MOLECULAR OUTFLOWS FROM THE PROTOCLUSTER SERPENS SOUTH

Since both the CO (J = 3–2) and HCO⁺ (J = 4–3) transitions have higher critical densities (approximately 10⁴ and 10⁷ cm⁻³, respectively) and higher transition energies (∼33 and 43 K, respectively) than those of the lower transition lines such as CO (J = 1–0), it allows us to examine higher density and/or higher temperature gas. In Figure 2, we present the CO (J = 3–2) velocity-integrated intensity map in the ranges from v_LSR = −2 km s⁻¹ to +15 km s⁻¹, which shows that the CO (J = 3–2) emission tends to be much stronger in the southern box with about 20' × 20' area (Boxes 1 and 2), while a relatively weak emission can be seen in the northern box with about 13' × 13' area (Box 3). In fact, the Serpens South protocluster resides in Box 1, and the strong CO (J = 3–2) emission originates mainly from the powerful molecular outflows of the cluster member YSOs, as described in the next subsection. We note that the weak CO (J = 3–2) emission was detected in the entire observed area, indicating that the molecular gas is widely distributed in a much larger area.

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We also present in Figures 3(a), (b), and (c) the CO (J = 3–2) peak intensity, HCO⁺ (J = 4–3) peak intensity, and 1.1 mm continuum maps, respectively, toward Box 2. The 1.1 mm continuum map was taken by the AzTEC camera (Wilson et al. 2008) on the ASTE 10 m telescope (Gutermuth et al. 2011). The positions of Class I and II sources identified by Gutermuth et al. (2008) from the Spitzer IRAC observations are plotted in Figures 3(a) through (c). The 1.1 mm map indicates that the dense gas is distributed along a long filament running from north to south. This filament (hereafter, the main filament) has several sub-filaments that appear to converge toward the main filament. Such structures appear to be common in many star-forming region, as pointed out by Myers (2009).

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The CO (J = 3–2) peak intensity map in Figure 2 is not dominated by emission at the systemic velocity of the cloud, ∼7.5 km s⁻¹. Such a feature is prominent in the velocity channel maps presented in Figures 4 and 5, where the emission is weak in the range from ∼7 to ∼10 km s⁻¹. For comparison, we also present in Figures 6 and 7 the CO (J = 3–2) and HCO⁺ (J = 4–3) spectra, respectively. The CO (J = 3–2) spectra often show double-peak line profiles, whereas the HCO⁺ (J = 4–3) spectra often show single-peak line profiles. By comparing the CO (J = 3–2) and HCO⁺ (J = 4–3) spectra, it is clear that the CO (J = 3–2) line profiles appear to be caused by self-absorption in the range from ∼7 to ∼10 km s⁻¹, rather than by multiple velocity components.

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Strong CO (J = 3–2) and HCO⁺ (J = 4–3) emission come from almost the same part where the 1.1 mm emission is strongest and the Serpens South protocluster is located. In fact, the CO (J = 3–2) and HCO⁺ (J = 4–3) emission peaks coincide reasonably well with the 1.1 mm peak. The HCO⁺ (J = 4–3) emission is distributed in an elongated clump with the axis ratio of about 1.5–2. The HCO⁺ (J = 4–3) integrated intensity map presented in Figure 7 suggests that the clump contains several subfragments. The clumpy structure of the HCO⁺ clump is more evident in the HCO⁺ (J = 4–3) velocity channel maps presented in Figure 8. The typical size of the subfragments is about 0.05 pc. The positions of two subfragments (sources 1 and 2 indicated in Figure 11(b)) are indicated by the diamonds in Figure 8. As shown in the next subsection, these two subfragments contain the possible driving sources of the outflows. The HCO⁺ (J = 4–3) emission takes its maximum at the position of source 2 presented in Figure 11 that coincides with the position of the 1.1 mm peak. The positions of these two subfragments coincide reasonably well with those of the 3 mm compact sources recently identified by the Nobeyama Millimeter Array (NMA) observations (N. Fukuda et al. 2011, in preparation).

