4.56	2.21	3.91
2	9.66$_{-0.08}^{0.09}$	0.197$_{-0.005}^{0.005}$	0.06	0.19	0.09
3	10.25$_{-0.84}^{0.93}$	0.204$_{-0.008}^{0.014}$	4.38	1.45	1.03
4	8.49$_{-0.99}^{0.99}$	0.210$_{-0.012}^{0.011}$	0.31	0.34	0.05
5	9.65$_{-1.34}^{1.52}$	0.252$_{-0.016}^{0.018}$	1.74	1.93	0.71
6	9.47$_{-0.50}^{0.78}$	0.227$_{-0.020}^{0.005}$	0.77	1.15	0.50
6.5	9.49$_{-0.52}^{0.59}$	0.201$_{-0.009}^{0.028}$	1.85	1.61	1.39
7	9.48$_{-0.55}^{0.43}$	0.194$_{-0.005}^{0.006}$	0.88	0.98	0.77
7.5	9.29$_{-0.77}^{0.78}$	0.202$_{-0.009}^{0.022}$	9.52	3.89	7.58
8	9.26$_{-0.21}^{0.16}$	0.196$_{-0.003}^{0.002}$	0.26	0.47	0.37
8.5	8.99$_{-0.54}^{0.52}$	0.198$_{-0.005}^{0.008}$	3.20	1.88	3.64
9	8.61$_{-0.24}^{0.30}$	0.197$_{-0.005}^{0.007}$	1.02	0.89	1.35
10	9.63$_{-2.11}^{2.12}$	0.224$_{-0.012}^{0.029}$	0.41	0.61	0.25
11	10.00$_{-0.54}^{0.39}$	0.203$_{0.011}^{0.012}$	0.10	0.58	0.12
12	9.29$_{-0.38}^{0.67}$	0.213$_{-0.017}^{0.026}$	0.95	0.98	0.98
12.5	9.49$_{-0.57}^{0.94}$	0.220$_{-0.021}^{0.024}$	1.32	1.47	1.24
13	10.90$_{-1.41}^{1.06}$	0.236$_{-0.013}^{0.009}$	0.04	0.31	0.03
13.25	9.68$_{-0.75}^{1.18}$	0.227$_{-0.022}^{0.036}$	2.79	2.67	2.12
14	9.68$_{-0.37}^{0.59}$	0.226$_{-0.008}^{0.010}$	0.23	0.61	0.13
15	8.84$_{-0.50}^{0.39}$	0.217$_{-0.014}^{0.035}$	0.21	0.50	0.15
15.5	9.50$_{-1.06}^{0.64}$	0.206$_{-0.012}^{0.039}$	2.73	2.02	1.88
16	9.66$_{-0.30}^{0.27}$	0.196$_{-0.003}^{0.007}$	0.53	0.75	0.46
17	9.31$_{-0.54}^{0.59}$	0.196$_{-0.005}^{0.007}$	1.62	1.22	1.97
18	9.75$_{-0.40}^{0.43}$	0.222$_{-0.009}^{0.006}$	0.12	0.40	0.09
18.5	9.48$_{-0.47}^{0.54}$	0.220$_{-0.010}^{0.006}$	0.99	1.09	0.66
19	9.11$_{-0.47}^{0.71}$	0.214$_{-0.006}^{0.006}$	0.07	0.22	0.05
19.25	9.45$_{-1.24}^{0.99}$	0.217$_{-0.010}^{0.013}$	4.06	2.15	2.09
20	9.50$_{-1.29}^{1.22}$	0.217$_{-0.007}^{0.012}$	0.30	0.66	0.15
21	9.17$_{-1.30}^{1.36}$	0.201$_{-0.016}^{0.016}$	1.92	1.30	0.70
21.925	9.80$_{-0.82}^{0.87}$	0.203$_{-0.012}^{0.017}$	8.97	3.82	9.74
22	9.74$_{-0.75}^{0.58}$	0.203$_{-0.011}^{0.014}$	1.89	1.39	1.73
22.85	9.85$_{-0.77}^{0.82}$	0.203$_{-0.012}^{0.017}$	6.84	3.55	8.97
23	10.39$_{-0.54}^{0.51}$	0.210$_{-0.011}^{0.005}$	0.95	1.11	1.45
23.75	9.91$_{-0.80}^{0.94}$	0.203$_{-0.012}^{0.018}$	4.77	3.04	7.16
24	9.08$_{-0.16}^{0.15}$	0.191$_{-0.003}^{0.003}$	0.88	0.77	2.14
24.5	9.20$_{-0.23}^{1.05}$	0.192$_{-0.003}^{0.013}$	1.81	1.38	3.63
25	10.26$_{-0.78}^{0.48}$	0.204$_{-0.009}^{0.009}$	0.27	0.53	0.45
26	9.75$_{-1.22}^{1.31}$	0.202$_{-0.012}^{0.012}$	0.24	0.77	0.16
27	10.27$_{-1.09}^{1.01}$	0.203$_{-0.011}^{0.004}$	0.08	0.45	0.05
27.75	10.63$_{-1.31}^{0.99}$	0.204$_{-0.014}^{0.010}$	0.85	1.65	0.73
28	11.32$_{-0.58}^{0.95}$	0.213$_{-0.005}^{0.010}$	0.15	0.70	0.15
28.5	10.64$_{-1.32}^{0.99}$	0.205$_{-0.014}^{0.010}$	0.77	1.66	0.68
29	10.03$_{-0.97}^{0.67}$	0.195$_{-0.007}^{0.008}$	0.19	0.68	0.18
30	9.92$_{-1.18}^{1.08}$	0.212$_{-0.005}^{0.008}$	1.08	1.39	0.99
30.5	9.77$_{-1.09}^{1.14}$	0.220$_{-0.012}^{0.022}$	3.09	2.56	2.03
31	9.55$_{-0.52}^{0.49}$	0.231$_{-0.011}^{0.014}$	0.50	0.93	0.29
32	8.95$_{-1.32}^{1.96}$	0.207$_{-0.019}^{0.018}$	0.26	0.40	0.08
33	9.54$_{-0.58}^{0.93}$	0.206$_{-0.011}^{0.013}$	2.49	1.87	4.61
34	13.39$_{-0.91}^{0.57}$	0.270$_{-0.015}^{0.027}$	0.07	0.69	0.04
35	9.22$_{-1.11}^{0.80}$	0.208$_{-0.005}^{0.007}$	0.36	0.60	0.17
36	9.81$_{-0.92}^{1.62}$	0.205$_{-0.012}^{0.012}$	0.19	0.57	0.11
37	9.83$_{-0.62}^{0.50}$	0.209$_{-0.008}^{0.018}$	1.82	1.61	2.97
38	9.55$_{-1.48}^{0.62}$	0.212$_{-0.007}^{0.006}$	0.31	0.62	0.26
39	9.55$_{-0.56}^{0.68}$	0.199$_{-0.006}^{0.014}$	2.89	1.51	3.22

