The left portion of Figure 1 plots the velocity-integrated CS contours overlaid on an K'-band adaptive optics observation from the 3.6 m CFHT of the core stellar population (S. Wang et al. in preparation, Paper II hereafter). The right portion zooms into the core with this ∼0.1'' resolution K'-band image (Paper II), which illustrates not only the distribution of cluster members but also the morphology of a reflection nebulae with an hourglass structure in the northwest-southeast direction (called the hourglass axis). This Hokupa’a 36 (Graves et al. 1998) adaptive-optics near-infrared (JHK') observation and the photometry of cluster members will be presented in Paper II. The reflected light results from the existence of dense dust whose surface is illuminated by the UV radiation from MWC 1080.

Figure 1. Left: CS(2-1) emission toward the MWC 1080 system overlaid on a small adaptive optics K'-band image taken from CFHT (Paper II). The noise is 0.14 Jy beam–1 km s–1. The contours are linearly spaced from 2 to 10 times the noise. The beam, shown at the lower right-hand corner, is with a P.A. of –62°. Negative contours, mainly from resolved-out large-scale emission, are not shown here in order to simplify the image. The dotted box indicates the zoomed field of the K'-band image (right) in order to show the distribution of young cluster members more clearly.

The CS map shows two distinct branches of emission (Fig. 1), which we call East and West for the left and right branches, respectively. Figure 1 shows that the distribution of CS emission is clearly aligned with the obscuring and scattering dust seen in the near-infrared map. This suggests the existence of a previous bipolar outflow that cleaned out the natal material along the direction perpendicular to the hourglass axis (the outflow axis), and helped clear the view to the stellar population along this direction. However, the CS emission is only associated with the upper part of the dense dust, revealing only the upper half of the cavity structure; the molecular gas is denser in the upper part than the lower part.

Moreover, the ¹³CO map also supports the suggestion of bipolar outflows by revealing a nearly complete biconical cavity around MWC 1080 (see Fig. 2). Figure 2 plots the velocity-integrated ¹³CO and C¹⁸O contours as well as the μm and mm dust continuum. The ¹³CO morphology also gives a lower limit of the estimation for the outflow cavity with ∼0.3 and 0.05 pc for the semimajor and semiminor axis and ∼45° position angle. This is just a lower limit because possible inclination or projection effects have not been taken into account. Fuente et al. (1998a, 2002) investigates the evolution of dense gas dispersal around HAeBes by presenting IRAM single-dish ¹³CO and CS observations. They propose an evolutionary sequence from stars that are still embedded within dense clumps and associated with bipolar outflows (type I) to stars that have dispersed their natal clouds and formed cavities (type III). MWC 1080 is shown to be their type II system. Our high spatial resolution observations further show that although this system is still young, Myr, the bipolar outflows in the MWC 1080 system have already constructed a small cavity, which is revealed for the first time. The size of this cavity is much smaller compared to the cavities seen in older systems such as HD 200775, a HAeBe with age of 8 Myr and a cavity of size ∼ (Fuente et al. 1998b). This might suggest that the bipolar outflow activity around MWC 1080 is still an ongoing process that will form a larger cavity.

Figure 2. 13CO, C18O, and continuum emissions. For 13CO, the noise is 0.3 Jy beam–1 km s–1. The contours are linearly spaced from 2 to 20 times the noise. The beam is with a P.A. of –51°. For C18O, the noise is 0.12 Jy beam–1 km s–1. The contours are linearly spaced from 2 to 10 times the noise. The beam is with a P.A. of –13°. For the 3 mm continuum map, the noise is 0.009 Jy beam–1 km s–1. The contours are linearly spaced from 2 to 6 times the noise. The beam is with a P.A. of –70°. Beams are shown at the lower right-hand corner of each panel. The stars indicate the location of MWC 1080, and the triangles indicate the NIR-identified cluster members from Paper II.

From Figure 2, the dust morphology at μm is similar to the morphology of dense gas, which infers that the dense gas traces the dust around MWC 1080 well. The high resolution of the mm continuum BIMA map reveals five dust clumps, which are consistent with dense gas distribution as well.

