EVIDENCE FOR CLOUD–CLOUD COLLISION AND PARSEC-SCALE STELLAR FEEDBACK WITHIN THE L1641-N REGION

In Figure 1, we present a ¹²CO (J = 1–0) total integrated intensity map toward a 48' × 48' area, including the L1641-N cluster. The ¹²CO (J = 1–0) emission tends to be optically thick in the entire molecular cloud, thus representing the spatial extent of the global molecular gas distribution instead of the density distribution. For comparison, in Figure 1(b), the 1.1 mm continuum map taken by the AzTEC camera mounted on the ASTE 10 m telescope is overlaid on the ¹²CO (J = 1–0) total integrated intensity map with the contours.

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The ¹²CO (J = 1–0) integrated intensity map indicates that the parent filamentary cloud roughly runs from north to south. The filament appears to bifurcate in the southern part of the image. The L1641-N cluster resides at the bifurcation point. The most intense ¹²CO emission is associated with the L1641-N cluster at the position of (R.A., decl.) = (5:36:18, −6:21:48). The position of the ¹²CO integrated intensity peak almost coincides with that of the bright, compact continuum source, L1641-N MM1, which was identified by Stanke & Williams (2007) with the Submillimeter Array (SMA) interferometer; however, it deviates about 22'' toward south. This is probably because the single-dish continuum peak traces the whole clumpy structures identified by SMA, including L1641-N MM1, as shown in Figure 6 of Stanke & Williams (2007). A comparison between the 1.1 mm continuum image and the ¹²CO integrated intensity map indicates that several filamentary dense clumps are located near the parts where the ¹²CO emission drops sharply. These parts are in good agreement with the edges traced by ¹³CO (J = 1–0) emission (see Figure 2); therefore, we hereafter refer to these parts as the cloud edges for simplicity. For comparison, several main filamentary dense clumps are labeled with the letters A through E in Figure 1(b), indicating that filaments A and E are located at the eastern and western cloud edges, respectively.

In Figure 2, we also present the ¹³CO (J = 1–0) integrated intensity map toward the same area shown in Figure 1. Since the fractional abundance of ¹³CO is smaller than that of ¹²CO by a factor of about 40, the ¹³CO emission tends to be optically thinner than the ¹²CO emission; thus, its spatial distribution is expected to represent the distribution of molecular gas with intermediate densities of about 10³ cm⁻³. Although the spatial extent of the ¹³CO integrated intensity is well covered by that of ¹²CO, its spatial distribution appears different from that of ¹²CO. The ¹³CO emission tends to be concentrated in elongated or filamentary structures that reasonably trace the parsec-scale filamentary clumps identified by the 1.1 mm dust continuum emission (see Figure 2). The 1.1 mm dust continuum emission and ¹³CO (J = 1–0) integrated intensity also take their maxima nearly at the same position, i.e., toward the L1641-N cluster center, suggesting that the dense gas is concentrated into the L1641-N cluster-forming filamentary clump (the filament C).

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In Figure 3, we present a ¹²CO (J = 1–0) peak intensity map, which indicates that the ¹²CO (J = 1–0) emission drops sharply both at the eastern and western sides of the parent filamentary cloud. At the same places, the ¹²CO and ¹³CO integrated intensity drops sharply. A prominent feature is the existence of many arcs or elongated structures, most of which tend to be across the filamentary structures traced by the ¹³CO (J = 1–0) integrated intensity map. The peak intensity map of the optical thick ¹²CO (J = 1–0) emission typically represents the distribution of the excitation temperature instead of the local density distribution. However, the structures traced by the ¹²CO (J = 1–0) peak intensity map are sometimes seen in the ¹³CO (J = 1–0) integrated intensity map and are therefore likely to reflect the cloud density distribution in some parts. For example, some arcs located at the southwest part near the cloud edge are recognized in both the ¹²CO (J = 1–0) peak intensity and ¹³CO integrated intensity maps (e.g., (R.A., decl.) ≃ (5:35:0, −6:40:0) and (5:35:30,−6:35:30)).

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Here, we present several aspects of the parsec-scale filamentary dust clumps by comparing the spatial distributions of several molecular emission lines such as ¹²CO (J = 1–0) and ¹³CO (J = 1–0) with the 1.1 mm continuum emission.