^aIDs with decimal points are branches in dendrograms. ^bMedian T_k of the NH₃ leaves and branches. Subscripts and superscripts are 15.9% and 84.1% of the T_k distribution within NH₃ leaves and branches. ^cMedian ${{\sigma }_{v}}$ of the NH₃ leaves and branches with the mean molecular weight μ = 2.33. Subscripts and superscripts are 15.9% and 84.1% of the ${{\sigma }_{v}}$ distribution within NH₃ leaves and branches. ^dThe NH₃ leaves and branches are assumed to be homoeoidal ellipsoids for the virial mass calculation. ^eThe fractional abundance of NH₃ is assumed to be 1.5 × 10⁻⁹ (typical fractional abundance ranges from 10⁻⁹ to 10⁷; e.g., Jijina et al. 1999; Tafalla et al. 2004).

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Table 3.  Geometrical Properties of NH₃ Sources

IDa	Short Axis	Long Axis	Axis Ratio	Phase Angleb
	(10−2 pc)	(10−2 pc)		(Degree)
1	0.65	2.27	0.287	38.9
1.5	3.79	10.1	0.376	43.9
2	0.46	0.8	0.581	44.8
3	2.8	5.98	0.469	152.5
4	0.91	1.61	0.568	140.1
5	2.75	5.47	0.505	34.4
6	1.47	4.21	0.348	151.4
6.5	1.67	9.69	0.172	1.3
7	1.69	4.85	0.348	18.1
7.5	3.37	27.2	0.124	24.6
8	1.14	1.99	0.571	20.1
8.5	2.21	11.1	0.200	23.7
9	1.34	4.57	0.294	16.2
10	3.00	3.69	0.813	170.3
11	0.99	1.6	0.621	4.3
12	2.09	3.44	0.606	25.4
12.5	2.01	5.64	0.357	37.8
13	0.64	8.27	0.775	179.6
13.25	3.03	11.3	0.268	38.9
14	1.16	1.92	0.606	36.9
15	0.87	1.82	0.476	38.0
15.5	2.86	9.85	0.291	173.8
16	1.27	3.67	0.345	143.9
17	4.40	4.74	0.935	173.6
18	0.72	1.33	0.541	160.2
18.5	2.12	3.64	0.581	43.4
19	0.69	0.69	1.00	30.0
19.25	5.30	6.97	0.763	23.4
20	0.97	2.56	0.379	165.5
21	2.67	5.73	0.467	13.1
21.925	4.64	20.4	0.228	174.4
22	3.81	5.1	0.752	171.7
22.85	3.57	21.1	0.170	178.9
23	2.11	4.19	0.505	177.0
23.75	2.74	19.6	0.140	176.8
24	2.25	3.26	0.694	20.45
24.5	2.27	7.36	0.309	177.5
25	1.13	2.09	0.543	156.7
26	0.87	4.31	0.202	4.5
27	0.68	2.09	0.328	41.2
27.75	2.6	7.41	0.352	20.7
28	1.82	2.32	0.787	37.8
28.5	2.16	8.22	0.263	16.4
29	1.19	3.32	0.361	4.2
30	1.94	5.96	0.326	142.3
30.5	2.47	12	0.207	147.9
31	1.52	2.88	0.529	137.7
32	1.19	1.38	0.870	138.8
33	3.58	7.46	0.481	7.0
34	0.84	1.57	0.538	159.2
35	1.29	2.26	0.571	27.3
36	1.01	2.41	0.418	28.3
37	3.4	5.98	0.571	2.4
38	1.28	2.23	0.571	17.5
39	4.45	5.79	0.769	146.8