In addition to the morphology more information, such as the clumpiness, kinematics, and physical conditions inside this system, can be further investigated by extracting the mass and velocity distribution of dense gas. Studying the clumpiness of a molecular cloud is essential because it is usually closely related to the fragmentation and collapsing of molecular cores inside the cloud, which provides valuable insights to the ongoing star-forming activities in the system. On the other hand, the kinematics of gas and physical conditions reveal the natal environment where stars were born. As CS traces a denser region than ¹³CO, we mainly use CS to examine the clumpiness of dense gas and use both CS and ¹³CO to reveal the kinematics and physical conditions in this system.

Clumpiness is always observed in molecular clouds. This is not surprising, as a star forms through collapsing the natal cloud after reaching certain collapsing criteria. Therefore, local fragmentation and further clumping are naturally two typical characteristics in star-forming clouds. With the ability of interferometric observations to peer into dense layers of the molecular cloud, we can study how clumpy the dense gas is and its clump size compared to those cores forming isolated stars.

A clump is defined as a local density enhancement, which results in a flux density enhancement observationally. A molecular cloud without clumpy structures will not show multiple local emission peaks in its map, no matter how small the probing scale or beam size. On the other hand, if clumps exist in a molecular cloud, the number of local emission peaks will increase with decreasing scale until all clumps have been picked up or some clumps are too weak to be detected. Therefore, high-resolution maps are essential in distinguishing clumpy structures in the molecular clouds.

Figure 3 plots the CS contours at four different mapping scales with 8'', 4'', 3'', and 2'' beams. Fuente et al. (1998a) published the IRAM single-dish molecular line and continuum data of MWC 1080 and showed one emission peak near MWC 1080 in their ¹³CO (1-0) and CS (3-2) maps with 24'' and 16'' beams, respectively, and two emission peaks around MWC 1080 at the 1.3 mm continuum map with a ∼11'' beam. By comparing these maps, more and more clumps are seen from their maps to our Figure 3, and from Figure 3a to Figure 3c. This indicates that the dense gas around MWC 1080 is not a single big cloud centered on MWC 1080 but rather consists of small clumps, with clump sizes down to ∼3'' (6600 AU). However, there is not much difference in the clumpy structures between Figure 3c and Figure 3d, which suggests that the u, v weights used in Figure 3d are less suitable to the majority of the dense gas. The reason is that the dense gas in Figure 3d is resolved out with the interferometer. Therefore, in this paper we will use Figure 3c to further identify clumps and study their physical properties.

Figure 3. Beam sizes of with a P.A. of –46°, with a P.A. of –62°, with a P.A. of –67°, and with a P.A. of 72°, from (a) to (d), respectively. Beams are shown at the lower right-hand corner of each panel. The contours are linearly spaced from (a) 2 to 13 times the noise, 0.23 Jy beam–1 km s–1; (b) 2 to 10 times the noise, 0.14 Jy beam–1 km s–1; (c) 2 to 8 times the noise, 0.16 Jy beam–1 km s–1; and (d) 2 to 5 times the noise, 0.25 Jy beam–1 km s–1. The stars indicate the location of MWC 1080.

The main purpose of identifying clumps is to obtain individual star-forming building blocks that are capable of forming one or multiple low-mass protostars in order to investigate the physical conditions, such as mass, velocity dispersion, spectral feature, etc., in each system. In order to identify clumps, we basically adapt the idea of the Clumpfind method (Williams et al. 1994) to (1) select local peaks with fluxes above 3 σ in the velocity-integrated CS map Fig. 3c); (2) trace down to the half-maximum (HM) flux level of contours, which determines the sizes of clumps by fitting an ellipse; (3) assign the contour to the nearest peak once this contour is shared by more than one peak; (4) extract the spectrum and mass of each clump within the clump size; and (5) fit the extracted spectra with Gaussians to obtain the peak flux, peak velocity, and line width (FWHM). This is different from directly using three-dimensional cubes because it can avoid some specific star-forming features, such as a P Cyg profile being incorrectly separated into two clumps.