The dust filaments are likely to have high densities of ∼10⁴–10⁵ cm⁻³ because the CS (J = 1–0) emission is detected toward all of the dust filaments (see Figure 5(c) of Tatematsu et al. 1993). The H¹³CO⁺ (J = 1–0) emission is also detected toward the dense parts of the filaments (Ikeda et al. 2007). For comparison, the H¹³CO⁺ (J = 1–0) integrated intensity contours are overlaid on the 1.1 mm image in Figure 4, and the dust filaments are labeled A through E. Figure 4 indicates that the strongest H¹³CO⁺ (J = 1–0) emission comes from the most massive filament C associated with the L1641-N cluster. The H¹³CO⁺ emission peaks in this filament coincide reasonably well with those of the 1.1 mm continuum emission. The line-of-sight velocities of the H¹³CO⁺ (J = 1–0) peaks are around 7 km s⁻¹. Interestingly, the CS (J = 1–0) emission is strongest at V_LSR ∼ 10 km s⁻¹, but weaker at V_LSR ∼ 7 km s⁻¹ (see Figure 5(c) of Tatematsu et al. 1993), although the H¹³CO⁺ emission is strong at around 7 km s⁻¹. In addition, the CS emission associated with the massive filament C is distributed in the wide velocity range of 6–12 km s⁻¹. As mentioned below, the CS emission as well as ¹²CO indicates that the most massive filament C has two different velocity components, which may give us a clue about the formation mechanism of the filament. We note that filament A is out of the area observed by Ikeda et al. (2007), but it is detected in CS (J = 1–0) obtained by Tatematsu et al. (1993). Thus, the filament contains a dense gas with densities of 10⁴–10⁵ cm⁻³.

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The ¹²CO (J = 1–0) velocity channel maps presented in Figure 5 indicate that the velocity structure in this region can be divided into three components: blueshifted (3–6 km s⁻¹), main (7–9 km s⁻¹), and redshifted ones (10–14 km s⁻¹). For comparison, we present in Figure 6 a two-color image with redshifted ¹²CO integrated intensity in red and blueshifted ¹²CO integrated intensity in blue. The 1.1 mm continuum map is overlaid on the image with white contours. The integration ranges are 9.5–14.5 km s⁻¹ and 3.5–6.5 km s⁻¹ for the redshifted and blueshifted components, respectively. The two-color image indicates that the redshifted component is dominant in the upper half of the parent filament, whereas the blueshifted component is dominant in the lower half.

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The strong blueshifted component with a velocity range between 4 and 6 km s⁻¹ appears in the southern part where the filament C and the L1641-N cluster reside. The redshifted component with a velocity of 10–12 km s⁻¹ is also associated with the massive filament C. The presence of a couple of velocity components toward filament C can be clearly seen in the position–velocity (PV) map presented in Figure 7(c), showing that the filament consists of two separate components with different velocities toward the eastern part of the filament: one is about 6 km s⁻¹ and the other is 9 km s⁻¹. These two components with different velocities are in good agreement with the CS map by Tatematsu et al. (1993). The filament is surrounded by the blueshifted elongated component that apparently has a head–tail shape (see also Figure 6). Another faint velocity component is seen toward the western part of the filament at a velocity of about 11 km s⁻¹. This component is more evident in the PV diagrams of the ¹³CO (J = 1–0) emission (see Figure 8(c)).

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Other dust filaments also have two-component velocity structures. The PV diagram (Figure 7(b)) indicates that filament A, located at the eastern cloud edge, has two components with different velocities: a diffuse component is at 6 km s⁻¹ and a stronger emission component is at 9 km s⁻¹. The similar velocity components are associated with filaments B and D (see also Figure 5). The two-color image indicates that the eastern area outside of the parent cloud is filled with the diffuse component with about 6 km s⁻¹. According to Sakamoto et al. (1997) and Shimajiri et al. (2011), this diffuse component is distributed in a much larger area in the eastern area of the Orion A GMC complex. Filament E has the two components at 7 km s⁻¹ and 9.5 km s ⁻¹ (see Figure 7(e)). These velocity structures of the filaments are in good agreement with the PV map of the ¹³CO (J = 1–0) emission (see Figure 8(e)). It is worth noting that the two filaments labeled A and E are located near the cloud edges where the ¹²CO (J = 1–0) emission drops sharply.