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The CO line profiles have prominent blueshifted and/or redshifted wings near the region where the CO emission is strongest, as can be seen in Figure 6. The line wings sometimes extend over the velocity range of −10 to 30 km s⁻¹. These prominent wings indicate the presence of powerful molecular outflows in this region. The CO (J = 3–2) peak intensity map indicates that there are several local peaks and ridges near the central dense part of the protocluster. As shown in Section 3.2, these peaks trace the outflow lobes reasonably well. Similar high-velocity wings can also been seen in the HCO⁺ (J = 4–3) line profiles (see Figure 7) that are sometimes extended in the range from about 3 km s⁻¹ to 15 km s⁻¹ around the subfragments located near the 1.1 mm peak.

In the southern part of Box 2, the redshifted components of the identified outflows tend to be extremely weak (see also the line profiles presented in Figure 6(b)). It is unclear what causes the extremely asymmetric line profiles in the southern area. One possibility is the existence of a foreground cloud in the velocity of around 10 km s⁻¹ in the southern area. The foreground cloud, if cold, preferentially absorbs the redshifted outflow components. Another possibility is the existence of the global infall toward the southern part of the cloud. If the cloud envelope is infalling, the foreground infall gas having velocities similar to the redshifted outflow components can absorb the redshifted components. In the next subsection, we identify the molecular outflow lobes from CO (J = 3–2) data and discuss several features of the outflow lobes in detail.

Here, using the CO (J = 3–2) data cubes, we attempt to identify high-velocity components that originate from molecular outflows. First, we scrutinize the velocity channel maps (Figures 4 and 5) and the position–velocity diagrams to find localized blueshifted or redshifted emission (Figure 9). As can be seen in Figures 4 and 5, the ¹²CO high-velocity structure is very complex and crowded in the southern box with about 20' × 20' area (Box 2). Thus, identifying outflows from the ¹²CO emission alone is extremely difficult in this crowded area. Therefore, we compare the CO image with three-color Spitzer IRAC images (3.6 μm in blue, 4.5 μm in green, 8.0 μm in red) of this region, which are presented in Figure 10. The blow-up of the central area is shown in Figure 11. According to previous studies (e.g., Noriega-Crespo et al. 2004; Takami et al. 2010), extended objects that have strong emission in IRAC channel 2 (4.5 μm) compared to IRAC channel 1 (3.6 μm) and stand out as extended green objects in the three-color images are likely to be the objects shocked by the protostellar outflows. Here, we refer to such objects as infrared Herbig–Haro (H-H) objects. To identify the infrared H-H objects, we first made an image of the remaining emission in the Spitzer IRAC band 2 (4.5 μm) image after the subtraction of the emission in band 1 (3.6 μm). This image processing in practice allows us to discriminate between shocks and stars, displaying them with positive and negative values, respectively (Zhang & Wang 2009; Takami et al. 2010). We then visually inspected the image to search for mid-infrared outflows. We selected spatially extended sources that have significant excess at 4.5 μm as mid-infrared outflows. The positions of the identified infrared H-H objects are indicated by the crosses in Figures 10(b), 11(b), and 12(b). Some of the infrared H-H objects have bow shapes. For example, the infrared H-H objects labeled as K1 and K2 in Figure 12(a) have arc-like features, both of which appear to move toward the southwest direction (see Figures 12(b) and 13(a)). From our CO (J = 3–2) and Spitzer IRAC data, we identified 15 blueshifted and 10 redshifted components. The positions of the identified lobes are indicated in Figure 9. Table 1 gives a brief summary of the identified outflow lobes. We also show in Figure 16 the blueshifted and redshifted high-velocity components identified from HCO⁺ (J = 4–3). In the following, we describe some of the main features of the high-velocity components we identified from the CO (J = 3–2) data.

