THE DYNAMICAL STATE OF THE SERPENS SOUTH FILAMENTARY INFRARED DARK CLOUD

In 2012 January and March, we carried out N₂H⁺ (J = 1–0; the rest frequency of the main component ($F_1F \rightarrow F^{\prime }_1 F^{\prime } = 23 \rightarrow 12$) = 93.173777 GHz) observations toward the Serpens South cluster with the 25 element focal plane receiver BEARS equipped in the 45 m telescope at NRO. In Figure 1, the observed area is indicated by a dashed box on the three-color Herschel image. The observation box size is 95 × 11' with the map center of (R.A. [J2000], decl. [J2000]) = (18:30:1.85, −02:02:28.6). At 93 GHz band, the telescope has a FWHM beam size of 18'' and a main beam efficiency of η = 0.51. The beam separation of the BEARS is 411 on the plane of the sky (Sunada et al. 2000; Yamaguchi et al. 2000). At the back end, we used 25 sets of 1024 channel autocorrelators, which have a bandwidth of 8 MHz and a frequency resolution of 7.8 kHz, corresponding to a velocity resolution of 0.025 km s⁻¹ at 93 GHz (Sorai et al. 2000). The final velocity resolution was binned to 0.05 km s⁻¹. The N₂H⁺ (J = 1–0) consists of seven hyperfine components over 4.6 MHz. We determined the observed frequency range such that all the seven hyperfine components are distributed around the central frequency. During the observations, the system noise temperatures were in the range of 300–450 K in a double sideband. The standard chopper wheel method (Kutner & Ulich 1981) was used to convert the output signal into the antenna temperature T_A*(K), corrected for the atmospheric attenuation.

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The telescope pointing was checked every 1 hr by observing a SiO maser source, IRC+00363, and the typical pointing offset were 1'' ∼ 3'' during the whole observation period. Our mapping observations were made with the On-The-Fly (OTF) mapping technique (Sawada et al. 2008). We obtained an OTF map with xscan and yscan over 27 boxes and combined them into a single map in order to reduce the scanning effects. We adopted a convolutional scheme with a spheroidal function (Sawada et al. 2008) to calculate the intensity at each grid point of the final data with a spatial grid size of 75, about a half of the beam size. The resultant effective angular resolution was 24'', corresponding to 0.05 pc at a distance of 415 pc. The rms noise level of the final maps was 0.2 K in $T_{A}^*$ (1σ) at a velocity resolution of 0.05 km s⁻¹. We adopted the rest frequency of the main hyperfine component to make the data cube. To make the channel map and apply the clumpfind, we used the data cube whose rest frequency is set to that of the isolated hyperfine component.

We carried out single-point observations toward the Serpens South cluster in HCO⁺ (J = 3–2) and H¹³CO⁺ (J = 3–2) on 2011 May 15 and 2011 August 27, using the 10.4 m telescope of the Caltech Submillimeter Observatory (CSO) at Mauna Kea, Hawaii. The observed points have the following coordinates: (R.A. [J2000], decl. [J2000]) = (18:30:03.80, −02:03:03.9) and (18:29:57.40, −01:58:45.9). The former (hereafter referred to as CSO-C) and latter (hereafter referred to as CSO-N) are pointing toward the 1.1 mm dust continuum emission peaks of the central and northern clumps, respectively, as discussed in Section 3. The observed points are indicated by the crosses in Figure 1. At 270 GHz band, the telescope has a main beam efficiency of η = 0.72 and a FWHM beam size of 30'', corresponding to 0.06 pc at a distance of 415 pc. The observations were made with a position-switch mode, using a 230 GHz receiver. At the back end, we used a FFTS1 spectrometer with 8192 channels that covers the 1 GHz bandwidth. The frequency resolution of 122 kHz corresponds to the velocity resolution of 0.14 km s⁻¹ at 270 GHz. During the observations, the system noise temperatures were about 500 K and 200 K on May 15 and August 27, respectively, in a double sideband. The rms noise levels of the HCO⁺ (J = 3–2) and H¹³CO⁺ (J = 3–2) data were ΔT_rms ∼ 0.05 K in $T_{A}^*$ (1σ) at a velocity resolution of about 0.3 km s⁻¹. The two molecular lines were detected toward CSO-C, whereas none of the molecular lines were detected toward CSO-N. For CSO-N, we observed additional two molecular lines, CS (J = 5–4) and HCN (J = 3–2). We could not detect these two line emissions with the same rms noise as that of HCO⁺ (J = 3–2) and H¹³CO⁺ (J = 3–2).

The 1.1 mm continuum data were taken toward a ∼20' × 20' area centered on the Serpens South cluster with the AzTEC camera mounted on the ASTE 10 m telescope. The observed area is the area enclosed by solid lines in Figure 1. The rms noise level was about 10 mJy beam⁻¹, and the effective beam size was 40'' after the FRUIT imaging, which is an iterative mapping method to recover the spatially extended component. The FRUIT method is based on an iterative mapping method applied to the BOLOCAM data reduction pipeline (Enoch et al. 2006). The FRUIT data reduction pipeline is written in IDL and was developed by the University of Massachusetts. The FRUIT algorithm is described in Liu et al. (2010) and Shimajiri et al. (2011). The detail of the AzTEC data will be presented in R. A. Gutermuth et al. (2013, in preparation).

We used the version 2.5 fits files of the Herschel archival data of the PACS 160 μm and SPIRE 250, 350, and 500 μm toward Serpens South. The detail of the data will be described in K. Sugitani et al. (2013, in preparation). In brief, all the data were convolved to the ones with the angular resolution of 363, and then adopting the gray-body approximation, we performed the spectral energy distribution (SED) fitting at each grid point to derive the physical quantities such as the column density and dust temperature.

Previous observations have demonstrated that the optically thin dust continuum emission at submillimeter wavelengths provides a powerful diagnostic to constrain the density and temperature structure of molecular clouds (e.g., André et al. 2000). Our 1.1 mm dust continuum data also indicate that the dust continuum emission traces well several YSO envelopes and the spatial distribution of the dense and/or warm molecular gas in this region.

In Figure 2, we present the 1.1 mm continuum emission map that was taken with the AzTEC camera mounted on the ASTE 10 m telescope. This is essentially the same as Figure 3 of Nakamura et al. (2011). For comparison, the positions of the YSOs identified by the Spitzer observations (Gutermuth et al. 2008) and the positions of the YSOs and prestellar cores identified from the MAMBO 1.3 mm observations (Maury et al. 2011) are indicated in Figures 2(a) and 2(b), respectively. The dust image was obtained by applying the FRUIT method to recover the spatially extended component. The resultant effective angular resolution is ∼40''.

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The dust continuum emission has its maximum toward the Serpens South cluster at the position of (R.A. [J2000], decl. [J2000]) = (18:30:03.81, −02:03:04), which is embedded in a dusty clump (hereafter referred to as the Serpens South clump or central clump). The Serpens South cluster is located near the southern edge of a long filamentary cloud that was revealed by the Herschel observations (André et al. 2010). The Serpens South clump is also located at the intersection between the two filaments (southeast and southwest filaments) seen in the southern part of the image. At the southern part of the main filament (southeast filament), the main filament appears to fragment into an elongated clump (hereafter referred to as the southern clump), at the peak of which a Herschel Class 0 object is located. In the northern part of the map, we found a V-shape clump (hereafter referred to as the northern or V-shape clump). Several starless cores and Class 0 sources identified by the Herschel observations can be recognized as compact structures, even in our FRUIT map. Aside from the main filamentary structure, there are a couple of faint filamentary structures that appear to converge toward the Serpens South clump. These faint filaments can also be recognized in the Spitzer image (see Gutermuth et al. 2008; Nakamura et al. 2011). The detail of the 1.1 mm continuum image will be presented in R. A. Gutermuth et al. (2013, in preparation).