Besides the filamentary structures, shell-like structures are prominent in our ¹²CO map, particularly in the peak intensity map. In this subsection, we describe some characteristics of these shell-like structures in detail.

In the ¹²CO (J = 1–0) integrated intensity map (Figure 1), a shell-like structure can be recognized at the position of (R.A., decl.) ∼ (5:36:9, −6:4:20). The radius of the shell is about 10', corresponding to about 1 pc at a distance of 400 pc. The shell is more clearly seen in the ¹³CO (J = 1–0) integrated intensity map presented in Figure 2. This shell was first found by Heyer et al. (1992) who carried out a wide-field mapping observation in ¹³CO (J = 1–0) toward the Orion A GMC complex with the FCRAO 14 m telescope. They found that the shell has two velocity components with a velocity difference of about 2–3 km s⁻¹, implying that it has an expanding motion. They also found a number of large holes surrounded by the expanding shells. The typical radius of the shells is 10'–26', corresponding to 1–3 pc at a distance of 400 pc. They interpreted that these structures stem from events associated with the energetic star formation activity within the cloud.

Similar shell-like structures can be seen in our ¹²CO maps. For example, in the central part of the ¹²CO peak intensity map, two prominent thin shell structures are seen (Figure 3). We labeled these shells as A1 and A2 on the peak intensity map presented in Figure 9. There is also a shell labeled as A3, which is almost parallel to the A1 and A2 shells. These three shells are spatially well ordered and appear to have a common center that is very close to the position of the L1641-N cluster. These shells have very small thicknesses of about 30''. Such thin shells may be difficult to be found in the ¹³CO map because of the spatial resolution.

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Another prominent shell-like structure can be recognized in the southern part of the CO-integrated intensity maps (Figures 1 and 2) where the CO emission appears weak. Here, we labeled three remarkable shell-like structures or arcs as B1, B2, and B3, although there are several similar arcs seen in the image (Figure 9). These arcs appear to be spatially well ordered and homocentric. Some of them are detected in the CS (J = 1–0) line (see Figure 5(c) of Tatematsu et al. 1993), indicating that the dense gas is associated with them. We note that the common center of these shells is very close to the position of the V 380 Ori cluster, which is just outside of our ¹²CO map, located at (R.A., decl.) = (5:36:25.43, −6:42:57.7).

The shells are also clearly seen in a volume-rendering image of the ¹²CO (J = 1–0) antenna temperature data presented in Figure 10. The volume-rendering technique is suitable to find and visualize the coherent structures in three-dimensional space. The green color typically represents the areas with relatively high T*_A of about 10–15 K. We designated the shells as A1, A2, A3, B1, B2, and B3 in the image. These shells are coherent in the position–position–velocity cube, suggesting that they were created by some dynamical events. Several arcs, parts of the shells, can also be recognized in the ¹³CO map presented in Figure 2. These coherent structures are remarkable since the surrounding gas is highly turbulent and such coherent structures would have been destroyed in a crossing time of the shells (about 10⁴ yr for the radius of 10''–30'' and velocity of 3 km s⁻¹). Their existence suggests that the events producing these coherent structures play a dominant role in determining the internal structure of the cloud. In Section 5.3, we will discuss these structures in more detail.

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Recent numerical simulations of cluster formation have suggested that protostellar outflow feedback plays an important role in regulating star formation in cluster-forming clumps because they inject a substantial amount of kinetic energy into the surroundings (Li & Nakamura 2006; Nakamura & Li 2007; Carroll et al. 2009; Wang et al. 2010). Here, we attempt to identify molecular outflows associated with the L1641-N cluster to assess the roles of the outflow feedback in the dynamical evolution of the cloud. The ¹²CO emission has been successfully adopted to identify high-velocity components driven by powerful protostellar outflows (e.g., Stanke & Williams 2007; Takahashi et al. 2008; Arce et al. 2010; Nakamura et al. 2011a, 2011b); therefore, we identify several molecular outflows in the L1641-N cluster using the ¹²CO (J = 1–0) data.