^aIDs with decimal points are branches in dendrograms. ^bThe phase angle of NH₃ leaves with respect to the Galactic longitude. For the phase angle with respect to the equatorial plane, 626 should be added.

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The column density of molecular hydrogen within each structure is estimated from the 500 μm continuum of Herschel Space Observatory using the following equation:

$$\begin{eqnarray}&&{{N}_{{{{\rm H}}_{2}}}}=\frac{{{S}_{\nu }}}{\mu {{m}_{{\rm H}}}{{B}_{\nu }}({{T}_{{\rm dust}}}){{\kappa }_{\nu }}{{{\Omega }}_{{\rm ap}}}}\frac{{{m}_{{\rm gas}}}}{{{m}_{{\rm dust}}}},\end{eqnarray} \tag{ 2 }$$

where ${{N}_{{{{\rm H}}_{2}}}}$ is column density of H₂ molecules, ${{S}_{\nu }}$ is observed flux at frequency ν, μ is mean molecular weight, m_H is mass of the hydrogen atom, ${{B}_{\nu }}$ is blackbody radiation at frequency ν, ${{T}_{{\rm dust}}}$ is temperature of a dust grain, ${{\kappa }_{\nu }}$ is opacity of a dust grain at frequency ν, ${{{\Omega }}_{{\rm ap}}}$ is the solid angle used in the observation, and ${{m}_{{\rm dust}}}/{{m}_{{\rm gas}}}$ is dust-to-gas ratio, which we set to 0.01. In this work, we assume ${{T}_{{\rm dust}}}={{T}_{k}}$, where T_k is the kinetic temperature deduced from our ammonia observations. μ is 2.8. We use ${{\kappa }_{\nu }}$ of 5.04 cm² g⁻¹ (OH5), which is column 5 of the "MNR with thin ice mantle" model from Ossenkopf & Henning (1994). The peak H₂ column density of NH₃ sources in the L1495-B218 filaments ranges from 6.0 × 10²¹ to 4.3 × 10²² cm⁻², which is similar to the typical dense core column density in other molecular clouds (e.g., Jijina et al. 1999; Rosolowsky et al. 2008).

We define the size of an NH₃ source as the radius of a circle that has an area equal to that of an NH₃ CSAR leaf contour. In the L1495-B218 filaments, the FWHM from Gaussian fitting may not be a useful representation of the size of a dense core because the FWHM contour of a dense core often overlaps with the FWHM contour of its neighboring dense core. Since CSAR separates neighboring sources through hierarchical structure, we use the area identified by CSAR to estimate the size of a structure. Structures were found on scales ranging from 2 × 10⁻² pc (4375 AU) to 0.1 pc (20,000 AU).

The masses of NH₃ sources are estimated by summing up the column density deduced from 500 μm continuum within each NH₃ leaf and branch (Table 2 and black circles in Figure 10). This is a typical method for estimating mass of a dense source since three-dimensional morphology is usually unknown. If three-dimensional morphology is known or assumed, mass of a local background may be subtracted, which will result in a smaller dense source mass than the dense source mass estimated by simply summing up the column density. The resulting masses of NH₃ leaves range from 0.05 to 4.3 ${{M}_{\odot }}$, which are similar to typical dense core masses observed in other studies (0.1–10 ${{M}_{\odot }}$; Onishi et al. 1996, 2002; Motte et al. 1998, 2001; Schmalzl et al. 2010; Kirk et al. 2013). The masses of NH₃ branches range from 0.78 to 9.5 ${{M}_{\odot }}$. In addition, we also compared three different methods of determining masses of NH₃ leaves in Table 2 and Figure 12 (mass estimated from dust continuum, virial mass shown in Section 4.1, and mass estimated from NH₃ column density with the fractional abundance of NH₃ relative to hydrogen molecules being 1.5 × 10⁻⁹). The masses are strongly correlated with each other, with a Spearmann's rank correlation coefficient of ρ = 0.93. This strong linear correlation suggests that the assumptions (i.e., opacity and temperature) used to derive mass from the dust emission do not have strong systematic variations from the lowest-mass to highest-mass leaves. It also suggests that the properties derived from NH₃ sources identified by CSAR are representative of the properties of dense regions in the L1495-B218 filaments, regardless of whether those regions are traced by dust emission or NH₃.