Figure 3(a) shows the N₂H⁺ (J = 1–0) intensity map toward Serpens South, integrated over the seven components of the hyperfine multiplet and taken with the Nobeyama 45 m telescope. Our N₂H⁺ (J = 1–0) intensity distribution is in good agreement with that obtained by Kirk et al. (2013) and has a finer angular resolution and higher sensitivity. On average, the integrated N₂H⁺ intensity closely follows the 1.1 mm continuum emission, suggesting that the N₂H⁺ emission is an excellent tracer of cold and dense emission, as is known from previous studies (e.g., Walsh et al. 2007). However, there are a couple of exceptions. For example, the V-shape clump identified by the 1.1 mm continuum emission is not so prominent in the N₂H⁺ intensity map. In addition, the N₂H⁺ integrated intensity takes its maximum at (R.A. [J2000], decl. [J2000]) = (18:30:03.7, −02:03:10), which is slightly offset from the continuum maximum by ∼10'', about half the size of the NRO 45 m beam. Since the pointing errors of both the 1.1 mm dust continuum map and N₂H⁺ are better than a few arcseconds, we consider that the offset is real. However, the offset may be due to the different angular resolutions of both maps.

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In addition, the positions of the dust continuum sources identified by the Herschel observations (Bontemps et al. 2010) often show deviations from the peaks of the N₂H⁺ emission. The N₂H⁺ integrated intensity tends to be weaker toward the Class 0 and Class 0/I candidates (the black crosses in Figure 3(a)), in particular toward the three sources located in the northern part of the image. The N₂H⁺ integrated intensity is very weak toward the Herschel starless cores (the white crosses in Figure 3(a)). The starless core located at the southwest edge of the image appears to be almost devoid of N₂H⁺ emission. There are two possibilities to explain these discrepancies. One possibility is that these dust cores are chemically young and that the abundance of a late-stage molecule, N₂H⁺, is still relatively low. Another possibility is that N₂H⁺ molecules tend to be destroyed by CO and the N₂H⁺ abundance has become small.

Very recently, we carried out CCS (J_N = 2₁–1₀), CCS (J_N = 4₃–3₂), and CCS (J_N = 7₇–6₅) observations toward a 20' × 10' area including the N₂H⁺ mapping area and found that the CCS emissions tend to be stronger toward the starless dust cores identified by Herschel. Therefore, we interpret that the weak N₂H⁺ emission toward the starless cores implies that the cores are chemically young. We will present the results of the CCS observations in a forthcoming paper.

In Figure 3(b), we compare the N₂H⁺ integrated intensity map with the ¹²CO (J = 3–2) integrated intensity map obtained by Nakamura et al. (2011). The strong CO emission is concentrated in the central clump that has the strongest N₂H⁺ emission. As shown by Nakamura et al. (2011), the CO emission represents the protostellar outflows blowing out of the central clump. The CO emission is more extended than the dense gas traced by N₂H⁺, implying that the outflows have broken through the dense clump.

The N₂H⁺ velocity channel maps are presented in Figure 4, which shows that the main filamentary structure is running from south to north. The filament has a large-scale velocity gradient of about 0.5 km s⁻¹ pc⁻¹ along its axis. The filament contains several velocity components, implying the existence of the internal structures. Figure 5 illustrates an example of the N₂H⁺ line profile showing two velocity components, where the rest frequency of the strongest hyperfine component is set to the velocity center. The profile presented is averaged in the 30'' × 30'' area centered on the position (R.A. [J2000], decl. [J2000]) = (18:30:04.4, −02:04:23.5), and the velocity resolution is set to 0.05 km s⁻¹. The isolated line at V_LSR ∼ −1 km s⁻¹ shows two velocity components with about a 1 km s⁻¹ separation. Such structure qualitatively resembles those of the B213 filament in Taurus (Hacar et al. 2013). At the velocity of 7.0 km s⁻¹, the central clump contains two filamentary structures (shown with the dashed curves). At the velocity of 7.8–7.9 km s⁻¹, the arc-like filamentary structure (shown with the dashed curve) can be recognized northeast of the central clump.

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We estimate the H₂ column densities by applying the SED fitting using the Herschel 160, 250, 350, and 500 μm data. The detail of the analysis will be described in K. Sugitani et al. (2013, in preparation). For the SED fitting, we used the gas-to-dust ratio of 100 and the dust opacity per unit mass of κ_ν = 0.005 (1.3 mm/λ)^β cm² g⁻¹ with β = 2. These parameters are the same as those adopted by Könyves et al. (2010).

Figure 6(a) shows the H₂ column density distribution in Serpens South obtained from the Herschel SED fitting. To compare $N_{{\rm H}_2}$ with the N₂H⁺ data, the H₂ column density data were remapped into the grid with the same pixels as that of the N₂H⁺ data. The estimated column density is essentially the same as that estimated by André et al. (2010) because the mass per unit length, line mass, is almost equal to their estimate of about 400 M_☉ pc⁻¹ at a distance of 415 pc. The N₂H⁺ column densities are calculated by using the formula given in Caselli et al. (2002). To take into account the effect of the optical depth, we used the optically thin (thick) formula when the optical depth of the strongest line is smaller (larger) than unity. The obtained column density distribution of N₂H⁺ is presented in Figure 6(b). Our hyperfine analysis reveals that the V-shape clump that has relatively weak emission in the velocity integrated intensity map has a large column density peak. This is due to the fact that the optical depths of the N₂H⁺ lines presented in Figure 6(c) are largest toward the V-shape clump. For comparison, we also show the spatial distribution of the excitation temperature T_ex in Figure 6(d). The excitation temperature tends to be higher toward the central cluster-forming clump. In the northern clump, the excitation temperature tends to be as low as about 4 K, in spite of the high column density. We note that at the position of the dust continuum emission peak (CSO-N), high-transition molecular lines such as CS (J = 5–4), HCO⁺ (J = 3–2), H¹³CO⁺ (J = 3–2), and HCN (J = 3–2) were not detected with our CSO observations. These lines are not likely to be sufficiently excited due to either low temperatures or low densities, or both.

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Figure 6(e) shows the N₂H⁺ fractional abundance across Serpens South. The mean fractional abundance of this region is estimated to be $X_{\rm N_2H^+} \simeq 2.5 \times 10^{-10}$, which is similar to the values derived for other dark clouds; e.g., $X_{\rm N_2H^+} \approx 10^{-10}$. For example, Di Francesco et al. (2004) and Friesen et al. (2010) estimated the N₂H⁺ fractional abundances of 1.3 × 10⁻¹⁰ and 5.6 × 10⁻¹⁰ for the Ophiuchus A and B2 regions, respectively. Figure 6(e) shows that the N₂H⁺ fractional abundance varies by a factor of a few with the lower values of around 1.5 × 10⁻¹⁰ at the 1.1 mm continuum peak, the northern part of the central clump, and the southwest filament, and the higher values of (4–5) × 10⁻¹⁰ at positions in the eastern and southern parts of the central clump and the northern V-shape clump. Table 2 lists the mean, rms, minimum, and maximum of the N₂H⁺ fractional abundances presented in Figure 6(e).