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The relatively strong blueshifted components B1 and B4 are well localized in the channel maps and appear at the maps within the wide range of 0.75–5.75 km s⁻¹. These lobes have extremely high-velocity blueshifted components. In particular, the B1 component has moderately strong emission even in the velocity range of about −10 km s⁻¹ (see Figure 6). There are also many infrared H-H objects associated with these two components. The B1 and B4 appear to move away from the central dense part toward north and south, respectively. In fact, the most distant infrared H-H object associated with B4 has a bow shape, consistent with the interpretation that it is moving away from the dense part (see Figure 11(b)). As mentioned below, the B4 component might originate from a compact 3 mm source located at the 1.1 mm peak, recently identified by the NMA observations (N. Fukuda et al. 2011, in preparation). If this is the case, the corresponding redshifted components are likely to be R2 and R3. The position of the 1.1 mm peak is indicated by a diamond (source 2 in Figure 11(b)) in the Spitzer image. It appears that no clear Spitzer sources are associated with the 1.1 mm peak. The 3 mm source discovered by the NMA observations may be a deeply embedded, extremely young protostar such as a Class 0 source. In fact, the HCO⁺ (J = 4–3) line profile toward source 2 shows blueshifted part stronger than the redshifted part (see Figure 14). Such a blue-skewed profile of an optically thick line may be indicative of infalling gas, suggesting that the 3 mm source located at the 1.1 mm peak is an infalling object having a powerful outflow.

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There are two faint blueshifted components labeled with B2 and B3. They are vaguely seen in the channel maps with high velocities (0.75–1.75 km s⁻¹). Some infrared H-H objects appear to be associated with the B3 component (see Figure 11). The position–velocity diagram indicates that the blueshifted component B8 is likely to be the outflow component that appears to move away toward south. The blueshifted components B14 and B7 are located near the edge of Box 1. Although B7 appears to move from northwest to southeast from its morphology, the driving source remains unknown. There is no redshifted counterpart associated with B7. The B7 component is also associated with some extended green objects, suggesting that the ambient gas is shocked by the B7 component (see Figure 12). The B14 component also do not have a redshifted counterpart. There is a compact dust continuum source immediately south of B14, where Bontemps et al. (2010) found two protostar candidates from the Herschel observations. The Spitzer image also shows two compact sources at the same places as the dust continuum source and the Herschel protostar candidates (Figure 12). We suggest that the northern source is likely to be the driving source of B14. This interpretation appears to be supported by the fact that the 1.1 mm emission is weak at the position of the B14 component, apparently breaking the main filament into two parts (see Figure 15(a)), and bending the northern part of the filament toward the south. There are some infrared H-H objects in the southern part of B14. These objects may originate from B14.

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The relatively faint blueshifted component B6 is clearly seen in the channel maps in the range of 3–5 km s⁻¹, apparently moving toward the southwest direction. The possible driving source is one of the Class I sources identified by Gutermuth et al. (2008; source 3 in Figure 11) because some H-H objects appear to be ejected from it. The B6 component appears to point toward the relatively strong blueshifted component B9. However, it is unclear whether B9 originates from the outflow lobe. The peak of B9 is about 0.4 pc away from the 1.1 mm peak. The position–velocity diagram may imply that this component has different LSR velocity (V_LSR ∼ 2 km s⁻¹) from the central dense part and does not show the velocity structure typical of the outflow lobe (see Figure 17(b)). However, there are no YSOs associated with the same area as the B9 component. Therefore, this component might be a fossil of the outflow lobe or infalling gas toward the central dense part along a sub-filament. Further investigation is needed to clarify the origin of this component.