Molecular outflow activity in the L1641-N region was first found by Fukui et al. (1986) at the position of the near-IR bright source IRAS 05338-0624 (see also Fukui et al. 1988). Further outflow surveys have been made through molecular line studies by several authors (e.g., Wilking et al. 1990; Stanke & Williams 2007). Stanke & Williams (2007) conducted ¹²CO (J = 2–1) mapping observations toward the L1641-N cluster using the IRAM 30 m telescope and the SMA interferometer, and they identified a number of molecular outflow lobes. Recently, Davis et al. (2009) carried out a near-IR H₂ survey of outflows in Orion A that included the L1641-N region. To identify the molecular outflows, we first scrutinize the velocity channel maps of our ¹²CO (J = 1–0) (Figure 5) and the PV diagrams to find localized blueshifted and redshifted emissions.

In Figure 11, we present the ¹²CO (J = 1–0) integrated intensity contours overlaid on the 1.1 mm continuum image obtained by Shimajiri et al. (2011). The velocity intervals for the integration are 0–5 km s⁻¹ and 10–16 km s⁻¹ for blueshifted and redshifted components, respectively. Stanke & Williams (2007) labeled the outflow lobes identified from ¹²CO (J = 2–1), and their names are also designated in Figure 11. The collimated redshifted lobe identified by Stanke & Williams (2007), R-S, is not as prominent in our ¹²CO (J = 1–0) map because this lobe is divided into several distinct knots. A number of H₂ knots labeled with SMZ 49 in Davis et al. (2009) are associated along this redshifted lobe. The blueshifted emission elongated along the northeast to southwest line is also seen north of the dust peak near the cluster center. This corresponds to the B-NE and B-N lobes in Stanke & Williams (2007). In the ¹²CO (J = 2–1) map, this lobe has a Y shape; however, in our ¹²CO (J = 1–0) map, the B-NE emission dominates over the faint B-N emission. This ¹²CO (J = 1–0) blueshifted lobe also corresponds to the one identified by Fukui et al. (1986). These are probably due to the fact that our ¹²CO (J = 1–0) data tend to trace relatively low-velocity outflow components. In fact, according to Stanke & Williams (2007), at low velocities, the two lobes identified by the ¹²CO (J = 2–1) emission blend together with a broad patch of ¹²CO emission. The most intense dust continuum emission is associated with the area between the redshifted (R-S) and blueshifted (B-NE and B-N) lobes, which is in good agreement with the HCN and HCO⁺ ridge found by Fukui et al. (1988) and the position of IRAS 05338-0624. The H₂ flows labeled with SMZ 51 and SMZ 53 appear to follow the B-NE and B-N lobes, respectively (see Figure 6 of Davis et al. 2009).

Another highly collimated, redshifted lobe is seen to the west of the R-S lobe, which is in good agreement with the R-SW lobe in Figure 2 of Stanke & Williams (2007). Similarly with the ¹²CO (J = 2–1) map, this lobe does not appear to have any obvious blueshifted counterlobes. The R-W, B-E, and B-SE2 lobes identified by Stanke & Williams (2007) can be clearly recognized in our map. The R-W lobe probably corresponds to the redshifted lobe identified by Fukui et al. (1986).

From our ¹²CO map, the total outflow mass, momentum, and energy are estimated to about 13 M_☉, 80 M_☉ km s⁻¹, and 273 M_☉ km² s⁻², respectively, by assuming the local thermodynamical equilibrium (LTE) condition and optically thin emission. Here, we adopt the same systemic velocity of 7.5 km s⁻¹ for all the outflow lobes and the values are corrected for the inclination angle ξ = 573 (Bontemps et al. 1996). The excitation temperature is adopted to 30 K, which is close to the peak brightness temperature of the ¹²CO (J = 1–0) line profile at the L 1641-N cluster center. We also integrated the physical quantities in the velocity intervals of 0–5 km s⁻¹ and 10–16 km s⁻¹ for the blueshifted and redshifted components, respectively. We note that the physical quantities estimated above are insensitive to the assumed excitation temperature. The estimated quantities increase only by a few tens of percents over the range of T_ex = 20–50 K.

Our ¹²CO map suggests that we identified the outflow lobes driven by about five embedded sources in the central part of L1641-N, and the mean outflow momentum for a single outflow may be estimated to be about 80/5 = 16 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 32 km s⁻¹, corresponding to the nondimensional parameter f of about 0.32, which gauges the strength of an outflow, where the wind velocity of 100 km s⁻¹ is adopted. This value is consistent with the fiducial values adopted by Matnzer & McKee (2000), Li & Nakamura (2006), and Nakamura & Li (2007).