Table 2. Column Densities and N₂H⁺ Fractional Abundances in Serpens South

Physical Quantities	Meana	σb	Mina	Maxa
Whole area
$N_{\rm H_2}$ (1022 cm−2)	6.9 ± 1.4	1.5	1.5 ± 0.3	20.1 ± 4.0
$N_{\rm N_2H^+}$ (1013 cm−2)	1.7 ± 0.5	0.8	0.4 ± 0.1	4.0 ± 1.0
$X_{\rm N_2H^+}$ (10−10)	2.5 ± 1.4	0.7	1.1 ± 0.4	6.3 ± 4.2
North
$N_{\rm H_2}$ (1022 cm−2)	8.3 ± 1.7	1.2	2.4 ± 0.5	14.2 ± 2.8
$N_{\rm N_2H^+}$ (1013 cm−2)	2.0 ± 0.6	0.8	0.8 ± 0.4	4.0 ± 1.0
$X_{\rm N_2H^+}$ (10−10)	2.5 ± 1.1	0.7	1.5 ± 0.6	6.3 ± 4.2
Center
$N_{\rm H_2}$ (1022 cm−2)	7.2 ± 1.4	1.7	1.5 ± 0.3	20.1 ± 4.0
$N_{\rm N_2H^+}$ (1013 cm−2)	1.6 ± 0.5	0.7	0.5 ± 0.2	3.5 ± 0.7
$X_{\rm N_2H^+}$ (10−10)	2.6 ± 1.7	0.8	1.1 ± 0.4	4.9 ± 2.0
South
$N_{\rm H_2}$ (1022 cm−2)	4.8 ± 1.0	0.5	2.4 ± 0.5	7.4 ± 1.5
$N_{\rm N_2H^+}$ (1013 cm−2)	1.2 ± 0.5	0.4	0.4 ± 0.1	2.0 ± 0.5
$X_{\rm N_2H^+}$ (10−10)	2.4 ± 1.5	0.5	1.1 ± 0.4	3.6 ± 1.6

Notes. The definitions of the subareas are the same as those of Table 1. ^aWith standard deviation of the error of the hyperfine fitting including the flux calibration error of about ± 20% and the spectrometer's velocity resolution of 0.05 km s⁻¹. ^bstandard deviation of the fitted data points from the mean values.

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In Figure 7, the fractional abundances $X_{\rm N_2H^+}$ are presented as a function of the H₂ column density. Figure 7 indicates that the N₂H⁺ fractional abundance decreases with increasing H₂ column density. For comparison, we plot the best-fit power-law function that is given by

$$\begin{eqnarray} \log X_{\rm N_2H^+}& = & (-9.66\pm 0.60) + (-0.237\pm 0.026)\nonumber\\ &&\times \log (N_{\rm H_2}/10^{23} {\rm \,cm}^{-2}), \end{eqnarray} \tag{ 1 }$$

with the correlation coefficient of ${\cal R}=0.49$. Although the correlation is weak, the dependence of $X_{\rm N_2H^+}$ on $N_{\rm H_2}$ is consistent with a theoretical consideration of the ionization fraction in molecular clouds, as also pointed out by Maruta et al. (2010). In molecular clouds, the ionization fraction is determined roughly by the balance between the ionization rate by cosmic rays and the recombination rate of ions and electrons (Elmegreen 1979). Here, the ionization and recombination rates are proportional to n_n and n_in_e, respectively, where n_n, n_i, and n_e (≈n_i) are the densities of the neutral gas, positive ions, and electrons, respectively. As a result, the ionization fraction decreases with increasing neutral density n_n, as $n_i/n_n \propto n_n^{-1/2}$. The ionization fraction is expected to be proportional to $N_{\rm H_2} ^{-1/4}$ because $N_{\rm H_2} \propto n_n^{1/2}$ in a self-gravitating cloud.

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Figure 8(a) shows a map of the centroid velocity (the first moment map) that was measured by the isolated hyperfine component ($F_1F \rightarrow F^{\prime }_1 F^{\prime } = 01 \rightarrow 12$), the second weakest hyperfine component, where we calculated the centroid velocity by integrating the antenna temperatures of the isolated hyperfine component for all the pixels above the 4σ noise level. A prominent characteristic of the centroid velocity distribution is a steep velocity change of 0.2–0.3 km s⁻¹ near the southern part of the central clump at (R.A. [J2000], decl. [J2000]) ∼ (18:30:05, −02:05:00). There is also a velocity jump of about 0.5 km s⁻¹ at the intersection between the main filament and the southwest filament of (R.A. [J2000], decl. [J2000]) ∼ (18:30:00, −02:05:00). In the northwest part of the central clump, the centroid velocity takes its maximum at 7.8 km s⁻¹, which is shifted about 0.5 km s⁻¹ from that of the central clump (about 7.2 km s⁻¹). The area with this large centroid velocity in the central clump is in good agreement with the position of the prominent redshifted outflow lobe discovered by Nakamura et al. (2011), labeled as "R3", implying that the dense gas is interacting with the redshifted outflow lobe R3 (see Figure 8(b)).

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Figure 8(c) shows a map of the one-dimensional (1D) velocity dispersion, $\sigma _{\rm v, 1D} (=\Delta V/\sqrt{8\ln 2})$ (the second moment map), measured by the isolated hyperfine component. The 1D velocity dispersion tends to be larger at the central clump where active cluster formation is ongoing. In the central clump, the velocity dispersion takes its maximum of about 0.5 km s⁻¹. The area having a large velocity dispersion appears to overlap well with the blueshifted and redshifted outflow components blowing out of the central clump (see Figure 8(d)). In the other areas, the velocity dispersion tends to be narrow with a mean of about 0.2–0.3 km s⁻¹, which indicates that the internal motions are transonic. In particular, the northern and southern clumps have narrow velocity dispersions of 0.25 km s⁻¹ and 0.2 km s⁻¹, respectively. The spatial distribution of the velocity dispersion suggests that the star formation activity has increased the internal turbulent motions in this region.

From the dust continuum map, we can recognize several local peaks along the main filament, as already shown in Section 3.1. In other words, the filament apparently fragments into several pieces. Here we define the subparsec-size substructures having the local peaks as the clumps. We identified three dense clumps along the main filament: northern (V-shape), central (cluster-forming), and southern clumps. The clumps are defined as the regions enclosed by a contour of 5 × 10²² cm⁻² on the H₂ column density map in each (northern, central, or southern) area presented in Figure 6. We interpret these clumps as subunit of star or cluster formation in this region. The threshold column density is somewhat arbitrary. However, our main conclusions given in the present paper are not influenced by the actual value of the threshold column density in the range of ∼5 × 10²² cm⁻² to ∼1 × 10²³ cm⁻². The clumps also contain substructures that are recognized in the velocity channel maps of N₂H⁺ presented in Figure 4. We identify the internal structures of the clumps as the cores in the next section. Here we perform the virial analysis by using the Herschel and N₂H⁺ data to investigate the dynamical states of the clumps.