There is a redshifted component R1 between the two blueshifted components B1 and B2. This redshifted component is clearly seen in the peak intensity map and appears to move away from the dense part. This component appears to be associated with a blueshifted component, which can be seen in the velocity channel maps with 4.75 km s⁻¹ and 5.75 km s⁻¹. Therefore, this component may be almost parallel to the plane-of-sky direction. The possible driving source is indicated by a diamond in Figure 11(a) (source 1), from which many H-H objects are apparently ejected.

The strong redshifted components R2 and R3 appear to move away from the central dense part, clearly showing the velocity structure typical of the outflow components. Several infrared H-H objects are associated with these components. Interestingly, at the area between R2 and R3, the 1.1 mm emission shows a double-peak feature and the 1.1 mm emission tends to be weak on the line connecting between R2 and R3 (see Figure 15(b)). In addition, there is an area having relatively strong 1.1 mm emission just at the north of R2. This morphology leads us to the following possibility: the redshifted lobes R2 and R3 come from the same source and R2 went through the dense part, reaching and hitting the dense part located at the north. The R3 component appears to coincide with the high-velocity component identified by the HCO⁺ (J = 4–3) map (see Figure 16). Such high-velocity dense gas may suggest that the outflow is very young. As mentioned above, the possible driving source is a 3 mm source recently discovered by the NMA observations, whose position almost coincides with the 1.1 mm peak (source 2 in Figure 11; N. Fukuda et al. 2011, in preparation). However, other unknown sources might be the real driving sources of these outflow lobes because this central part is very dense and crowded.

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There is a faint redshifted component R4 in the southwest part of the dense part. Several infrared H-H objects are associated with the R4 component. This component is clearly seen in the channel maps with 11.75 through 13.75 km s⁻¹, apparently moving toward the southwest direction. In fact, the most distant infrared H-H object (K2 in Figure 13(b)) has a bow shape, consistent with the interpretation that it is moving away from the dense part. Since a faint blueshifted component labeled by B5 is associated with the R4 component, this component might be almost parallel to the plane of sky. The possible driving source is one of the Class I objects identified by Gutermuth et al. (2008; source 4 in Figure 11) because some infrared H-H objects are apparently ejected from it.

Several bipolar outflows can be identified clearly in the CO (J = 3–2) data. For example, the southernmost outflow with the B15 and R8 lobes looks relatively powerful and clearly shows a bipolar feature. The driving source is probably one of the Herschel candidate protostars identified by Bontemps et al. (2010; see their Figure 5) whose position is (R.A., decl.) ≃ (18^h30^m2^s, −2°10'20''). The candidate protostar is also seen in the 1.1 mm continuum image presented in Figure 15(b) and the Spitzer IRAC image in Figure 10, as a point-like source. Another bipolar outflow can be seen near the upper right corner of panel (c) of Figure 9. The driving source may be either a Herschel candidate protostar or a Class 0 object located at the upper right corner of Figure 5 of Bontemps et al. (2010). In the northern box with about 13' × 13' area (Box 3) we found three molecular outflows, all of which show clear bipolar features: B10 and R5, B11 and R6, and B12 and R7. Since this region is out of our Spitzer image, we cannot identify the driving sources.

In Box 2, we identified four additional high-velocity components labeled B13 and R9. These components possibly originate from some outflows. However, further observations would be needed to clearly identify the outflow lobes.

We note that the directions of the outflow lobes often appear to be roughly along the global magnetic field direction that is running almost perpendicularly to the main filament (Sugitani et al. 2011), e.g., B2, B5, B6, B9, B15, B16, R4, R8, and R10. However, several components, e.g., B1, B3, B4, R2, and R3, appear to be independent of the global magnetic field direction. This indicates that the central dense part is magnetically supercritical, and therefore the local supersonic turbulence have presumably perturbed the magnetic field significantly. In fact, recent numerical simulations of cluster formation indicate that even a moderately strong magnetic field causes a significant misalignment between the global field direction and the outflow propagation directions because of the strong turbulence (Nakamura & Li 2011).