Table 1 lists parameters of 32 identified clumps, including coordinates, sizes, and integrated fluxes ( ). The , , , a, b, and P.A. are the observed and deconvolved sizes, including the major axis (a), minor axis (b), and the position angle (P.A.), respectively. We directly use the beam size as the upper limit of clumps with deconvolved sizes smaller than the beam size. The is , the equivalent size assuming a spherical clump. The sizes of identified clumps range from ∼4000 to 10000 AU. This is generally consistent with a typical system forming a single isolated low-mass star (e.g., ∼5000 AU; Looney et al. 2003).

Moreover, the eccentricity of clumps, ε, derived by a and b, can be used to characterize the clump shape. From the derived values of projected eccentricity we can see that not all clumps have circular morphology, especially those closer to MWC 1080, which show somewhat elongated structures with larger eccentricities. In order to examine the spatial distribution of clump eccentricity, we plot the eccentricity versus the distance to MWC 1080 (Fig. 4a) and to the outflow axis (Fig. 4b) for those resolved clumps. This plot shows that clumps closer to both the outflow axis and MWC 1080 tend to have larger projected eccentricities. This implies that clumps are more elongated when located closer to MWC 1080. This also suggests possible effects from outflows on the morphology of dense gas, especially modifying the shape of clumps.

Figure 4. Projected eccentricity of clumps vs. the distance to (a) MWC 1080 and (b) outflow axis.

Figure 5 displays the integrated spectra of CS, ¹³CO, and C¹⁸O emission, and Figure 6 shows the integrated CS spectra of East and West. From Figure 5, we can see that all CS and C¹⁸O and most ¹³CO emission is blueshifted, compared to the . In addition, a double-peaked feature is seen in the integrated spectra of ¹³CO and CS. Figure 6 shows that the spectrum of East is single peaked with a broad line width, while West contains two components. Table 2 lists the Gaussian-fitted parameters of these integrated spectra. From all integrated spectra, a large velocity gradient of the dense gas is seen throughout the whole system; the separation of peak velocity between two components in West is as large as 3.3 km s^–1.

Figure 5. Integrated spectra for overall gas traced by CS, 13CO, and C18O.

Figure 6. Integrated spectra for CS East and CS West. East shows a broad line width, while West shows double-peaked features. This double-peaked feature actually comes from two gas components with different velocities.

In order to reveal the velocity distribution and investigate the double-peaked feature, Figure 7 shows the position-velocity (PV) diagrams for East and West from CS and ¹³CO maps. This is made by applying two cuts from south to north toward both portions, as the dense gas of two portions is elongated along the outflow axis. Interestingly, it shows that two components seen in the integrated CS spectrum of West are also spatially distinguishable; the blue and red components in the spectrum are related to the northern and southern parts of the dense gas in West, respectively. Canto et al. (1984) also detected a double-peaked feature on the spectrum of dense gas around MWC 1080, but explained it as the results from self-absorption due to poor spatial resolution. Our high-resolution interferometric data shows that this double-peaked feature actually comes from two sets of gas with different velocities. In addition to West, Figure 7 also shows that there is a systematic velocity gradient in East from –35 km s^–1 (bluer, south) to –30 km s^–1 (redder, north), seen especially in the ¹³CO map. This gradient may result from an inclination of the outflow cavity, as the direction of the gradient is along the outflow axis.

Figure 7. Position-velocity (PV) diagrams along the outflow axis for (a) CS East, (b) CS West, (c) 13CO East, and (d) 13CO West. Contours are plotted from 1.5, 2, and 3 σ to maximum, with Jy beam–1.

Not only is there a velocity variation along the outflow axis, there is also a velocity gradient along the hourglass axis, which is perpendicular to the outflow axis. Figure 8 is the PV diagrams of the CS map with three cuts perpendicular to the outflow axis and moving away from MWC 1080. This also shows that the velocity dispersion along the farther cut is larger than that along the closer cut from MWC 1080. This is contrary to the idea that outflows or stellar winds from MWC 1080 contribute to the nonthermal motion, and thus increase the velocity dispersion, of gas closer to MWC 1080.

Figure 8. PV diagrams along the hourglass axis from (a) closer to MWC 1080 to (d) farther to MWC 1080. Contours are plotted from 1.5, 2, and 3 σ to maximum, with Jy beam–1.