Following Nakamura et al. (2011), we adopt the virial equation of a spherical gas cloud that is given by

$$\begin{equation} \frac{1}{2} \frac{\partial ^2 I}{\partial t^2} = 2U+W, \end{equation} \tag{ 4 }$$

where I is the moment of inertia, U is the internal kinetic energy, and W is the gravitational energy. In the above equation, the surface pressure term is omitted. A clump is in virial equilibrium when 2U + W = 0. The internal kinetic energy term U and the gravitational energy term W are expressed as follows:

$$\begin{equation} U=\frac{3M\Delta V^2}{16\ln 2} \end{equation} \tag{ 5 }$$

and

$$\begin{equation} W=-a\frac{GM^2}{R} \left[1-\left(\frac{\Phi }{\Phi _{\rm cr}}\right)^2\right], \end{equation} \tag{ 6 }$$

where Φ is the magnetic flux penetrating the clump and Φ_cr is its critical value above which the clump is fully supported by the magnetic field against the self-gravity (Nakano 1998). In the discussion of this subsection, we assume Φ = 0, which means that the clumps are not supported by the magnetic forces. We will discuss the contribution of the magnetic field to the cloud support in Section 6.3. The value a is a dimensionless parameter of order unity that measures how much the mass distribution deviates from a sphere with the profile of ρ∝r⁻² (Bertoldi & McKee 1992). For example, for a uniform sphere and a centrally condensed sphere with ρ∝r⁻², the dimensionless parameter a is given by 3/5 and 1, respectively. For the identified clumps, we assume that the effects of the nonspherical mass distribution is negligible. This is a reasonable assumption because the aspect ratios of the clumps identified are not so far from unity and in such cases, the value of a is close to unity (Bertoldi & McKee 1992). Below, we assume a to be unity because each clump has a more or less centrally condensed density distribution.

Table 3 summarizes the physical quantities of the three clumps. Here we estimate the masses and radii from the Herschel column density map. The clump radius is determined by taking the area enclosed by the threshold H₂ column density of 5 × 10²² cm⁻² and computing the radius of the circle required to reproduce the area. The clump line widths are estimated by taking the intensity-weighted average of the 1D velocity dispersion obtained from hyperfine fitting of the N₂H⁺ data. The mass of the northern clump is estimated to be about 200 M_☉, which is comparable to that of the central cluster-forming clump. In spite of the relatively large mass, only several YSOs are identified in the northern clump. This may imply that the northern clump is likely to be the site of future cluster formation or that star formation may be precluded by some additional clump support. The southern clump has about 40 M_☉ and is less massive than the other two. The line width of the northern clump is evaluated to be about 0.7 km s⁻¹, which is as small as that of the typical molecular cloud core in quiescent regions. The southern clump, with which only a few YSOs appear to be associated, also has a similar line width. On the other hand, the central cluster-forming clump has a larger line width of about 1.3 km s⁻¹. This may indicate that the star formation activity enhances the internal motions in the central clump.

For all the clumps, the terms U and W are estimated to be U ≈ 40–110 M_☉ km² s⁻² and W ≈ −40 ∼ −1000 M_☉ km² s⁻², respectively, which yields the virial ratio, the ratio between 2U and W, of 0.1–0.3. For all the clumps, the virial ratios are estimated to be well below the unity, indicating that the internal turbulent motions play only a minor role in the clump support. This conclusion is inconsistent with the previous estimation by Nakamura et al. (2011), who concluded that the Serpens South clump as a whole is close to quasi-virial equilibrium. The main difference between the two estimations comes from the different line widths. Nakamura et al. (2011) obtained the line width of the central clump by using HCO⁺ (J = 4–3). However, this line tends to be optically thick toward the central clump, which may lead to the overestimation of the line width. We believe that the present estimation is more reasonable because N₂H⁺ (J = 1–0) tends to be more optically thin than HCO⁺ (J = 4–3) in the densest part. This cloud as a whole seems to be extremely gravitationally unstable in the absence of the additional support mechanisms such as the magnetic support.

We note that the virial ratios of the clumps are not sensitive to the threshold column density that defines the clump boundary (N_cr). For example, for the threshold density of N_cr ≲ 1 × 10²³ cm⁻², the virial ratios of the northern and central clumps are almost the same as those in Table 3. For the southern clump whose peak column density is 7 × 10²² cm⁻², the virial ratio is almost the same as that in Table 3 as long as N_cr ≲ 6 × 10²² cm⁻².

The clumps and cores having small virial ratios have recently been reported by a couple of groups. For example, Li et al. (2013) carried out NH₃ observations toward OMC-2 and OMC-3 and found that the clumps in this area have small virial ratios. Pillai et al. (2011) performed the virial analysis of the IRDC clumps and found that the IRDC clumps often have low virial ratios (see also T. Pillai et al. 2013, in preparation).

As shown above, the cloud as a whole seems not to be supported by the internal turbulent motions, and therefore the global infall motions are expected. In fact, the profile maps of the optically thick lines often show the blueshifted part stronger than the redshifted part, i.e., blue skewed (see Nakamura et al. 2011). Such blue-skewed profiles are probably indicative of global infall motions.

In Figure 9, we present a HCO⁺ (J = 3–2) line profile detected toward CSO-C (in the Serpens South clump), whose coordinate is (R.A. [J2000], decl. [J2000]) = (18:30:03.80, −02:03:03.9). At CSO-C, the HCO⁺ (J = 3–2) line is likely to be optically thick. For comparison, an optically thin line H¹³CO⁺ (J = 3–2) is presented in Figure 9. The HCO⁺ (J = 3–2) line shows a clear blue-skewed profile, whereas the H¹³CO⁺ (J = 3–2) line shows a single-peak profile. This indicates that the densest part has an infall motion.

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Applying a simple model of Myers et al. (1996), we evaluated the infall speed of 0.024 km s⁻¹, which is subsonic. If the central clump as a whole is contracting with this subsonic infall speed, the mass infall rate is estimated to be $\dot{M}= 4\pi R_{\rm clump}^2 \rho V_{\rm infall} \sim 9\times 10^{-5} \,M_\odot$ yr⁻¹, where ρ is set to the mean density in the clump, ρ ∼ 5 × 10⁻¹⁸ g cm⁻³. This implies that the mass of the central clump will be doubled within 2.5 Myr. The estimated mass infall rate is in good agreement with that obtained by Kirk et al. (2013), within a factor of a few.

The estimated infall speed is, however, too slow compared with the free fall velocity of $V\sim \sqrt{GM/R} \sim 1\hbox{--}2$ km s⁻¹, corresponding to the FWHM line widths of 2–4 km s⁻¹. The clump FWHM line widths of 0.5–1.3 km s⁻¹ are smaller than this free fall velocity. Hence, the additional support mechanism should be needed.

As discussed above, the internal turbulent motions play only a minor role in the clump support in this region. However, there is no clear evidence showing the free fall global infall motions of the order of a few km s⁻¹. The line widths along the line of sight are at most 0.5–1 km s⁻¹. This implies that the additional support mechanism is needed. The most promising mechanism of the additional support is the magnetic support. Here we discuss whether the magnetic field plays an important role in the clump support in this region.

Sugitani et al. (2011) carried out the near-infrared (JHKs) polarimetric observations toward Serpens South and found that the Serpens South filament is penetrated perpendicularly to the large-scale ordered magnetic field. The global magnetic field also appears to be curved in the southern part of the main filament. Such morphology is consistent with the idea that the global magnetic field is distorted by gravitational contraction along the main filament toward the central cluster-forming clump. Applying the Chandrasekhar–Fermi method, they estimated a magnetic field strength of about 80 μG at the filament envelope with a density of 10⁴ cm⁻³, where we rescaled the distance to 415 pc and used the smaller line width estimated from our N₂H⁺ data. Assuming an inclination angle of 45°, the magnetic field strength is roughly estimated to be about 120 μG.