3.3.1. Outflow Parameters

Figure 9 shows that the high-velocity components are crowded in the central dense part where the protocluster resides, and therefore it is very difficult to clearly discriminate the individual outflow lobes from the data. Therefore, we postpone the accurate evaluation of the physical properties of the individual outflows until high spatial resolution data taken by interferometric observations become available. In the following, we calculate some global physical properties of the outflowing gas located at the cluster center. On the other hand, five bipolar outflows mentioned in the previous subsection can be easily identified in the CO (J = 3–2) map because they are found in relative isolation. However, we postpone the calculation of the individual outflow parameters of these bipolar outflows because the rms noise level is relatively high with a significant scanning effect, precluding accurate estimation of the outflow parameters.

Examination of the spectra in the cloud shows that ambient ¹²CO spectra away from the outflows appear to cover a velocity range of 6–11 km s⁻¹. We thus assume that the emission in this velocity range include ambient emission for the entire cloud. Therefore, the integration ranges used are −15 to 4 km s⁻¹ for the blueshifted emission and 11 to 30 km s⁻¹ for the redshifted emission, respectively. The outflow masses were calculated under the assumption of LTE, a distance of 260 pc, and optically thin emission in the line wings with an excitation temperature of 30 K. We note that the physical quantities estimated below are insensitive to the excitation temperature. The estimated quantities increase only by 20% over the range of T_ex = 20–50 K.

Following Nakamura et al. (2011), the outflow mass M_out, the outflow momentum P_out, and kinetic energy E_out are estimated as

$$\begin{equation} M_{\rm out}=\sum _j M_j, \end{equation} \tag{ 1 }$$

$$\begin{equation} P_{\rm out}=\sum _j M_j |V_j - V_{\rm sys}| / {\rm cos} \xi, \end{equation} \tag{ 2 }$$

and

$$\begin{equation} E_{\rm out} = \sum _j \frac{1}{2} M_j (V_j-V_{\rm sys})^2 / {\rm cos} ^2 \xi, \end{equation} \tag{ 3 }$$

respectively, where M_j is the mass of the jth channel, V_j is the LSR velocity of the jth channel, and V_sys is the systemic velocity of the driving source. Here we adopt V_sys = 7.5 km s⁻¹. The angle ξ is the inclination angle of an outflow, which is generally uncertain. Here, we adopt ξ = 573, following Bontemps et al. (1996). The mass of the jth channel, M_j, is expressed as

$$\begin{eqnarray} M_{j} &=& \mu _g m_{\rm H_2} X_{\rm CO}^{-1} \Omega D^2 \sum _i N_{\rm CO,\it i,j} \nonumber \\ &=& 3.2\times 10^{-9} \left({X_{\rm CO} \over 10^{-4}}\right)^{-1} \left({D \over 260\, {\rm pc}}\right)^2 \left({\Delta \theta \over {\rm arcsec}}\right)^2 \nonumber \\ &&\times \left({\eta \over 0.57}\right)^{-1} \left({\sum _i T_{{\rm A},i,j}^* \Delta v \over {\rm K \ km \ s^{-1}}}\right) T_{\rm ex} \exp \left[{33.2 \ {\rm K} \over T_{\rm ex}}\right] M_\odot, \nonumber\\ \end{eqnarray} \tag{ 4 }$$

where i is the grid index on the jth channel, $N_{\rm CO, \it i,j}$ is the CO column density at the ith grid on the jth channel, η (=0.57) is the main beam efficiency of the ASTE telescope, $m_{\rm H_2}$ is the mass of a hydrogen molecule, X_CO is the fractional abundance of CO relative to H₂, and the mean atomic weight of the gas μ_g is set to 1.36. We adopt X_CO = 10⁻⁴. Ω is the solid angle of the object and D is the distance to the object. From these quantities, we calculate the characteristic velocity as V_out = P_out/M_out.