Figure 9 displays example spectra of our identified clumps. Table 3 lists Gaussian-fitted parameters of the clumps that can be fitted with Gaussians. A few of them show P Cyg-like absorption; several of them contain two peaks, which might come from either self-absorption or a secondary component (another clump along the line of sight).

Figure 9. Integrated CS spectra for identified CS clumps.

By assuming LTE with an excitation temperature , small opacity, and negligible background continuum contribution, the total column density from a single transition using an array can be derived by (e.g., Miao et al. 1995) I is the total integrated intensity in Jy beam^–1 km s^–1, and are the FWHM sizes of beams in arcseconds, S, μ², ν, Q, and are the line strength, dipole moment in debye, line frequency in GHz, partition function, and energy in K of the upper state, respectively (Table 4). We use the deconvolved source sizes, a and b, as and here. is the opacity correction factor (Goldsmith & Langer 1999), The optical depth, τ, can be derived by (Rohlfs & Wilson 2000) where is the main beam brightness from observations and is given by . Table 1 lists some of these parameters for CS(2-1), ¹³CO(1-0), and C¹⁸O(1-0) (Rohlfs & Wilson 2000).

With estimated column density, mass can be obtained by assuming the abundance ratio to H₂, where , , and , , and , respectively (Rohlfs & Wilson 2000). An excitation temperature, K, is assumed as a medium value often seen in dense cores forming massive stars (see review by Zinnecker & Yorke 2007). Therefore, the mass can be derived by where is the mean molecular weight, is the mass of a hydrogen atom, and D is the distance (=2.2 kpc for MWC 1080; Canto et al. 1984; Ábrahám et al. 2000).

The estimated CS column densities and masses for CS clumps are listed in Table 5, labeled as , along with the estimated optical depth. The masses of these clumps range from ∼1 to 10 , with mean optical depth τ less than 1. We also estimate the maximum optical depth based on the peak emission of the CS map, which gives optical depth ∼1.2 in this system.

Using the same assumptions and equations (1) and (2), the total masses of dense gas are also calculated. There are ∼800, 1000, and 900 for CS, ¹³CO, and C¹⁸O, respectively, within an area of 0.7 pc radius from MWC 1080.

Another method that is frequently used, especially for optical thick lines, is the large velocity gradient (LVG) approximation (Goldreich & Kwan 1974). This is a radiative transfer model that takes optical depths into account for photon transport. It basically assumes a cloud with a systematic velocity gradient with velocity increasing away from the cloud center, so that a local treatment for photon transport can be approximated. We also estimate column densities and masses of CS clumps based on the LVG model in order to compare to the previous LTE calculation. We only apply LVG for those 14 CS clumps with well-fitted spectral information from Table 3.

We use the lvg task in MIRIAD to generate grids of the LVG model with kinetic temperatures of 10-30 K, number densities of 10⁴-10⁸ cm^–3, and column densities of 10¹³-10¹⁵ cm^–2. By using these grids to fit the observed brightness temperature, a range of CS column density can be found that can produce the observed emission. We further narrow the obtained range of CS column density by assuming the optical depth . As there is a lack of observations of NH₃ to further constrain the kinetic temperature, we simply use the range of 10-30 K, which is typically used for both low-mass and massive star-forming regions. The derived column densities and masses of CS clumps are listed in Table 5.

We also compare the estimation of and for these clumps. All clumps, except clumps A2 and A4, show a roughly good agreement between the derived and . This consistency suggests that most CS clumps are under good LTE approximation with small opacity. Clumps A2 and A4 have the brightest peak emission. The reason the LVG model gives much larger column density than the LTE approximation is that there is either a larger opacity or a higher temperature inside these two clumps. Large opacity will give a larger column density in the LTE approximation, while higher temperature than 30 K will allow smaller column densities in the LVG model to produce lines with such strong intensities. Both are reasonable explanations, especially the temperature in these two clumps likely being higher than usual, as they are located very close to the source of strong UV radiation, MWC 1080. In this paper, we will use the for further discussion.