The mean densities of the clumps can be estimated to be about 10⁵ cm⁻³ [${=}M_{\rm cl}/(4\pi R_{\rm cl}^3/3)$]. Assuming that the magnetic field strength is proportional to the square root of the density, B∝ρ^1/2, the strength of the magnetic field associated with the clumps is evaluated to be about 400 μG. If the clumps have the field strengths of about 400 μG, the mass-to-magnetic-flux ratios are estimated to be around unity, close to critical. In other words, the magnetic support is expected to play a crucial role in the clump dynamics and evolution.

According to our estimation, the parent cloud was presumably close to magnetically critical and either the ambipolar diffusion or mass accretion along the magnetic field lines may have triggered the slow global infall and eventually the active cluster formation that is observed in the central clump (Nakamura & Li 2010; Bailey & Basu 2012).

Recently, Kauffmann et al. (2010) and Kauffmann & Pillai (2010) analyzed the mass and radius of cloud substructures in several nearby molecular clouds over a wide range of spatial scales (0.05 ≲ r/pc ≲ 3) and found that the clumps forming massive stars (M ≳ 10 M_☉) have masses larger than M ≳ 1300 M_☉(r/pc)^1.33, where we rescaled Kauffmann & Pillai's relation by a factor of 1.5 to take into account the difference in the adopted dust parameters. On the other hand, Krumholz & McKee (2008) proposed the threshold column density of 1 g cm⁻² for massive star formation. In Figure 10, we plot the three Serpens South clumps (northern, central, and southern clumps) on the mass–radius diagram with Kauffmann & Pillai's relation and Krumholz & McKee's criteria for massive star formation. The northern and central clumps are located above the critical mass–radius relation but below the Krumholz criteria. Thus, we expect that these two clumps are borderline clumps for forming massive stars.

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Interestingly, all the Serpens South clumps have column densities comparable to about 10²³ cm⁻². Such clumps are the densest ones found among nearby star-forming molecular clouds whose distances are less than about 400 pc, except in the Orion molecular cloud, the nearest massive star-forming region. In the Orion molecular cloud, a number of clumps have column densities similar to or larger than the Serpens South clumps (see Figure 1 of Kauffmann et al. 2010). In fact, the clumps containing the most massive core found for small radii in the Perseus and Ophiuchus molecular clouds have column densities comparable to the Serpens South clumps. Therefore, we expect that the physical conditions of the Serpens South clumps resemble at least those of the nearby cluster-forming clumps where only low-mass and intermediate-mass stars are forming (e.g., NGC 1333).

The central clump already harbors a cluster of protostars, whereas the northern and southern clumps show no active star formation. Since the northern clump has a mass and radius comparable to the central clump, the northern clump is a promising candidate of pre-protocluster clump.

We propose the following scenario of the clump formation and evolution in Serpens South. Figure 11 shows the conceptual diagram of the scenario.

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(1) Fragmentation phase. Dense clumps form by fragmentation of a filamentary cloud that was close to magnetically critical. The fragmentation is likely to be driven by the ambipolar diffusion. In the absence of the ambipolar diffusion, the magnetically critical filaments cannot fragment into clumps. Without the ambipolar diffusion, even in the mildly magnetically supercritical filaments, it is difficult to obtain the clumps whose separations are several times as large as the filament diameter, as seen in the dust continuum image, because the clump separations would become much larger.

(2) Pre-protocluster phase. The clumps grow in mass by gas accumulation either along or across the magnetic field lines, or both. The merging of the fragments along the filament axis may also play a role in increasing the clump mass. This stage corresponds to the one immediately before active cluster formation is initiated. Thus, we refer to this stage as the pre-protocluster stage. The pre-protocluster clumps are the magnetically supported clumps of cold, quiescent, dense gas.

(3) Early protocluster phase. When the density becomes high enough, active cluster formation is initiated and protostellar outflows start injecting supersonic turbulence in the clumps. Hence, the line widths of the clumps become larger.

(4) Quasi-virial equilibrium phase. Eventually, the clumps reach quasi-virial equilibrium due to the supersonic turbulence driven by protostellar outflows (see also Sugitani et al. 2010).

The southern, northern, and central clumps are presumably in stages (1), (2), and (3), respectively.

We note that the physical properties of the pre-protocluster clumps identified in Serpens South are different from those expected from the accretion-driven turbulence scenario (Klessen & Hennebelle 2010; Vazquez-Semadeni et al. 2010), for which the supersonic turbulence is maintained by the accretion flows onto the dense clumps. The accretion-driven turbulence scenario considers that star formation proceeds dynamically and predicts that the turbulent energy balances with the gravitational energy in the dense clumps in formation. In contrast, the dense clumps in Serpens South appear more quiescent, particularly prior to the cluster formation. In Serpens South, stellar feedback is likely to be more responsible for driving turbulent motions in the dense clumps.

On the other hand, it remains unclear how the main filament was formed. The collision between the multiple filaments may have played a role because in the channel maps, several velocity-coherent components can be recognized. Further investigation is needed to understand how the Serpens South filament was formed.

We apply the clumpfind to identify dense cores from the N₂H⁺ data cube (Williams et al. 1994). The conditions adopted for the core identification are essentially the same as described in Ikeda et al. (2007). The threshold and stepsize of the core identification are set to the 2σ noise level. An identified core must contain more than two continuous velocity channels and each channel must contain more than three pixels with intensities are larger than the 3σ noise levels. In addition, the core must have pixels connected to both the velocity and space domains (see Ikeda et al. 2007 for further details). Most of the N₂H⁺ (J = 1–0) hyperfine components are blended significantly over much of the area observed. Therefore, we used only the isolated component ($F_1F \rightarrow F^{\prime }_1 F^{\prime } = 01 \rightarrow 12$) to identify the cores. A minimum mass of the core identified by this procedure is evaluated to about 0.17 M_☉ (corresponding to about 60σ levels) for T_ex ≈ 7 K and $X_{\rm N_2H^+} \approx 2.5 \times 10^{-10}$. In total, we identify 70 dense cores.

The physical properties of the cores are determined by using the definitions described in Section 3.3 of Ikeda et al. (2007). The position and local standard of rest (LSR) velocity of a core are set to the values at the pixel having the largest antenna temperature, $T_{\rm A, peak}^*$. The core radius, R_core, is calculated, by using Equation (2) of Ikeda et al. (2007), as the radius of a circle having the same area projected on the position–position plane as the identified core. The aspect ratio of the core is calculated by the two-dimensional Gaussian fitting to its total integrated intensity distribution. The FWHM line width, dV_core, is corrected for the velocity resolution of the spectrometers (=0.025 km s⁻¹). The local thermodynamic equilibrium (LTE) mass is estimated under the assumption that all the hyperfine components are optically thin (see Ikeda et al. 2007 for further details). As mentioned in the previous section, the optically thin assumption is reasonable in most of the area because the mean total optical depth derived from the hyperfine fitting is τ ∼ 4–6 except for the northern part. For simplicity, the N₂H⁺ fractional abundance relative to H₂ is assumed to be spatially constant and equal to the mean fractional abundance of the observed area, 2.5 × 10⁻¹⁰. The excitation temperatures are also set to be spatially constant at 4, 7, and 6 K (the mean values listed in Table 1) for the northern, central, and southern regions, respectively.

We note that the physical properties of the identified cores are partly affected by the core identification method and its adopted parameters (see Section 4.1 of Maruta et al. 2010 for further discussion).