Table 2 summarizes the outflow parameters derived from the CO (J = 3–2) data. The physical quantities presented in Table 2 depend on the adopted velocity interval for the integration. For example, if we change the velocity intervals to −15 to 6 km s⁻¹ (−15 to 2 km s⁻¹) for the blueshifted emission and 9 to 30 km s⁻¹ (13 to 30 km s⁻¹) for the redshifted emission, the total mass, momentum, and energy change by +65% (−50%), 20% (−30%), and 5% (−13%), respectively. This indicates that the total momentum and energy do not depend strongly on the adopted velocity intervals, although the total mass does. This is probably due to the fact that the outflow components with lower velocities have lower momenta and kinetic energies. As mentioned above, the distance to Serpens South remains uncertain. If we adopt D = 410 pc (e.g., Dzib et al. 2010) instead of 260 pc, then the mass, momentum, and energy increase further by a factor of 2.5. Therefore, a main uncertainty on the estimation of the outflow parameters comes from the adopted distance to the cloud, rather than from the adopted velocity intervals.

Table 2. Global Outflow Properties Derived from CO (J = 3–2)

Lobe	Mass (M☉)	Momentum (M☉ km s−1)	Energy (M☉ km2 s−2)	Vout (km s−1)
Blue	0.34	3.7	25.9	10.9
Red	0.27	3.9	38.7	14.4
Total	0.61	7.6	64.6	12.5

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3.3.2. Mass of Dense Clump

The HCO⁺ (J = 4–3) line emission has a critical density of 10⁷ cm⁻³, and thus traces the dense molecular gas. Here, we estimate the mass and radius of the central dense clump, using the HCO⁺ (J = 4–3) data (see Figure 7(a)). The mass of the HCO⁺ (J = 4–3) is evaluated from

$$\begin{eqnarray} M &=& \mu _g m_{\rm H_2} X_{\rm HCO^+}^{-1} \Omega D^2 \sum _i N_{\rm HCO^+,\it i,j} \nonumber \\ &=& 3.1\times 10^{-8} \left({X_{\rm HCO^+} \over 1.2 \times 10^{-9}}\right)^{-1} \left({D \over 260\, {\rm pc}}\right)^2 \left({\Delta \theta \over {\rm arcsec}}\right)^2 \nonumber \\ &&\times \left({\eta \over 0.57}\right)^{-1} \left({\sum _{i,j} T_{{\rm A},i,j}^* \Delta v \over {\rm K \ km \ s^{-1}}}\right) T_{\rm ex} \exp \left[{43 \ {\rm K} \over T_{\rm ex}}\right] M_\odot. \nonumber\\ \end{eqnarray} \tag{ 5 }$$

From the above expression, the mass and radius of the central clump are estimated to be about 80 M_☉ and 0.1 pc, respectively, where we assumed LTE and the excitation temperature of 14 K (André et al. 2010). The mean density is estimated to be M_clump/(4πR³_clump/3) ∼ (3 − 7) × 10⁵ cm⁻³. The estimated mean density is smaller than the critical density of the HCO⁺ (J = 4–3) line by an order of magnitude. This may suggest that the central clump contains multiple small subfragments that are not spatially resolved in our observation. In fact, recent numerical simulations of cluster formation suggest that the central dense region of a cluster-forming clump consists of multiple thin filaments that tend to fragment into denser blobs by the destruction due to the outflow feedback (Li et al. 2010). However, it is difficult to verify such a clumpy structure only from our observations. Higher spatial resolution observations will be needed to reveal the density structure of the dense clump. The fractional abundance of HCO⁺ relative to H₂ is assumed to be 1.2 × 10⁻⁹, which is adopted from Maruta et al. (2010). We note that the fractional abundance of the HCO⁺ remains uncertain toward Serpens South. However, from the 1.1 mm data, the 1.1 mm mass in the same area as that of the HCO⁺ clump is evaluated to be ∼10² M_☉, which is not far from the mass estimated from the HCO⁺ emission. Therefore, the adopted HCO⁺ abundance is likely to be reasonable. The FWHM one-dimensional velocity width of HCO⁺ is estimated to be ΔV ≃ 2.5–3.0 km s⁻¹ near the cluster center. The estimated velocity width corresponds to the Mach number of about 5.