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We also compared nonthermal support to thermal support within NH₃ leaves identified by CSAR in Figure 12. All of the NH₃ sources are dominated by thermal support, with an average value of R_p = $c_{s}^{2}/\sigma _{{\rm nt}}^{2}$ equal to 4.9, and there is no dependency on R_p versus mass. This shows that nonthermal motions are efficiently dissipated in dense regions, making it easier to initiate star formation.

3.2.3. Shape and Orientation

The two-dimensional morphology of the NH₃ sources is estimated using the moment of integrated intensity of NH₃ (1, 1) with the center at the location of the intensity peak within a leaf or a branch. From the moment of integrated intensity we derive the principal axes, the axis ratios, and the angles with respect to galactic longitude, which are also summarized in Table 3. The distribution of angles of NH₃ leaves with respect to their lowest-level branches in the dendrogram is shown in the third panel of Figure 13. The minimum and the maximum phase angles of NH₃ leaves with respect to their lowest-level branches are −49° and 53°, respectively. Most of the NH₃ leaves are well aligned with their lowest-level branches within a range of ±40°. Since a lowest-level branch corresponds to a filament, this suggests that NH₃ leaves are well aligned with filaments and were likely formed within the filaments.

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The axis ratio of the NH₃ leaves is estimated as short axis/long axis (Table 3). The distribution of axis ratios is shown in the fourth panel of Figure 13. The axis ratios range from 0.2 to 1.0 and are mostly around 0.5, which is close to the average value obtained from dense core observations by Myers et al. (1991). In order to deduce the three-dimensional morphology of NH₃ leaves, we compared the observed axis ratio distribution to the probability distribution of apparent axis ratios of spheroids using a Monte Carlo method (see Appendix B for more details). We found the best-fit axis ratio distribution when the spheroids are prolate and the orientation angles (the angle between the equatorial planes of spheroids and the observer's line of sight) range from −80° to 80° (thick solid line in the fourth panel of Figure 13). The parameters of the prolate spheroids of the best-fit model are a mean axis ratio (short axis/long axis) of 0.40 and a dispersion of 0.11 with ${{\chi }^{2}}$ = 5.92. We could not fit the distribution model using oblate spheroids within 3σ uncertainty (${{\chi }^{2}}$ = 9) unless we limit the orientation angles much narrower than the observed distribution of the angles between the axes of NH₃ leaves and the axes of filaments (third panel of Figure 13). Thus, the NH₃ leaves are more likely prolate spheroids than oblate spheroids.

We investigate the dynamical states of NH₃ leaves using the virial theorem. An equation of the virial theorem without magnetic contributions is

$$\begin{eqnarray}&&\frac{1}{2}\frac{{{d}^{2}}I}{d{{t}^{2}}}=W+2(T+{\bf \Pi })-\int p\vec{x}\cdot \hat{n}dS\end{eqnarray} \tag{ 3 }$$

where I is the moment of inertia, W is the gravitational energy, T is the kinetic energy of systemic motions, Π is the internal energy of thermal and nonthermal motions, and the integral term is the work done by the external pressure p. S is the core surface, and $\hat{n}$ is the unit vector perpendicular to the core surface. We omitted the terms related to magnetic fields because there is no measurement of magnetic fields within NH₃ leaves. There are studies using the virial theorem including all terms except magnetic fields (e.g., Hunter 1979; Seo et al. 2013), but only the gravitational and the internal energies are conventionally used for studying dynamical stability of a dense core in observational studies because it is hard to estimate other terms. We also start with only the gravitational and the internal energies in estimating the virial mass and further check whether or not the pressure term is important in confining dense cores. We assume a time-independent steady state so that ${{d}^{2}}I/d{{t}^{2}}$ = 0.

We assumed an NH₃ leaf as a homoeoidal ellipsoid with density falling as $\rho \sim {{r}^{-\beta }}$ (Bertoldi & McKee 1992). The gravitational energy of a homoeoidal ellipsoid is

$$\begin{eqnarray}&&W=-\frac{3}{5}\frac{1-\frac{\beta }{3}}{1-\frac{2\beta }{5}}\frac{G{{M}^{2}}}{R}\frac{{\rm arcsin} e}{e},\end{eqnarray} \tag{ 4 }$$

where e is the eccentricity of a homoeoidal ellipsoid and R is the semimajor axis. The internal energy is estimated by

$$\begin{eqnarray}&&{\bf \Pi }=\frac{3}{2}M\bar{\sigma }_{v}^{2},\end{eqnarray} \tag{ 5 }$$

where ${{\bar{\sigma }}_{v}}$ is a representative value of velocity dispersion including thermal and nonthermal motions within an NH₃ leaf. It can be either the average, median, or mass-weighted values. In this study, we use median values of ${{\sigma }_{v}}$ within NH₃ leaves. Finally, the virial mass when $W=2U$ is given as

$$\begin{eqnarray}&&{{M}_{{\rm vir}}}=5\frac{1-\frac{2\beta }{5}}{1-\frac{\beta }{3}}\frac{R\bar{\sigma }_{v}^{2}}{G}\frac{e}{{\rm arcsin} \;e}.\end{eqnarray} \tag{ 6 }$$