With the estimated masses and the velocity dispersion of clumps, we can further study the virial condition inside each clump by comparing clump mass with the virial mass, . is the mass when the system is in virial equilibrium, when the time average over the kinetic energy is equal to half of the potential energy. In this situation, the system is gravitationally bound.

We assume a spherical symmetric clump with total mass M, radius R, and a density profile , where is the central density and r is the radial distance from the clump center. Therefore where . Either uniform density or isothermal condition is often assumed while deriving the virial mass of a cloud. In these two cases, for uniform density, and for the isothermal cloud with density .

In order to understand the density profile in our system, we investigate the relation between the total mass and size of CS clumps by plotting and (Fig. 10), as used in Saito et al. (2006). We obtain a linear relation between these parameters via least-square fittings, with . This assumes that all clumps in this system around MWC 1080 have the same density structure. Since , which gives , then pc^–3 and are obtained. Therefore in our case shows that our systems are consistent with a standard isothermal sphere density (Shu 1977).

Figure 10. Mass vs. size of clumps. The solid line is the fitted relation.

Given and FWHM from Table 1 and Table 3 as R and , is calculated and listed in Table 5. ranges from ∼1 to 10 . By comparing with , we find that the is ∼0.4-2 times the , except A8, C1, and C5, the farthest three clumps away from MWC 1080, which are 2-4 times larger than . In general, we can conclude that the virial mass is similar to the clump mass, as the mass estimation usually has an uncertainty to an order of 2. This is similar to low-mass star-forming cores, rather than massive cores (e.g., Saito et al. 2006).

Outflows are the primary sources that remove the natal material during the formation of stars, in addition to stellar winds and stellar radiation in the core of starburst clusters. However, the gas removal process via outflows in clusters has not been clearly characterized. As there are both high-mass and low-mass members forming in a cluster, the gas removal process might be different from that in a single star-forming system. Especially, does the most massive star still dominate the outflows that result in similar gas removal processes as seen from an isolated star? What is the role of low-mass cluster members in the strength and collimation of outflows?

In fact, the existence of a bipolar outflow in this cluster around MWC 1080 has been suggested based on its blue and red components on CO spectra in previous single-dish studies (e.g., Canto et al. 1984; Yoshida et al. 1991). However, due to poor angular resolution of single-dish observations, the outflow properties, such as the direction of the outflow axis, have not been well characterized. From our data, a biconical cavity is distinctly revealed around the most massive star in this system, MWC 1080, suggesting that the bipolar outflow has been dominated by MWC 1080. This also implies evidence of the gas removal by outflows in clusters. With the observed outflow cavity, the outflow axis is also clearly defined to have a P.A. of 45°.

Our data also show that this outflow cavity has a size of . This roughly gives an opening angle of 20° and a collimation factor of 3. This also means that the outflow activity has begun and formed a small cavity at an age of <1 Myr for a HAeBe star like MWC 1080. However, gas removal via outflows is still an ongoing process in this system, as a larger outflow cavity has been seen in a similar but older system (HD 200775, 8 Myr; Fuente et al. 1998b). A future ¹²CO high-resolution observation will be helpful in confirming the ongoing outflow activity in this system, as ¹²CO can trace low-density outflow gas. Assuming a homogeneous mass distribution of gas in the initial natal cloud and an initial mass density the same as the remaining gas, we can estimate that there was ∼1000 of gas in the cavity before outflows removed it. Therefore, an outflow mass-loss rate >10^–3 yr^–1 is required to form this cavity, either assuming a outflow age of ∼0.2 Myr (Levreault 1988) or an age <1 Myr (Fuente et al. 1998a). This value is higher than the typical mass-loss rate of outflows from a single OB star (10^–3 to 10^–4 yr^–1). In fact previous CO observations, which trace outflow gas at larger scale than this study, have estimated an outflow mass-loss rate of ∼10^–4 yr^–1 (e.g., Yoshida et al. 1991; Canto et al. 1984; Levreault 1988). One explanation of a possible higher mass-loss rate for CS gas is that the outflows from other cluster members are strong enough to strengthen the overall effects, but not strong enough to change the outflow direction at the scale of our study. Another possibility is that the remaining gas does not just include the natal material but also the swept-up gas by outflows, so the mass-loss rate is overestimated.