In Table 4, we show the physical quantities of the 70 dense cores identified from the N₂H⁺ data cube. In Table 5, we also list the minimum, maximum, and mean values of R_core, dv_core, M_LTE, M_vir/M_LTE, $\bar{n}$, and aspect ratio. Here we compute these values by dividing the observed area into the three parts as in Table 1: north, center, and south.

Figures 12(a)–(f) indicate the histograms of the radius (R_core), LTE mass (M_LTE), mean density ($\bar{n}$), line width (ΔV_core), virial ratio (α_vir), and aspect ratio of the N₂H⁺ cores. In Figures 12(a)–(f), the cyan, gray, and magenta histograms show the cores located in the northern, central, and southern areas, respectively. The distribution of the core radius takes its maximum at about 0.06 pc, ranging from 0.04 to 0.11 pc. The peak of its distribution is close to the mean of 0.065 pc (see Figure 12(a)). The maximum and minimum radii of the N₂H⁺ cores are very close to the mean core radius, indicating that the distribution of the core radius is very narrow. The cores in the southern part tend to be somewhat smaller than those in the other parts. On the other hand, the histogram of the LTE mass shows a much broader distribution than that of the core radius. The distribution of the LTE mass takes its maximum at about 4 M_☉, ranging from 0.8 to 40 M_☉ (see Figure 12(b)). The distribution of the mean density of the N₂H⁺ cores has a single peak at about 1 × 10⁵ cm⁻³ that is close to the mean value (see Figure 12(c)). The distribution of the core mean density is also broad, ranging from 0.25 × 10⁵ to 3.2 × 10⁵ cm⁻³ (see Figure 12(c)). The cores located in the northern part tend to have larger LTE masses and larger mean densities compared with the cores in the other parts.

Table 4. Properties of the N₂H⁺ Cores in Serpens South

ID	R.A.	Decl.	VLSR	$T^*_{A, \rm peak}$a	Rcore	Rcore	Aspect	Δvcore	MLTE	Mvir	αvir	$\bar{n}$	Areab
	(J2000.0)	(J2000.0)	(km s−1)	(K)	(arcsec)	(pc)	Ratio	(km s−1)	(M☉)	(M☉)			(105 cm−3)
1	18 29 44.9	−02 05 33.0	8.87	0.65	27.4	0.0551	3.26	0.438	1.48	5.12	3.45	0.37	s
2	18 29 47.1	−02 00 46.6	7.51	0.61	35.0	0.0705	1.12	0.312	2.09	5.16	2.47	0.25	c
3	18 29 49.5	−02 05 09.4	7.62	0.56	31.3	0.0629	1.05	0.324	2.01	4.70	2.33	0.34	c
4	18 29 49.6	−01 58 08.0	7.85	0.76	25.7	0.0518	1.29	0.370	6.19	4.22	0.68	1.84	n
5	18 29 52.3	−01 57 46.9	7.88	0.71	27.1	0.0545	1.41	0.331	5.12	4.12	0.80	1.31	n
6	18 29 54.2	−02 00 48.2	7.43	0.61	38.0	0.0764	1.03	0.677	4.50	11.34	2.52	0.42	c
7	18 29 55.2	−01 58 39.8	7.51	0.94	52.3	0.1052	1.22	0.342	23.62	8.12	0.34	0.84	n
8	18 29 55.7	−01 59 29.6	7.72	0.63	25.5	0.0513	1.47	0.364	5.47	4.13	0.75	1.68	n
9	18 29 55.9	−01 58 34.9	7.93	0.61	32.7	0.0658	1.23	0.275	5.90	4.51	0.76	0.86	n
10	18 29 56.4	−02 01 21.4	8.02	0.62	31.2	0.0628	1.27	0.396	4.34	5.38	1.24	0.72	c
11	18 29 56.6	−01 57 51.8	7.62	0.92	29.9	0.0601	1.77	0.502	16.53	6.34	0.38	3.15	n
12	18 29 56.8	−01 59 58.8	7.74	0.61	23.4	0.0471	1.45	0.374	4.59	3.86	0.84	1.82	n
13	18 29 57.5	−01 59 44.8	7.22	0.67	24.9	0.0500	1.45	0.389	5.02	4.23	0.84	1.66	n
14	18 29 57.6	−02 00 40.3	7.30	0.63	30.6	0.0615	1.18	0.727	6.85	10.04	1.47	1.22	c
15	18 29 57.8	−02 01 44.3	7.17	0.60	37.1	0.0746	1.81	0.849	4.78	15.16	3.17	0.48	c
16	18 29 58.3	−02 06 27.1	7.71	0.61	33.8	0.0679	1.82	0.515	3.18	7.35	2.31	0.42	s
17	18 29 58.6	−02 01 15.2	7.65	0.89	32.0	0.0644	1.24	0.391	7.35	5.46	0.74	1.14	c
18	18 29 58.8	−02 01 50.0	7.98	0.67	26.2	0.0528	2.45	0.308	2.12	3.84	1.81	0.60	c
19	18 29 58.8	−01 59 05.0	7.54	0.66	34.6	0.0695	1.01	0.503	12.21	7.34	0.60	1.50	n
20	18 29 59.5	−02 03 33.7	7.53	0.65	42.9	0.0864	1.28	0.768	6.48	15.21	2.35	0.42	c
21	18 29 59.5	−01 58 13.0	7.80	0.78	31.3	0.0630	1.05	0.644	10.28	8.79	0.86	1.70	n
22	18 29 59.6	−02 00 51.6	8.04	0.64	30.5	0.0614	1.16	0.330	2.90	4.64	1.60	0.52	c
23	18 29 60.0	−02 05 43.0	7.75	0.66	29.2	0.0588	1.46	0.399	2.91	5.06	1.74	0.59	s
24	18 30 00.2	−01 59 55.6	7.37	0.91	29.6	0.0596	1.13	0.518	13.10	6.49	0.50	2.56	n
25	18 30 00.7	−02 02 19.9	7.04	0.97	47.7	0.0961	1.16	0.733	18.03	15.86	0.88	0.84	c
26	18 30 00.8	−02 06 15.3	7.43	0.65	22.7	0.0458	1.01	0.285	1.75	3.19	1.82	0.76	s
27	18 30 01.0	−02 07 11.9	7.91	0.69	32.0	0.0644	1.12	0.533	2.74	7.23	2.64	0.42	s
28	18 30 01.2	−02 01 22.6	7.96	0.91	19.9	0.0400	1.01	0.353	3.84	3.15	0.82	2.49	c
29	18 30 01.3	−02 04 21.3	7.70	0.59	38.3	0.0771	1.22	0.418	3.81	6.89	1.81	0.34	c
30	18 30 01.3	−02 04 18.0	6.54	0.66	38.7	0.0779	1.13	0.540	3.54	8.85	2.50	0.31	c
31	18 30 01.5	−02 01 26.1	7.49	0.98	22.0	0.0444	1.38	0.338	3.39	3.40	1.00	1.61	c
32	18 30 01.6	−02 07 18.3	5.30	0.69	21.3	0.0428	2.02	0.078	0.79	2.31	2.93	0.42	s
33	18 30 01.8	−02 05 29.5	7.87	0.70	36.1	0.0727	1.23	0.466	4.91	7.14	1.46	0.53	c
34	18 30 02.0	−02 01 00.6	7.04	0.95	38.4	0.0773	1.00	0.449	10.90	7.34	0.67	0.98	c
35	18 30 02.5	−02 02 12.9	7.90	1.04	42.2	0.0849	1.07	0.513	14.22	9.14	0.64	0.96	c
36	18 30 03.0	−02 03 01.2	7.22	1.65	49.0	0.0986	1.29	0.296	22.11	7.01	0.32	0.95	c
37	18 30 03.1	−02 03 07.4	6.75	1.21	43.9	0.0884	1.16	0.450	15.01	8.41	0.56	0.90	c
38	18 30 03.1	−02 04 41.6	7.07	1.39	46.6	0.0937	1.29	0.595	19.75	11.87	0.60	0.99	c
39	18 30 03.4	−02 03 15.0	7.71	1.48	54.1	0.1088	1.30	0.545	39.86	12.49	0.31	1.28	c
40	18 30 03.5	−02 00 45.1	7.58	0.65	28.0	0.0564	1.42	0.319	3.13	4.18	1.33	0.72	c
41	18 30 03.7	−02 06 12.3	7.62	0.75	24.8	0.0499	1.28	0.545	3.66	5.73	1.57	1.22	s
42	18 30 03.8	−01 59 54.4	7.19	0.61	40.9	0.0823	1.47	0.468	9.98	8.12	0.81	0.74	n
43	18 30 04.0	−02 03 58.2	6.88	1.20	33.0	0.0664	2.01	0.579	13.74	8.16	0.59	1.94	c
44	18 30 04.3	−02 01 45.5	7.49	0.90	34.2	0.0687	1.38	0.503	9.76	7.27	0.74	1.24	c
45	18 30 05.0	−02 05 01.8	6.68	0.68	33.4	0.0672	1.30	0.384	3.94	5.62	1.43	0.54	c
46	18 30 05.3	−02 05 27.5	7.41	0.60	30.5	0.0613	1.08	0.455	5.30	5.88	1.11	0.95	c
47	18 30 05.4	−02 01 06.8	6.80	0.59	41.5	0.0834	1.18	0.697	5.59	12.88	2.30	0.40	c
48	18 30 06.1	−02 06 12.5	7.56	0.61	21.8	0.0439	1.02	0.541	2.44	5.00	2.05	1.20	s
49	18 30 06.2	−02 04 44.1	7.54	0.68	30.3	0.0610	1.24	0.460	5.29	5.91	1.12	0.96	c
50	18 30 06.8	−02 05 20.5	6.93	0.94	34.5	0.0695	1.33	0.477	9.09	6.98	0.77	1.12	c
51	18 30 07.0	−02 07 04.4	7.51	0.82	20.8	0.0419	1.29	0.391	1.37	3.55	2.59	0.77	s
52	18 30 07.1	−02 03 15.8	7.58	0.70	34.9	0.0703	1.41	0.507	5.62	7.48	1.33	0.67	c
53	18 30 07.2	−02 01 05.6	7.76	0.61	36.5	0.0735	1.27	0.422	3.68	6.61	1.79	0.38	c
54	18 30 07.8	−02 06 26.2	7.14	0.59	24.7	0.0496	1.59	0.401	1.90	4.29	2.25	0.65	s
55	18 30 07.9	−02 04 13.1	6.86	0.64	29.0	0.0584	1.09	0.244	2.45	3.81	1.55	0.51	c
56	18 30 08.1	−02 04 14.0	7.42	0.74	30.3	0.0610	1.42	0.392	4.99	5.18	1.04	0.91	c
57	18 30 08.1	−02 03 36.8	7.20	0.67	27.2	0.0548	1.64	0.320	2.83	4.06	1.44	0.71	c
58	18 30 08.2	−02 05 53.1	7.29	0.59	23.9	0.0481	1.84	0.460	2.67	4.67	1.75	0.99	s
59	18 30 08.7	−02 05 14.3	7.30	0.64	22.8	0.0459	1.14	0.321	2.11	3.41	1.62	0.90	c
60	18 30 09.7	−02 05 44.3	6.73	0.92	26.7	0.0538	1.69	0.344	4.08	4.17	1.02	1.09	s
61	18 30 09.9	−02 02 06.4	7.57	0.60	41.4	0.0834	1.30	0.403	3.96	7.22	1.82	0.28	c
62	18 30 10.8	−02 03 42.8	7.45	0.69	25.1	0.0505	1.58	0.324	3.34	3.77	1.13	1.08	c
63	18 30 11.0	−02 06 12.5	6.90	1.04	26.6	0.0535	1.56	0.544	7.02	6.13	0.87	1.90	s
64	18 30 11.4	−02 04 25.6	7.07	0.61	29.2	0.0587	1.10	0.423	2.59	5.30	2.05	0.53	c
65	18 30 11.5	−02 06 53.4	6.91	0.90	27.4	0.0552	1.42	0.563	5.37	6.57	1.22	1.32	s
66	18 30 13.3	−02 04 17.7	7.50	0.66	26.0	0.0522	1.09	0.531	3.18	5.84	1.84	0.92	c
67	18 30 13.4	−02 07 00.7	6.17	0.59	30.2	0.0608	1.11	0.343	1.70	4.70	2.77	0.31	s
68	18 30 13.5	−02 03 23.5	7.48	0.59	35.9	0.0722	1.32	0.476	4.19	7.23	1.73	0.46	c
69	18 30 13.7	−02 06 41.9	6.70	1.29	40.6	0.0817	1.08	0.436	14.77	7.56	0.51	1.12	s
70	18 30 15.9	−02 04 43.6	7.49	0.66	30.1	0.0606	1.41	0.478	3.20	6.10	1.91	0.59	c