We first estimated a virial mass with $\rho \sim {{r}^{-2}}$ ($\beta =2$), which is listed in Table 2. The eccentricities of leaves are estimated from the axis ratios of NH₃ leaves, which are given in Table 3. The virial masses of NH₃ leaves are shown as red circles in Figure 10. The virial mass is calculated for only the NH₃ leaves because the NH₃ branches usually have either very elongated or irregular shapes, which makes it difficult to calculate the virial mass with conventional assumptions. We find that 30 out of 39 leaves have observed masses smaller than their corresponding virial masses (the first panel in Figure 13), which suggests that most leaves are gravitationally unbound (the median ratio is about 2). Seven out of nine gravitationally bound leaves are active (red), while only 2 out of 22 inactive (blue) leaves are gravitationally bound. A virial mass of a homoeoidal ellipsoid with $\rho \sim {{r}^{-1}}$ is 50% larger than the corresponding virial mass of a homoeoidal ellipsoid with $\rho \sim {{r}^{-2}}$. For $\rho \sim {{r}^{-1}}$, there are only two gravitationally bound leaves, both of which are active leaves.

In order to assess the validity of the virial analysis, we must first carefully analyze the uncertainties. One uncertainty may come from a choice of ${{\bar{\sigma }}_{v}}$. In this study, we chose median values of ${{\sigma }_{v}}$ within NH₃ leaves, but one may use a mean of ${{\sigma }_{v}}$ or a mass-weighted mean of ${{\sigma }_{v}}$ (mass-weighted mean is $\bar{\sigma }_{v}^{2}$ = $\int {{N}_{{{{\rm H}}_{2}}}}\mu {{m}_{{\rm H}}}\sigma _{v}^{2}dA/\int {{N}_{{{{\rm H}}_{2}}}}\mu {{m}_{{\rm H}}}dA$) within an NH₃ leaf. We found that the mean values of ${{\sigma }_{v}}$ are at most 10% larger (typically 5%) than the corresponding median values, which may result in at most 20% increase of corresponding virial mass. The mean values may be larger than the median values because ${{\sigma }_{v}}$ tends to be lower at the center of an NH₃ leaf and considerably increases toward edges of the NH₃ leaf. Mass-weighted means, on the other hand, range from 95% to 105% of the corresponding median ${{\sigma }_{v}}$ values. Thus, uncertainties originating from choices of ${{\bar{\sigma }}_{v}}$ do not strongly affect the conclusion of virial mass analysis since ratios of viral masses to observed masses are quite large with respect to these uncertainties.

The largest uncertainties in estimating the observed mass from 500 μm continuum data are mainly due to assuming T_d = T_k and uncertainty in dust opacity κ. Comparing the dust temperature, which is estimated by spectral energy distribution fitting of 70, 160, 250, 350, and 500 μm dust continuums (Palmeirim et al. 2013) to the gas kinetic temperature deduced from NH₃ (1, 1) and (2, 2), we found that the dust temperature is typically 3–5 K higher than the gas kinetic temperature. If the dust temperature is 5 K higher than the gas kinetic temperature, the mass estimated from the dust temperature is 35% less than the mass estimated with the T_d = T_k assumption, and only four active NH₃ leaves are gravitationally bound.

Another uncertainty is from the dust-to-gas ratio. In this study, we use 0.01, which is a standard value assumed in a molecular cloud (e.g., Beckwith et al. 1990; Lombardi et al. 2006; Schmalzl et al. 2010; Kirk et al. 2013). However, detailed observations of interstellar dust grains in the diffuse ISM indicate that the dust-to-gas ratio is close to 0.0064 (Draine 2011 and reference therein). This increases observed mass of the leaves by about 55% from the current values. In this case, 20 out of 39 leaves are gravitationally bound, and 19 leaves are still gravitationally unbound.

Not knowing three-dimensional morphologies of leaves also brings uncertainty in estimating masses of leaves. We estimate the mass of a leaf by simply summing up the column mass of pixels that belongs to the leaf, which corresponds to a cylindrical morphology rather than a spheroidal morphology. This has been a conventional method to estimate the masses of dense structures since we do not know three-dimensional morphologies (e.g., Kirk et al. 2013). In order to check the uncertainty from assuming different morphologies in estimating the mass of a dense structure, we estimated the masses of leaves by summing up the column density of pixels within leaves after subtracting the average column density of local backgrounds/branches. We found that the masses of leaves are typically 20%–50% less than the original values if we subtract a local background from the leaves in estimating leaf mass and that only 2 out of 39 leaves are gravitationally bound.