Following Nakamura et al. (2011), we estimate the total energy injection rate (mechanical luminosity) due to the protostellar outflows and energy dissipation rate of supersonic turbulence in the dense clump. From Figure 9, the mean length of the outflow lobes can be estimated to be 0.1–0.2 pc, and the mean velocity along the line-of-sight direction is about 7 km s⁻¹ (see Table 2). From these values, the mean dynamical time of the outflows, t_dyn, can be evaluated as (1–2) × 10⁴ yr, assuming ξ = 573. Thus, the total energy injection rate due to the outflows is obtained as

$$\begin{equation} L_{\rm out} \sim E_{\rm out} / t_{\rm dyn} \sim (0.5\hbox{--}1) L_\odot. \end{equation} \tag{ 6 }$$

On the other hand, the energy dissipation rate of supersonic turbulence is estimated to be

$$\begin{equation} L_{\rm turb} \simeq C \frac{1/2 M\Delta V^2}{\lambda _d/\Delta V} \end{equation} \tag{ 7 }$$

where C (≃ 0.33) is the nondimensional coefficient, ΔV is the one-dimensional FWHM velocity width corrected for the contribution of the thermal pressure assuming a temperature of 14 K (see Equation (3) of Maruta et al. 2010), and λ_d is the driving scale of supersonic turbulence. From the HCO⁺ (J = 4–3) data, we can derive the energy dissipation rate as

$$\begin{equation} L_{\rm turb} \simeq (0.1\hbox{--}0.3)L_\odot, \end{equation} \tag{ 8 }$$

where we adopted the velocity width and the driving scale λ_d as ΔV ∼ 2.5–3.0 km s⁻¹ and the clump diameter of 0.2–0.4 pc, respectively. Both the energy injection rate L_out and energy dissipation rate L_turb are proportional to the distance to the cloud, D. Therefore, the relative importance between L_out and L_turb is irrespective of the distance uncertainty. The energy injection rate due to the outflows is somewhat larger than the energy dissipation rate. Therefore, we conclude that the outflow feedback can contribute significantly to the generation of supersonic turbulence in the clump.

Since we identified about five pairs of the outflows in the densest part, the mean outflow momentum for a single outflow may be estimated to be about 2 M_☉ km s⁻¹. If we assume the median stellar mass of 0.5 M_☉, then this gives the outflow momentum per unit stellar mass of about 4 km s⁻¹, corresponding to the nondimensional parameter f of about 0.04 (see also Maury et al. 2009 for the case of NGC 2264-C), which gauges the strength of an outflow, where the wind velocity of 100 km s⁻¹ is adopted. This value is somewhat smaller than the fiducial values adopted by Matzner & McKee (2000), Li & Nakamura (2006), and Nakamura & Li (2007). The estimated value may be somewhat underestimated because the outflow lobes are assumed to be optically thin. If the effect of the optical depth is taken into account, the value of f is presumably larger than the estimated value by a factor of a few. Even for a small value of f ∼ 0.1, Nakamura & Li (2007) demonstrated that the outflow feedback can supply sufficient momentum to dynamically support a parsec-scale cluster-forming clump for several free-fall times, by means of the three-dimensional MHD turbulent simulations. We note that if the distance to Serpens South is as large as about 900 pc, the upper limit of the distance to W40 (Rodney & Reipurth 2008), the outflow strength f is estimated to be f ∼ 0.4.