Notes. Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds. Taking into account the calibration error of the observed intensities of about ±20%, the derived LTE masses, virial ratios, and mean densities also have an error of at least about ±20%. ^a$T_A^*$ denotes the peak antenna temperature of the isolated hyperfine component. ^bThe symbols n, c, and s mean, respectively, the northern, central, and southern areas where the cores are located.

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Table 5. Summary of the Physical Properties of the N₂H⁺ Cores

Property	Minimum	Maximum	Meana
Whole area
Rcore (pc)	0.0400	0.1088	0.0649 ± 0.0154
dvcore (km s−1)	0.078	0.849	0.448 ± 0.132
MLTE (M☉)	0.79	39.86	6.81 ± 6.49
Mvir/MLTE	0.313	3.45	1.42 ± 0.76
$\bar{n}$ (× 105 cm−3)	0.25	3.15	0.96 ± 0.58
Aspect ratio	1.00	3.26	1.36 ± 0.36
North
Rcore (pc)	0.0471	0.1052	0.0634 ± 0.0158
dvcore (km s−1)	0.275	0.644	0.423 ± 0.100
MLTE (M☉)	4.59	23.62	9.83 ± 5.57
Mvir/MLTE	0.344	0.86	0.68 ± 0.18
$\bar{n}$ (× 105 cm−3)	0.74	3.15	1.64 ± 0.67
Aspect ratio	1.01	1.77	1.33 ± 0.21
Center
Rcore (pc)	0.0400	0.1088	0.0693 ± 0.0150
dvcore (km s−1)	0.244	0.849	0.464 ± 0.141
MLTE (M☉)	2.01	39.86	7.16 ± 7.12
Mvir/MLTE	0.313	3.17	1.43 ± 0.67
$\bar{n}$ (× 105 cm−3)	0.25	2.49	0.81 ± 0.45
Aspect ratio	1.00	2.45	1.30 ± 0.27
South
Rcore (pc)	0.0419	0.0817	0.0546 ± 0.0101
dvcore (km s−1)	0.078	0.563	0.426 ± 0.122
MLTE (M☉)	0.79	14.77	3.61 ± 3.27
Mvir/MLTE	0.512	3.45	1.97 ± 0.79
$\bar{n}$ (× 105 cm−3)	0.31	1.90	0.85 ± 0.43
Aspect ratio	1.01	3.26	1.54 ± 0.54

Note. ^aWith standard deviation.