The typical uncertainty in the dust opacity is a factor of a few (e.g., Shirley et al. 2011), and this results in quite a large uncertainty in estimating mass since M ∝ $1/\kappa$. We use OH5 dust opacity, but this is not a direct measurement of dust opacity from molecular clouds but a simulated dust opacity based on a coagulated dust model. Shirley et al. (2011) made a direct measurement of the dust opacity at 450 and 850 μm in the outer envelope of a low-mass Class 0 core, B335, through a comparison between infrared extinction and submillimeter dust continuum. We compared the dust opacity of Shirley et al. (2011) to OH5 dust opacity at 450 μm and applied the same uncertainty range of dust opacity to OH5 dust opacity at 500 μm (κ = 5.04$_{-1.10}^{3.91}$ cm² g⁻¹). The uncertainty in the observed mass ranges from 57% lower to 28% higher with respect to the observed mass given in Table 2. If we take the lower limit of uncertainty in the observed mass, two active NH₃ leaves are gravitationally bound, while if we take the upper limit of uncertainty in the observed mass, 15 out of 39 are gravitationally bound.

Thus, uncertainties in ${{\sigma }_{v}}$, T_d, ${{m}_{d}}/{{m}_{g}}$, geometry, backgrounds, and dust opacity are unlikely to change our conclusion that most leaves are gravitationally unbound. This result suggests that a dense core may first form as a gravitationally unbound structure, evolve to a gravitationally bound core, and then undergo collapse to form a protostar. Indeed, 10 out of 15 bound leaves in the extreme opacity limit are in more evolved regions.

External pressure may be a source to confine gravitationally unbound structure. Dib et al. (2007) carried out a detailed virial analysis for dense cores forming in a turbulent environment using a numerical method. They showed that the work done by the external pressure in the virial theorem is comparable to the other terms such as internal energy and gravitational energy (Dib et al. 2007). Since most of the NH₃ leaves are not gravitationally bound in our simple virial analysis, we checked whether or not work done by the external pressure is comparable to the internal and gravitational energy. The work done by external pressure is estimated as follows:

$$\begin{eqnarray}&&\int p\vec{x}\cdot \hat{n}dS=\frac{4}{3\sqrt{1-{{e}^{2}}}}{\rm min} {{\{{{N}_{{{{\rm H}}_{2}}}}\mu {{m}_{{\rm H}}}\sigma _{v}^{2}\}}_{C}}A,\end{eqnarray} \tag{ 7 }$$

where A is the projected area of the NH₃ leaf. ${{N}_{{{{\rm H}}_{2}}}}\mu {{m}_{{\rm H}}}\sigma _{v}^{2}$ is the integration of pressure along the line of sight, where ${{N}_{{{{\rm H}}_{2}}}}$ is column density estimated from 500 μm and ${{\sigma }_{v}}$ is velocity dispersion of molecular gas with μ = 2.33. We chose the minimum value at the circumference of the NH₃ leaf, ${\rm min} {{\{{{N}_{{{{\rm H}}_{2}}}}\mu {{m}_{{\rm H}}}\sigma _{v}^{2}\}}_{C}}$, because it corresponds to the minimum external pressure exerted on an NH₃ leaf. The coefficient of $4/(3\sqrt{1-{{e}^{2}}})$ is for spheroid geometry when one of the principal axes is aligned with the observer's line of sight. We estimate the work done by external pressure using ${\rm min} {{\{{{N}_{{{{\rm H}}_{2}}}}\mu {{m}_{{\rm H}}}\sigma _{v}^{2}\}}_{C}}$ because the external pressure is not well known. The estimated work done by external pressure ranges from 5 × 10⁴⁰ to 1 × 10⁴² erg. In a majority of leaves, gravitational energies are larger than the corresponding work done by external pressure except for 12 leaves (the second panel of Figure 13), which suggests that those 12 leaves are pressure confined. Active leaves tend to have a lower average ratio than that of inactive leaves, which indicates that the gravity becomes more important than external pressure as a dense core evolves. Moreover, in 9 out of 12 leaves, the ratios of the work done by external pressure to the gravitational energy are larger than that of the critical Bonnor–Ebert sphere (black dashed vertical line; Bonnor 1956; Ebert 1955, 1957). Thus, these results suggest that the youngest condensations are pressure confined.

A source of the external pressure may be investigated by comparing the internal pressure of the NH₃ leaves and the pressure of the surrounding media. The mean internal pressure of NH₃ leaves is $\lt p/k\gt$ = 2 × 10⁶ K cm⁻³, where p is roughly estimated as

$$\begin{eqnarray}&&p=\frac{M\bar{\sigma }_{v}^{2}}{V},\end{eqnarray} \tag{ 8 }$$

where V is the leaf volume and ${{\bar{\sigma }}_{v}}$ is the median value of ${{\sigma }_{v}}$ within an NH₃ leaf. We assumed that the leaf volume is the same as the volume of a prolate spheroid having the observed axis ratio (see Section 3.2.3 for shapes of NH₃ leaves). If we assume that the density structure of a leaf resembles the critical Bonnor–Ebert sphere, the surface pressure is about 40% of the mean internal pressure, $\lt {{p}_{{\rm surface}}}/k\gt$ = 8 × 10⁵ K cm⁻³. This is significantly higher than the gas pressure of the interstellar medium ($\lt {{p}_{{\rm ISM}}}/k\gt$ ≈ 10⁴ K cm⁻³; Bertoldi & McKee 1992; Draine 2011) and still a bit higher than the interstellar turbulence ram pressure, $\lt {{p}_{{\rm ram}}}/k\gt$ ≈ 5 × 10⁴ K cm⁻³ (Lada et al. 2008).