As shown in Section 4, some dust filaments are located near the cloud edge where the ¹²CO emission drops sharply, rather than along the ridge of the parent filamentary cloud (i.e., filaments A and E). The dust continuum emission associated with the filaments also tends to have very steep gradients in the envelopes of the filaments, particularly for filament B. In addition, the dust filaments have two components with different velocities. The velocity difference between the two components is significantly larger than the typical local turbulent speed. According to the line-width–size relation obtained by Heyer & Brunt (2004), the typical turbulent velocity is estimated to be around 1 km s⁻¹, which is about three times smaller than the velocity difference observed in the dust filaments. Thus, it is unlikely that the filaments were created by the dynamical compression due to the local turbulent flow. From these observational facts, we propose here that the dust filaments in this region were created by external compression instead of spontaneous gravitational contraction.

On the larger scale of around 10 pc, there is a significant velocity gradient along the parent filamentary cloud. The cloud component with velocities smaller than about 6 km s⁻¹ is dominant in the southern part of the parent filamentary cloud, whereas the component with velocities larger than about 7 km s⁻¹ is dominant in the northern part (see Figure 6 and Figure 2 of Bally et al. 1987). The interaction between the two components is likely to have created filaments A, B, C, and D in this region. Here, we refer to such a possible dynamical interaction as a cloud–cloud collision. Since the two components tend to overlap toward the dust filaments on the plane of the sky (see Figures 7(b), (c), 8(b), and (c)), the collision may have occurred almost along the line of sight. The collision may also have triggered a star formation in the L1641-N cluster as well as the formation of the massive filament C. Cluster formations triggered by a cloud–cloud collision have been recently discussed by several authors for other star-forming regions (Xue & Wu 2008; Furukawa et al. 2009; Duarte-Cabral et al. 2010, 2011; Galvan-Madrid et al. 2010; Higuchi et al. 2010).

Besides the possible cloud–cloud collision, other parts of this region appear to have a velocity structure that is in good agreement with the expanding motion created by a shell. A typical example is filament E, which has two velocity components inside the shell A1, but appears to converge into a single velocity component at the outer part (see Figures 7(e) and 8(e)). Such an arc-like structure in the PV diagrams can be interpreted as an expanding motion of the shell. Filament C, the most massive filament, also has such an arc-like structure in the PV diagram in the western side (Figure 8(c)). This massive filament may have recently been compressed by an expanding shell after it was created by the cloud–cloud collision and the cluster formation was initiated. The compression due to the expanding shell may have accelerated the recent star formation in the L1641-N cluster. We do not think that filaments A, B, C, and D were created by the expanding shells created by the stellar feedback from the protoclusters because their main axes tend to cross the shells and they appear more or less straight, rather than curved like filament E.

Hence, the cloud–cloud collision and the expanding shells appear to have influenced the cloud structure and kinematics in this region. In Sections 5.2 and 5.3, we discuss these two dynamical events, the cloud–cloud collision and the expanding shell, in more detail.

According to our CO channel maps, the two components with velocities of 4–6 km s⁻¹ and 7–12 km s⁻¹ appear to be interacting to form the dense filaments. This interpretation is consistent with the previous ¹³CO (J = 1–0) observations that suggested that two or more different velocity components are associated with the Orion A GMC complex (Bally et al. 1987; Bally 1989). The velocity difference between the two components is about 3 km s⁻¹, which corresponds to the Mach number of 10; this is assuming that the gas temperature is 20 K. The supersonic collision between the two components would have increased the local density by a factor of 10² if the shock is isothermal. Therefore, such a shock can create filaments whose densities are as large as 10⁴–10⁵ cm⁻³ from preshock gas with 10²–10³ cm⁻³. In addition, the shock crossing time is estimated to be a few × 10⁵–10⁶ yr when the typical size of the filaments is adopted as a few pc. The estimated shock crossing time is shorter than the lifetime of the L1641-N cluster (a few × 10⁶ yr, see, e.g., Hodapp & Deane 1993; Galfalk & Olofsson 2008) by a factor of only a few. Consequently, it is possible for such a collision to have triggered a star formation in the dense filaments of this area. Since the shock crossing time is somewhat shorter than the lifetime of the cluster, the filament is expected to be in the postshock stage in which the observed two components may be passing over, thus traveling away from each other. According to Sakamoto et al. (1997), the blueshifted component is extended over the larger low-density area toward the eastern part of the cloud. This fact suggests that a collision with large clouds or flows (1–10 pc), instead of a collision with smaller clouds, may have occurred. The dynamical interaction with such an external flow has been recently suggested by Shimajiri et al. (2011) for the northern area of the Orion A GMC complex. The diffuse blueshifted component found from our ¹²CO data may be related to the flow pointed out by Shimajiri et al. (2011).