In order to clarify whether the observed dense gas is the remaining gas from the initial cluster-forming cloud or the swept-up gas by outflows, we further inspect the possible nonthermal contribution from outflows in dense gas next.

Molecular clouds, except for single star-forming prestellar cores, are generally observed to have broader line widths than those caused by the thermal motion from their thermal temperatures. It has been suggested that this results from the presence of turbulence (see review by Mac Low & Klessen 2004). Is this also true for single star-forming clumps in a cluster around an intermediate- to high-mass star, such as the MWC 1080 system? What is the role of the cluster environment in the kinematics of dense gas and clumps within one cluster-forming cloud?

Our data show that the line widths of clumps range from 0.85 to 2.48 km s^–1, which is much larger than 0.63 km s^–1, the line width of thermal broadening at 20 K. If only thermal motion contributes to the line width, the kinematic temperatures of these clumps would range from 36 to 310 K. This is unlikely, except for those clumps very close to MWC 1080, which heats its surroundings via UV radiation. Therefore, our results suggest that most gas in this system has a nonthermal contribution to kinetic motions. However, what contributes to these nonthermal motions? Initial turbulence, outflows from forming stars, and stellar winds from massive stars are possible candidates.

Initial turbulence is the general nonthermal random motion caused by turbulence in the molecular cloud before forming stars. Larson (1979, 1981) found the line width-size relation for molecular clouds with different scales. This relation indicates that there is a power-law relation between the velocity dispersion of molecular clouds and cloud size. Caselli & Myers (1995) further suggested that the nonthermal line widthsize relation follows different power-law trends for low-mass and massive cores. In other words, nonthermal motion still dominates at small scales for massive clumps, while low-mass clumps show only thermal motions at these scales. Nevertheless, there exist nonthermal components in the kinematics of molecular clouds, which provides the initial turbulence. Based on our data, we roughly estimate that the radius of this cluster-forming cloud is ∼0.7 pc. This gives an estimation for the initial turbulence with line width of ∼1 km s^–1 in our system, assuming the line width-size relation from Larson (1981). This value is smaller than the line width from our integrated spectra (Table 3), which implies that the initial turbulence may not be the only contributor to the nonthermal motion in this system.

In order to confirm more carefully whether there are extra contributors to broaden the line width of clumps, we plot the line width-size relation for identified clumps in Figure 11, compared to Caselli & Myers (1995). Caselli & Myers (1995) shows the nonthermal line width-size relations for massive and low-mass cores. Therefore, in this figure, we add the thermal components to their relations with thermal temperatures of 18 and 10 K for massive (solid line) and low-mass (dashed line) cores, respectively, as assumed in Caselli & Myers (1995). The dotted line indicates the thermal motion of 20 K, which is well below the line widths of all clumps. It also shows that there is either a flat relation or no correlation between the line width and the clump size. When using the relation from Caselli & Myers (1995) as expected initial turbulence contribution, this figure suggests that extra contributions dominate over the initial turbulence and affect the smaller clumps more. Not only the relation, but the line width values of identified clumps are also larger overall than those in Caselli & Myers (1995). In addition, Figure 11 also plots the relation between the line width and the LTE mass of clumps, compared to the result shown in Larson (1981). It shows that the low-mass clumps seem to deviate more from Larson’s relation. This indicates that the lower mass clumps are possibly affected more, which implies that the extra contributor to the nonthermal motions may come from a common source outside these clumps, instead of heated contribution from embedded forming stars inside individual clumps.

Figure 11. Relationship between line width and (a) size and (b) LTE mass of CS clumps. The solid and dashed lines in (a) indicate the massive cores and low-mass cores (Caselli & Myers 1995), respectively, and the dotted line is the thermal motion at temperature of 20 K. The solid line in (b) indicates the mass-line width relation from Larson (1981).