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Figure 12(d) shows the distribution of the FWHM line width of the N₂H⁺ cores. The distribution of the line width has a single peak at around a mean of 0.45 km s⁻¹, ranging from 0.078 to 0.85 km s⁻¹. Its distribution also appears to be concentrated in the range of 0.3–0.5 km s⁻¹. Some cores in the central part have large line widths. Applying the procedure described by Myers et al. (1991), we classify the identified cores into the following two groups: thermal core and turbulent core, on the basis of the critical line width, dV_cr. The critical line width is defined as follows:

$$\begin{equation} dV_{\rm cr}=\left[8\ln 2 \, k_B T \left({1\over \mu m_H}+{1\over m_{\rm obs}}\right)\right]^{1/2}, \end{equation} \tag{ 7 }$$

where k_B is the Boltzmann constant, μ = 2.33 is the mean molecular weight, m_H is the mass of a hydrogen atom, and m_obs is the mass of a observed molecule, i.e., N₂H⁺ in this paper. The critical line width of the N₂H⁺ cores is evaluated to be 0.55 km s⁻¹ when the gas temperature of T = 14 K is adopted. We note that T = 14 K is close to the dust temperature obtained from the SED fitting of the Herschel data. Among the 70 identified N₂H⁺ cores, most of the cores (about 76%) are categorized as the thermal cores. Even for the cores classified as the turbulent cores, most of them have transonic nonthermal motions. In other words, the cores in the Serpens South IRDC are relatively quiescent.

Figure 12(e) shows the distribution of the virial ratios. First, most of the cores have the virial ratios not so far from unity. In addition, the virial ratios appear to depend weakly on area. For example, in the northern part, almost all the cores have virial ratios smaller than unity. In contrast, in the central and southern parts, the majority of the cores have virial ratios larger than unity.

Figure 12(f) shows the distribution of the aspect ratios of the cores. The majority of the cores have aspect ratios close to unity. The cores in the southern part tend to be somewhat more elongated than those in the other parts.

7.3.1. Line-width–Radius Relation

Figure 13(a) shows the line-width–radius relation of the 70 dense cores identified from the N₂H⁺ data cube. For comparison, we show in Figure 13(a) the best-fit power-law that is given by

$$\begin{eqnarray} \log \left(\Delta V_{\rm core} \over \ {\rm km \ s}^{-1}\right) &=& (0.335 \pm 0.194) \nonumber\\ &&+ (0.587\pm 0.161) \log \left({{R_{\rm core} \over {\rm pc}}}\right), \end{eqnarray} \tag{ 8 }$$

where the correlation coefficient is ${\cal R}=0.40$. The line-width–radius relation of the identified cores does not show a clear power-law like the so-called Larson's (1981) law. The weak dependence on the line widths of the core radius is also pointed out by recent studies of other star-forming regions such as in Orion A (Ikeda et al. 2007), ρ Oph (Maruta et al. 2010), and massive star-forming regions (Saito et al. 2008; Sanchez-Monge et al. 2013). The weak dependence of the line-width–radius relation may suggest that the identified cores are in various dynamical states as discussed below.

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Figure 13(a) indicates that the nonthermal components of the line widths appear to be important in the identified cores. To quantify the contribution of the nonthermal components in the line widths of the cores, we plot in Figure 13(b) the nonthermal line width $\Delta V_{\rm NT} [\equiv (\Delta V_{\rm core}^2\hbox{--}8\ln 2 \, k_B T/m_{\rm obs})^{1/2}]$ as a function of core radius. For comparison, we also plot in Figure 13(b) the best-fit power-law that is given by

$$\begin{eqnarray} \log \left(\Delta V_{\rm NT} \over {\rm km \ s}^{-1}\right)&=& (0.037\pm 0.150)\nonumber\\ && + (0.315\pm 0.125) \log \left({R_{\rm core} \over {\rm pc}}\right), \end{eqnarray} \tag{ 9 }$$

where ${\cal R}=0.36$. Again, the correlation between the nonthermal line width and core radius is weak.

The weak dependence of the line width on the core radius is consistent with the results of the recent numerical simulations of turbulent, magnetized molecular clouds. The numerical simulations show that the cores formed in turbulent media are not in perfect virial equilibrium but rather in various dynamical states that are influenced by the ambient environments (Nakamura & Li 2008, 2011; Offner et al. 2008).

7.3.2. Mass–Radius Relation

In Figure 13(c), we present the LTE mass as a function of core radius. For comparison, we plot with a solid line the best-fit power-law that is given by

$$\begin{eqnarray} \log \left(M_{\rm LTE} \over M_\odot \right)&=& (3.32\pm 0.35) + (2.17\pm 0.29) \nonumber\\ &&\times\,\log \left({R_{\rm core} \over {\rm pc}}\right), \end{eqnarray} \tag{ 10 }$$

where ${\cal R}=0.69$. The relation of $M_{\rm LTE}=4\pi \mu m_H \bar{n} R_{\rm core}^3 /3$ is also shown with a dashed line in Figure 13(c), where the mean density is set to $\bar{n}=9.6\times 10^4$ cm⁻³, which is close to the critical density of N₂H⁺ (J = 1–0), n_cr ≃ 1.5 × 10⁵ cm⁻³.

7.3.3. Virial-ratio–LTE–Mass Relation

The importance of the self-gravity in a core is often assessed by using the virial ratio, the ratio between the virial mass and core mass (α_vir = M_vir/M_LTE). In Figure 13(d), we present the virial ratio as a function of the LTE mass, where we adopt a dimensionless parameter of a = 1, corresponding to a uniform sphere. For comparison, we show in Figure 13(d) the best-fit power-law function that is given by

$$\begin{equation} \log \alpha _{\rm vir} = (0.53 \pm 0.04) + (-0.651\pm 0.050) \log \left({M_{\rm LTE} \over M_\odot }\right), \end{equation} \tag{ 11 }$$

with the correlation coefficient of ${\cal R}=0.85$. The virial ratio ranges from 0.3 to 3.5, having a mean of 1.4. Figure 13(d) indicates that the cores with larger LTE masses tend to have smaller virial ratios. The majority of the cores have virial ratios smaller than 2, indicating that the total energy (the gravitational plus internal kinetic energies) of a core is negative. Therefore, the self-gravity of the individual cores appears to be important for the majority of the cores.

However, we note that the physical properties of the cores identified by the above procedure (and any other core identification schemes) depend strongly on the telescope beam size because the structures smaller than the beam size cannot be spatially resolved (see Maruta et al. 2010). According to Maruta et al. (2010), the cores identified from the data having the higher spatial resolution tend to be gravitational unbound and the external pressure due to the ambient turbulence plays an important role in the formation and evolution of the cores (see also Figure 10 of Nakamura & Li 2011). It remains uncertain whether a core identified here is a basic structure that is separated dynamically from the ambient turbulent media. In fact, Nakamura et al. (2012) recently revealed that the two starless cores, which were previously identified as single cores using the single-dish telescopes, contain several substellar-mass condensations whose masses are larger than or at least comparable to the critical Bonner–Ebert mass. The substellar-mass condensations might be real basic units of star formation in molecular clouds. The data with higher angular resolution on the basis of the interferometric observations will be necessary to address the issue of identifying the basic units of star formation in star-forming molecular clouds.