Recently, an interesting scenario on the formation of the Orion A GMC complex has been proposed by Hartmann & Burkert (2007) who performed two-dimensional numerical simulations of gravitational collapse of a thin gas sheet. According to their model, two large filaments are first created near the edge of the gas sheet by the gravitational effects of the cloud edge where the gravitational potential takes its local minimum (see also Larson 1976 and Bastien 1983 for the effect of the cloud edge on the gravitational fragmentation). They demonstrated how an elongated rotating gas sheet with a density gradient along the major axis can gravitationally collapse to produce a structure qualitatively resembling the whole Orion A GMC complex. This complex would have a fan-shaped structure at the southern part, ridges along the fan, and a narrow integral-shaped filament at the northern part. In their model, our observed area, L1641-N, is located at the intersection between the fan and the narrow main filament, which is where the two large filaments collide with each other. Such a large-scale interaction might explain the origin of the dust filaments, although it remains unclear how the hypothetical parent gas sheet was created.

As shown in Figure 9, our CO map revealed that several shells appear to shape the cloud structure in this region. The radii of the circles are about 10'–20', corresponding to about 1–2 pc at a distance of 400 pc. Interestingly, the centers of circles A1, A2, and A3 are close to the L1641-N cluster center, and the centers of circles B1, B2, and B3 are close to the V 380 Ori center. Such large shells are unlikely to form by stellar feedback from a single young star unless it is massive. Since the spectral types of the most massive cluster members are late B or early A for the two clusters, the shells may be difficult to create only by the stellar feedback of the most massive stars. Therefore, we suggest that these parsec-scale shells were created by multiple winds and/or outflows from cluster member YSOs. The reason why three or more shells are associated with each cluster remains unclear. One possibility is that the total momentum injection rate from cluster member YSOs is not constant but episodic because the star formation rate is likely to fluctuate or oscillate with time. Another possibility is that these circles represent dense parts of an expanding shell that is propagating into inhomogeneous media. Here, we call these YSO winds "protocluster wind." In the next subsection, we consider the dynamical evolution of the shell driven by the protocluster wind by using a simple analytic model.

Kinematical evidence that the protocluster wind is responsible for the cloud dynamical evolution comes from filament E, which is located at the western edge of the cloud and has an arc-like shape. Filament E has two velocity components inside circle A1, but appears to converge into a single velocity component at the outer part (see Figures 7(e) and 8(e)) as mentioned in Section 5.1. It is also distributed along circle A1 whose center coincides with the L1641-N cluster, suggesting that it may have been created by the shell driven by the protocluster wind from that cluster.

Another example of the parsec-scale expanding shell is the one whose center is close to V 380 Ori. This shell is fully covered by the ¹³CO (J = 1–0) map obtained by Bally et al. (1987), although the southern part of the shell is not covered by our ¹²CO data. We show in the ¹³CO integrated intensity map presented in Figure 12 that the circles appear to fit the shells. The ¹³CO PV diagrams of the shells toward the two positions (Figures 8(d) and (f)) clearly show the existence of the two different velocity components, which is consistent with the expanding motion. The expanding motion of the shell is in good agreement with Heyer et al. (1992) who found a similar expanding motion of the shell.

In the following, we discuss how the protocluster wind evolves in the parent molecular cloud using a simple analytic model. Here, we consider the motion of an expanding shell driven by protostellar winds from cluster member YSOs in a uniform media with a density of ρ₀. For simplicity, we do not take into account the effects of protostellar outflows in the following calculations; instead, we discuss the effect of the protostellar outflow feedback in the next subsection.