Both outflows and stellar winds can contribute to the observed nonthermal components of line width. From Figure 11, those extra contributors need to broaden the line width by ∼1-1.5 km s^–1. Furthermore, Figure 12 plots the relations for the line width and mass versus the distance to MWC 1080. From the line width-distance relation, no correlation is shown. As outflows or stellar winds from MWC 1080 are possible contributors to the nonthermal motions of natal gas, the affected line widths are expected to be broader for clumps closer to MWC 1080. Therefore, this plot possibly suggests that there is less initial turbulence deep inside the core region of this cluster-forming cloud. Besides, it is shown in the line width-mass relation that more massive clumps form closer to MWC 1080, which is the center of this cluster-forming cloud, or close to it.

Figure 12. (a) CS line width and (b) derived LTE mass vs. the distance to MWC 1080.

In short, the kinematics of dense gas in this cluster has been effectively modified by outputs from forming stars, such as outflows and stellar winds, instead of still being sustained by the initial turbulence. This further suggests that the observed hourglass dense gas is much more likely to be swept-up gas.

Which forms first in a cluster, massive or low-mass stars? This has been a fundamental but difficult question in the study of cluster formation because the highly embedded nature of protoclusters, where massive stars form, have prevented us from catching the earliest stage of the formation of low-mass cluster members. However, clarifying this question is essential, as it helps in understanding the star-forming environment in clusters, and after all most low-mass stars actually form in such cluster environments. This also plays an important role in studying massive star formation as massive stars often form in clusters along with many low-mass stars.

Our results have suggested that the observed molecular lines most likely trace the swept-up gas on the outflow cavity wall, instead of outflows or remaining gas with initial density. The kinematics of the swept-up gas has also been effectively modified by outflows or stellar winds from MWC 1080. The biconical cavity implies a domination of MWC 1080 and eliminates the contribution of other cluster members. In addition, Paper II also presents that there are ∼50 low-mass stars within a 0.3 pc radius around MWC 1080. Most of these stars are located inside the outflow cavity (also see Figs. 1 and 2).

These results may imply that it is unlikely that low-mass cluster members formed after MWC 1080 in this system. If low-mass cluster members formed after MWC 1080 did, then the gas dispersal from MWC 1080 should eliminate the formation of low-mass cluster members along the outflow direction. Hence, the stellar density in the cavity should have been lower than observed, if these low-mass stars formed after MWC 1080.

However, one puzzle remains about the morphology; why does CS emission only trace the upper half of the outflow cavity? In other words, why is the gas in the upper part denser than the lower part? One explanation is an inhomogeneous distribution of initial natal gas; the gas is just denser in the upper side than the lower side. Another explanation is that this is due to the inclination of outflow cavity, as all CS emission is blueshifted and a gradient has been seen in Figure 8. The asymmetry of the opening angle between both sides from the ¹³CO map may also result from the inclination.

As stars form, they disperse their natal material, so studying the morphology of molecular gas around newly forming stars has been very helpful in distinguishing stars with different evolutionary stages (e.g., Fuente et al. 1998a, 2002). A star-forming cloud typically evolves from compact dense gas centered on the star, to dense gas with bipolar outflows, then finally to a cavity with little gas left. However, not just the natal molecular cloud, but the clumpiness of dense gas in the cloud may be actively affected by the dispersal processes from the forming star. Therefore, the clumpiness of dense gas might be able to provide an alternative point of view to describe the evolutionary stages of star formation.

The clumpiness of dense gas can be defined as: (1) the fraction of mass inside clumps to total mass; or (2) the number density of clumps, the number of clumps per projected area. The first definition is determined by the intrinsic star-forming efficiency in the cloud and the degree of gas dispersal; the second definition is determined by the intrinsic fragmentation in the cloud and the degree of gas dispersal. Both definitions depend on the gas dispersal history because the mass inside clumps decreases and the clumps disappear as stars form. Therefore, the clumpiness can actually be used to trace the evolutionary stages of the forming stars, assuming the same initial conditions in the cloud and similar star-forming processes. This assumption is valid if we simply apply and compare the clumpiness to similar systems, for example to clusters around HAeBes such as MWC 1080. However, we have to keep in mind that the cloud’s initial conditions may dominate the clumpiness, as different star- or cluster-forming mechanisms could result in various initial cloud conditions.