Another source of external pressure may be the weight of the filament material outside of NH₃ leaves since the self-gravity of the filaments produces a gravitational potential well and the weight of filament material outside of NH₃ leaves exerts a confining pressure on the NH₃ leaves. We estimated the pressure due to the weight of the filament material outside of the NH₃ leaves as (Bertoldi & McKee 1992; Lada et al. 2008)

$$\begin{eqnarray}&&{{p}_{{\rm filaments}}}=\frac{3\pi }{20}aG{{{\bf \Sigma }}^{2}},\end{eqnarray} \tag{ 9 }$$

where Σ is the mean mass surface density of material outside of leaves and a is a correction factor for the non-spherical geometry of the filaments. The values of a range from 1.0 to 3.3 depending on the eccentricities and density structures of the filaments (for a = 3.3, we took the maximum axis ratio of the NH₃ branches, max(Z/R) ∼ 10, and a density structure of $\rho \sim {{r}^{-2}}$). The mean of the pressure of the filaments due to their weight is $\lt {{p}_{{\rm filament}}}/k\gt$ = 6 × 10⁵ K cm⁻³, which is a bit smaller than the surface pressure estimated from Equation (8) but within a factor of 2. This suggests that the weight of the filaments is one of the main sources that confines gravitationally unbound leaves.

Ram pressure due to the inflow of materials onto the filaments and dense cores from the molecular cloud may be another source of confining dense structures. Theoretical studies demonstrated that ram pressure due to mass accretion to dense structures may provide considerable confining pressure (Heitsch 2013a, 2013b) if a converging flow or an inflow is relatively isotropic (a non-isotropic converging flow may disrupt a dense structure; Did et al. 2007). ¹²CO and ¹³CO observations of the L1495-B218 filaments show that there is a difference of 2 km s⁻¹ in the LSR velocities from the northeast to the southwest of B211 (Goldsmith et al. 2008; Palmeirim et al. 2013). This is similar to an infall velocity predicted in a similarity solution of gravitational infall onto a cylinder (Kawachi & Hanawa 1998). If we accept that the difference in the LSR velocity is due to relatively isotropic inflow of materials from the molecular cloud to the filaments, the ram pressue due to an inflow motion is

$$\begin{eqnarray}&&{{p}_{{\rm accretion}}}={{\rho }_{{\rm p}}}(R)\delta {{V}^{2}},\end{eqnarray} \tag{ 10 }$$

where ${{\rho }_{{\rm p}}}$ is the density of the best-fit Plummer model to the filament (Palmeirim et al. 2013) and R is the outer radius of the filament, which is 0.4 pc for the B211–B213 regions. $\delta V$ is the difference in the LSR velocity across the B211 and B213 regions, which is about 2 km s⁻¹. The ram pressure due to the accretion of materials from the molecular cloud to filaments is $\lt {{p}_{{\rm filament}}}/k\gt$ $\simeq$ 4.5 × 10⁵ K cm⁻³, which is smaller than the surface pressure estimated from Equation (8) but still within a factor of 2. Since there is projection effect in measuring the true inflow velocity, this may be a lower limit of ram pressure due to an inflow motion. Thus, ram pressure due to inflow of materials from the molecular cloud to the filaments may also be one of the main sources of pressure that confine gravitationally unbound leaves.

The formation of a filament or a dense core through the gravoturbulence fragmentation scenario predicts that a dense structure may not be strongly aligned with magnetic fields (Nakamura & Li 2008) unless the magnetic field pressure is considerably stronger than the ram pressure of turbulence. On the other hand, formation through a quasi-static gravitational contraction may result in a strong alignment of the dense core with magnetic fields because contraction occurs more efficiently along magnetic field lines. Although magnetic field directions are not measured within the NH₃ sources, magnetic field directions on filament scales (a few 0.1 pc) have been measured through dust polarization in optical and infrared wavelengths along the L1495-B218 filaments (Chapman et al. 2011 and references therein). In B7 and B10 the magnetic fields are relatively parallel to the long axes of a filament. From B213 to B216 the magnetic fields are perpendicular to the long axes of filaments. Dust polarization in B218 is not measured. Since we do not know the magnetic field directions within dense cores and magnetic field directions are aligned in only some regions, it is difficult to ascertain the role of magnetic field in aligning dense cores.