If a wind from a protostar with a radius of R_* is driven by a ram pressure of ρ_wV²_w, then the motion of an expanding shell is described as

$$\begin{equation} \frac{d}{dt}\left(\frac{4\pi }{3}R^3 \rho _0 \frac{dR}{dt}\right) =\sum _{i=1}^N 4\pi R_*^2 \rho _{\rm w} V_{\rm w}^2, \end{equation} \tag{ 1 }$$

where ρ_w is the wind density, V_w is the wind velocity, R is the radius of the shell, and N is the number of YSOs. For simplicity, all of the stars are assumed to simultaneously inject the wind momentum at the same constant rate. From the above equation, the time evolution of the shell radius is given by

$$\begin{eqnarray} R &=& \left(\frac{3\sum _{i=1}^{N}\dot{M} V_{\rm w}}{2\pi \rho _0}\right)^{1/4} t^{1/2} \simeq 2 \,{\rm pc}\ \left(\frac{N}{100}\right)^{1/4}\nonumber \\ &&\times\, \left(\frac{\dot{M}}{10^{-7} \,M_{\odot }\,{\rm yr}^{-1}}\right)^{1/4} \left(\frac{V_{\rm w}}{200 \,{\rm km \ s}^{-1}}\right)^{1/4} \nonumber \\ && \times \left(\frac{\rho _0}{10^3 \,{\rm cm}^{-3}}\right)^{-1/4} \left(\frac{t}{10^6 \,{\rm yr}}\right)^{1/2} \, \end{eqnarray} \tag{ 2 }$$

where $\dot{M}$ is the mass-loss rate from a single YSO and given by 4πR²_*ρ_wV_w. The expanding velocity of the shell, V_s, is evaluated as

$$\begin{eqnarray} V_s&=&\frac{dR}{dt} \simeq 1 \,{\rm km \ s}^{-1}\ \left(\frac{N}{100}\right)^{1/4} \left(\frac{\dot{M}}{10^{-7} \,M_{\odot }\,{\rm yr}^{-1}}\right)^{1/4} \nonumber \\ && \times\, \left(\frac{V_{\rm w}}{200 \,{\rm km \ s}^{-1}}\right)^{1/4} \left(\frac{\rho _0}{10^3 \,{\rm cm}^{-3}}\right)^{-1/4} \left(\frac{t}{10^6 \,{\rm yr}}\right)^{-1/2} . \nonumber\\ \end{eqnarray} \tag{ 3 }$$

The typical mass-loss rate and wind velocity from YSOs are somewhat uncertain. Some observations suggest that the mass-loss rate and wind velocity from a low-mass YSO are of the order of 10⁻⁷ M_☉ yr⁻¹ and a few × 10² km s⁻¹, respectively (e.g., Norman & Silk 1980; Wilkin & Stahler 1998). Here, we adopted $\dot{M}=10^{-7} \,M_{\odot }$ yr⁻¹ and V_w = 200 km s⁻¹ as their representative values. For the L1641-N and V 380 Ori clusters, the number of cluster member YSOs is of the order of 100. Adopting a density of 10³ cm⁻³ for the ambient gas and cluster lifetimes of 10⁶ yr, the radius of the expanding shell and the expansion velocity are evaluated to be about 2 pc and 1 km s⁻¹, respectively, which are comparable with those of the shells identified from our ¹²CO data. Therefore, the protocluster winds from these two clusters are likely to have enough energies to produce the parsec-scale shells within a few Myr.

In the previous subsection, we omitted the contribution of the outflow feedback on the dynamical evolution of the expanding shell. However, recent numerical simulations of cluster formation have suggested that protostellar outflow feedback plays an important role in regulating star formation in cluster-forming clumps because they inject a substantial amount of kinetic energy into the surroundings (Li & Nakamura 2006; Nakamura & Li 2007; Carroll et al. 2009; Wang et al. 2010). In addition, the propagation directions of the collimated outflows in the clustered environment are not preferentially aligned in the global magnetic field direction even in the presence of a strong magnetic field (Nakamura & Li 2011). Therefore, the total outflow momentum is expected to be injected isotropically on average. Here, we attempt to assess how the outflow feedback of the L1641-N cluster influences the surrounding gas and contributes to the dynamical evolution of the expanding shell.