In this paper, we will only use the second definition to discuss the clumpiness. This is because the true mass inside clumps cannot be fully obtained and the first definition will be biased with the dependence of mapping scales, due to the limitations of interferometry. Looney et al. (2006) identifies 16 clumps from another cluster around HAeBes including BD +40 4124. Using the second definition, we find that the clumpiness in the BD +40 4124 system is ∼1.6 times larger than that in the MWC 1080 system. This suggests that the dense gas seen in the BD +40 4124 system is at a younger stage than that in the MWC 1080 system.

From the infrared spectral energy distribution (SED) classification (Hillenbrand et al. 1992), BD +40 4124 and MWC 1080 are both classified as Group I objects, which have rising SED slopes. From the gas dispersal history (Fuente et al. 1998a, 2002), they are both associated with compact dense gas, which suggests a similar evolutionary stage. In addition, from the CS maps using high-resolution interferometric observations (Fig. 1 in Looney et al. [2006] for BD +40 4124 and Fig. 5b here), both systems show that the CS distributions are actually offset from the most massive stars (still at a similar evolutionary stage). Looney et al. (2006) show that the dense gas is around other younger stars, not BD +40 4124. The clumpiness discussed here suggests the youthfulness of dense gas in the BD +40 4124 system and shows that the dense gas in the MWC 1080 is dominated by MWC 1080, unlike the BD +40 4124 system. Indeed, the clumpiness provides an alternative point of view from which to examine the evolutionary stages of young stars, other than the morphology of dense gas or the SEDs of young stars.

Our data have shown that the mass of identified clumps ranges from ∼0.5 to 10 , capable of forming low-mass stars, with equivalent radius from 0.01 to 0.04 pc. These clumps are, in general, more massive than protostellar cores with similar sizes. This suggests that clumps formed in a cluster environment tend to have higher densities, which is also shown in Saito et al. (2006).

In addition, all clumps are estimated to have masses similar to the virial masses, which suggests that they are close to being in virial equilibrium. Figure 13 compares the LTE mass and LVG mass to virial mass for all clumps. This figure shows that most clumps have masses within 2 times their virial masses, which means that they are self-gravitational bound systems. This is usually seen in low-mass cores, but it is different from turbulent cores in massive star-forming regions (Saito et al. 2006), showing larger virial masses than LTE masses. This may be due to the external gas pressure helping support the turbulence (Saito et al. 2006). However, according to their Table 4, cores with LTE masses <10 are actually close to their virial masses, which is consistent with our results.

Figure 13. Comparison between differently derived masses. The solid lines are when the two masses are equal.

Nevertheless, our clumps in the MWC 1080 system are self-gravitationally bound, similar to low-mass star-forming cores, but have a higher density like massive cores. This is not surprising, as more mass is needed to bind clumps in order to overcome the nonthermal motions, which are contributed not only by initial turbulence but also inputs from massive stars, such as outflows and stellar winds. This does not necessarily mean that they will form massive stars eventually, because they will experience stronger external gas removal, such as outflows from nearby massive stars, than those isolated star-forming cores. In fact, we can simply assume that the identified clumps are possible precursors of those NIR-identified low-mass cluster members (Paper II), that are revealed just because their surrounding gas is strongly dispersed by outflows from MWC 1080. This means that these clumps will indeed be likely to form low-mass stars.

In addition, from § 5.3, we derive a density profile for the identified clumps, . This is consistent with Saito et al. (2006), which shows a density profile of for cores in massive star-forming regions. Our results show that clumps in our system are consistent with the density profile of many protostellar collapse models (e.g., Tassis & Mouschovias 2005). Therefore, along with the fact that these clumps are gravitationally bound, the ∼ profile from our data suggest that these clumps are likely collapsing protostellar cores.

We simply conclude that low-mass stars in a cluster environment such as the MWC 1080 system tend to be formed in dense and turbulent cores, which are different from isolated low-mass star-forming cores but similar to massive cores. However, gas dispersal contribution from the massive cluster member prevents these dense and turbulent cores from forming massive stars, instead forming low-mass stars, which are also revealed earlier than isolated low-mass stars are. This indicates that massive stars in clusters do have effects on the formation of their low-mass cluster members; they both help and hinder.