In the following, we investigate the dynamical state of the Serpens South clump, by applying the virial analysis. The virial equation for a sphere is given by

$$\begin{equation} \frac{1}{2} \frac{\partial ^2 I}{\partial t^2} = 2U+W, \end{equation} \tag{ 9 }$$

where the terms I, U, and W denote the moment of inertia, internal kinetic energy, and gravitational energy, respectively. For simplicity, we neglect the surface pressure term. A clump is in virial equilibrium when 2U + W = 0. The terms U and W are expressed as

$$\begin{equation} U=\frac{3M\Delta V^2}{16\ln 2} \end{equation} \tag{ 10 }$$

and

$$\begin{equation} W=-a\frac{{\it GM}^2}{R} \left[1-\left(\frac{\Phi }{\Phi _{\rm cr}}\right)^2\right], \end{equation} \tag{ 11 }$$

respectively, where the values Φ and Φ_cr are, respectively, the magnetic flux penetrating the clump and the critical magnetic flux above which the magnetic field can support the clump against self-gravity. Here, we adopt Φ = 0 for simplicity, which means no magnetic support. The value a is a dimensionless parameter of order unity which measures the effects of a nonuniform or nonspherical mass distribution (Bertoldi & McKee 1992). For a uniform sphere and a centrally condensed sphere with ρ∝r⁻², a = 3/5 and 1, respectively. For the HCO⁺ clump, the effects of the nonspherical mass distribution appear to be small because the aspect ratios are not so far from unity (see also Figure 2 of Bertoldi & McKee 1992). Here, we adopt a = 1 because the clump seems centrally condensed.

Then, the terms U and W are estimated to be 2U = 270–390 M_☉ km² s⁻² and W = −350 M_☉ km² s⁻², respectively, which yields the virial ratio, the ratio between 2U and W, of 0.8–1.1. This value increases by a factor of about 1.3, if we adopt the magnetic field strength derived by Sugitani et al. (2011). The dense clump as a whole is close to quasi-virial equilibrium. On the other hand, the outflow kinetic energy of the central dense part detected in the CO (J = 3–2) emission is derived as E_out ∼ 24 M_☉ km² s⁻², corresponding to about 7% the global gravitational energy, where we adopted the value corrected for the inclination angle ξ = 573. Therefore, the energy input due to the current outflows may not contribute to change the global kinetic energy significantly. In other words, the current outflow activity observed in Serpens South appears not to be enough to disperse the whole cluster-forming clump (see also Maury et al. 2009 for the case of NGC 2264-C). We note that the terms U and W increase with D² and D³, respectively, and therefore the virial ratio decreases by a factor of 1.6 if we adopt D = 410 pc, instead of 260 pc. Since this factor and the factor due to the magnetic support almost cancel each other out, the dense clump is likely to be close to the virial equilibrium.

The presence of Class II YSOs in this region suggests that star formation has lasted over 10⁶ yr, assuming the typical Class II timescale of about 10⁶ yr. However, the low fraction of Class II relative to Class I sources implies that the ages of the YSOs in this region may be younger than those in other nearby cluster-forming regions (Gutermuth et al. 2009). The age of this region may be 10⁵–10⁶ yr. This corresponds to a few ∼20 free-fall times of the clump assuming the mean density of 5 × 10⁵ cm⁻³, where

$$\begin{equation} t_{\rm ff} = \left(\frac{3\pi }{32G\rho _0}\right)^{1/2}. \end{equation} \tag{ 12 }$$

According to Gutermuth et al. (2008), about 30 Class I and II stars are associated with the area where we detected the strong HCO⁺ emission. Assuming the median stellar mass of 0.5 M_☉, the SFE in the dense part is derived as about 15%–20%, as reasonably high as those of other nearby cluster-forming clumps. This corresponds to about 1%–5% of the star formation rate per free-fall time. This value is in good agreement with that estimated by Krumholz & Tan (2007). Since the current outflow activity does not provide enough kinetic energy to destroy the clump, subsequent star formation is expected to continue. This is consistent with the quasi-virial equilibrium model for which cluster formation continues for a few or more free-fall times.