5.5.1. Dynamical State of the L1641-N Cluster-forming Clump

Recently, Nakamura et al. (2011b) investigated how molecular outflow feedback influences the dynamical state of a nearby cluster-forming clump, Serpens South, by applying virial analysis. They found that the Serpens South clump is close to virial equilibrium and the total kinetic energy injected by the current outflow activity is less than the clump gravitational energy, concluding that the current outflow activity is not enough to destroy the entire cluster-forming clump. In the following, we follow Nakamura et al. (2011b) and clarify how the current outflow activity in the L1641-N cluster impacts the entire clump.

The virial equation for a spherical clump is given by

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

where I denotes the moment of inertia, U is the internal kinetic energy, and W is the gravitational energy. Here, we neglect surface pressure. A clump is in virial equilibrium when the right-hand side of Equation (4) is zero, i.e., 2U + W = 0. The kinetic energy and gravitational energy terms are expressed, respectively, as

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

and

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

where M is the clump mass, ΔV is the one-dimensional FWHM velocity width, G is the gravitational constant, R is the radius of the clump, and 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. Even though recent observations of magnetic fields associated with the nearby parsec-scale cluster-forming clumps suggest that the values of Φ/Φ_cr are estimated to be around 0.5 (e.g., Falgarone et al. 2008; Sugitani et al. 2010, 2011; Kwon et al. 2011), here we neglect the effect of the magnetic support for simplicity (i.e., Φ = 0). The dimensionless parameter, a, measures the effects of a nonuniform and/or nonspherical mass distribution (Bertoldi & McKee 1992) and is of the order of unity. For a uniform sphere and a centrally condensed sphere with ρ∝r⁻², a = 3/5 and 1, respectively. Here, we adopt a = 1 because the cluster-forming clump tends to be centrally condensed.

According to Stanke & Williams (2007), the radius and mass of the cluster-forming clump associated with the L1641-N cluster are roughly estimated to be 0.5 pc and 150 M_☉, respectively. Here, only the part involved in directly building the L1641-N cluster, i.e., a head of the clump, is defined as the cluster-forming clump, although the parent clump has a long tail extending southeast of the L1641-N cluster, as shown in the 1.1 mm map. The one-dimensional FWHM velocity width is estimated at about 2 km s⁻¹ from the ¹²CO data. Using these values, the kinetic energy and gravitational energy terms are estimated to be 2U ≃ 325 M_☉ km² s⁻² and W ≃ −194 M_☉ km² s⁻², respectively. These values are comparable with the estimate by Stanke & Williams (2007) who conducted a similar analysis using their ¹²CO (J = 2–1) data. Thus, the clump is likely to be close to virial equilibrium or somewhat gravitationally unbound. On the other hand, the total kinetic energy due to the outflows is evaluated at E_out ≃ 273 M_☉ km² s⁻¹. This is comparable to the clump gravitational energy. Although the substantial amount of the outflow kinetic energy appears to escape from the clump, the energy input due to the current outflow activity seems to significantly influence the clump dynamics.

5.5.2. Effects of the Molecular Outflows on the Expanding Shells

As shown in Figure 11, the identified outflow lobes often extend beyond the dense clump traced by the dust continuum emission, implying that the outflow momentum escaped from the clump is likely to influence the density and velocity structure in the surroundings. If the escaped momentum flux is about one-half of the total injected outflow momentum flux, it is estimated to be about 10⁻³ M_☉ km s⁻¹ yr⁻¹, assuming an outflow dynamical time of a few × 10⁴ yr. On the other hand, the total momentum flux injected from the protostellar winds is estimated to be $N \dot{M} V_{\rm w} \simeq 100 \times 10^{-7} \times 200 = 2\times 10^{-3} \,M_{\odot }$ km s⁻¹ yr⁻¹, where we adopted the values given in Equations (2) and (3). The estimated wind momentum flux is comparable with the protostellar outflow feedback. Therefore, we conclude that both the protostellar outflow and wind feedback can contribute to the dynamical evolution of the expanding shell created by the protocluster wind from the L1641-N cluster. However, the weak dependence on the injected momentum in Equations (2) and (3) indicates that even if we take into account both the protostellar outflows and winds, the estimated radius and expanding velocity of the shell do not change significantly.

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