In the gravoturbulence fragmentation scenario, a dense core forms as an oblate spheroid and quickly proceeds to a prolate spheroid or triaxial shape (e.g., Gong & Ostriker 2011; Kainulainen et al. 2014). The ratio of oblate dense cores to prolate dense cores depends on the Mach number of turbulence and the evolution time. A system with either a higher Mach number or a younger age shows a higher proportion of oblate dense cores. Since the NH₃ leaves are likely to be prolate (see Section 3.2.3), the L1495-B218 filaments may have been formed in a low Mach number turbulence (M $\leqslant$ 2; Gong & Ostriker 2011) if the filaments are formed through the gravoturbulence fragmentation scenario. The velocity dispersions of filaments in the Taurus estimated from ¹³CO observations are indeed low Mach number dispersions that range from 0.15 to 0.65 km s⁻¹ (Panopoulou et al. 2014), corresponding to Mach numbers of 0.65–3.2, if we take the kinetic temperature of 15 K (Goldsmith et al. 2008). Alternatively, magnetic fields may also make a dense core to have a non-spherical shape because a dense core tends to contract along the magnetic field lines whereas a direction perpendicular to the field is supported by magnetic pressure. If magnetic pressure is the main force making a dense core's non-spherical shape, the dominant shape is an oblate spheroid (Lizano & Shu 1989). Since most of the NH₃ leaves are likely prolate spheroids, magnetic pressure does not seem to be the main cause of shaping a dense core into an elongated morphology, but gravoturbulence fragmentation may have played important roles in shaping the NH₃ leaves.

Larson proposed that there is an empirical relation between line width and size of a structure in a cloud scale (Larson 1981). To see whether there is such a relation in a sub-filament scale, we compare the mean velocity dispersion of NH₃ sources with the NH₃ source size in Figure 14. The velocity dispersion is almost flat on a scale from 0.005 to 0.1 pc (the mean velocity dispersion of molecular gas with μ = 2.33 is 0.204 km s⁻¹), and it is close to the thermal velocity dispersion (0.188 km s⁻¹ at 10 K and μ = 2.33). This demonstrates that nonthermal motions are significantly dissipated on scales less than 0.2 pc in the L1495-B218 filaments, resulting in a breakdown in the cloud-scale supersonically turbulent scaling relation.

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Observations toward molecular clouds show that molecular clouds are supersonic turbulent (e.g., Larson 1981; Scalo 1984; Miesch & Bally 1994; Padoan et al. 1999). In a smaller scale, observations toward molecular cloud cores show that dense cores are typically thermally supported and turbulence is significantly dissipated (e.g., Caselli & Myers 1994; Goodman et al. 1998; Jijina et al. 1999; Caselli et al. 2002). The dense NH₃ structures in this study also have the mean R_p of 4.9 (Section 3.2.2). On the other hand, the R_p values measured in C¹⁸O J = 1–0 (Hacar et al. 2013) in the L1495-B218 filaments are close to unity, and the mean R_p value measured in ¹³CO J = 1–0 (Panopoulou et al. 2014) is 0.25. Since C¹⁸O J = 1–0 traces less dense and larger structures than those seen by NH₃ (1, 1) and ¹³CO J = 1–0 traces even more extended regions than those traced by C¹⁸O J = 1–0, the dependency of R_p values on the effective excitation density of the tracer suggests that supersonic turbulence cascades from a cloud scale to a core scale and is considerably dissipated on a scale smaller than molecular filaments ($\leqslant$ 0.5 pc) in the Taurus. A more detailed analysis of the velocity dispersion and associated kinematic structure will be presented in Paper II.

Mass–size relations are often pursued to investigate the correlation between density structures of sources and their size. The mass and size distributions of leaves and branches in the L1495-B218 filaments are shown in Figure 14. Mass and size show a strong correlation of $M\sim {{r}^{1.9}}$ (red solid line for NH₃ leaves and branches) (power-law indices of leaves only and that of branches only are close to 2 as well). This is close to a global relation for molecular clouds where the power-law index is 2 (Larson 1981), which indicates a nearly constant mean column density. Kirk et al. (2013) found a relation with a power-law index of 2.35 in the Taurus from Herschel dust continuum observations. Their analysis includes structures larger than 1 pc, whereas the largest structure in this study is only 0.1 pc. If we only take structures less than 0.1 pc from Kirk et al. (2013), the power-law index is shallower than 2.35 and close to 2. Kauffmann et al. (2010) studied mass–size relations resolved in several nearby molecular clouds. They also found that the power-law index is close to 2 in the Taurus when size is smaller than 0.1 pc, which agrees with our study.

A power-law index of 2 suggests that the dense structures in the L1495-B218 filaments are gravitationally unbound and have relatively constant column density while a gravitationally bound Bonner–Ebert-like core is expected to have a power-law index closer to 1 since $\rho \sim {{r}^{-2}}$ for the outer profile of a Bonnor–Ebert-like structure. Our virial analysis also shows that most of the NH₃ leaves in the L1495-B218 filaments are gravitationally unbound. If the NH₃ leaves are formed by colliding flows as shown in the gravoturbulence scenario (e.g., Gong & Ostriker 2011), density structures are more likely to be shallower than $\rho \sim {{r}^{-2}}$.