The Seven Most Massive Clumps in W43-Main as Seen by ALMA: Dynamical Equilibrium and Magnetic Fields

The W43-MM2 (hereafter MM2) clump is the second largest clump from the Motte et al. (2003) continuum survey. The most recent mass estimation places MM2 in the (3.5–5.3) × 10³ M_⊙, where the estimate was made by Bally et al. (2010), assuming an overall dust temperature of 23 K. In fact, this mass estimate means that MM2 is the most massive clump in W43-Main. The presence of OH and CH₃OH maser emission together with the lack of centimeter and 24 μm emission indicates that it is a high-mass star-forming clump in an early evolutionary stage. In addition, no molecular outflow has been detected so far. Figure 2 shows the ALMA 1 mm total intensity continuum map as well as the polarization map (see Section 3.2). The clump appears as a fragmented filament at length scales of 0.01 pc where the emission seems dominated by a single source, which seems to be the case for population 2 or the most massive clumps presented here. We label this source core A to follow the nomenclature from paper I, with a total recovered flux of 880 mJy and an estimated mass of 426 M_⊙. This core has ∼63% of the total flux from all the detected cores in MM2. It also appears to be monolithic, with no obvious indication of further fragmentation, although higher resolution observations with ALMA will indicate if the core has substructure. We treat the mass estimate of 426 M_⊙ as an upper limit given that it is unlikely that MM2-A is as cold as 23 K. Sridharan et al. (2014) detected a high-temperature hot core in MM1-A that had a similar initial mass estimate. However, and given that we do not have spectral line data from MM2-A at sufficient resolution, we can only speculate about the evolutionary stage of the core. Table 3 presents the source extraction parameters for this clump. The mass estimate derived here assumes T_d = 23 K for all the cores in the clump.

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W43-MM3 (hereafter MM3) is located in the southern part of W43-Main and to the east of MM2, with an estimated total mass between 1.5 and 2.3 × 10³ M_⊙ (Bally et al. 2010). The MM3 clump has been identified to contain the G30.720-0.083 radio continuum source showing emission from 0.6 to 21 cm, with a peak flux of 115 mJy at 6 cm, which is the brightest UC H ii region in W43 (Bally et al. 2010). The MM3 is also seen as an infrared dark cloud (IRDC) in absorption at 70 μm and as bright clump at 160 μm, as shown by Herschel data (Bally et al. 2010). In the ALMA data (see Figure 3), the MM3 clump appears as a fragmented filament, with eight extracted cores, where core A is the dominant core with a total flux of 150 mJy at 1 mm and an estimated mass of 59.4 M_⊙. The MM3 filament shows a double cavity feature, or maybe a dust shell, to the north of core A, with an S-type morphology as seen from north to south (as indicated in Figure 3). Furthermore, the cavity to the north is not associated with any millimeter-detected source.

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To ascertain the nature of this shell, we obtained SPITZER IRAC archival images toward MM3. Figure 4 shows the MM3 ALMA contours superposed on the IRAC map, where two sources, or stars, appear to coincide with the shell. The stars are indicated with red and green circles. Moreover, the G30.720-0.083 UC H ii region (α, δ = 18:47:41.808, −02:00:23.76) is also located within the shell and close to one of the IRAC sources (Zoonematkermani et al. 1990). The resolution of the Very Large Array (VLA) data used to detect G30.720-0.083 is about 5'', which is about the size of the shell. Despite the uncertainty introduced by the coarse VLA resolution, it is plausible that the UC H ii region coincides with one of the IRAC sources, and thus the UC H ii region might explain the origin of the shell. We should note that the 8σ to 16σ contours around the shell are closer toghether than the more significant contours, which may indicate spherical symmetry. Alternatively, morphologies like this have been observed as the result of outflow emission. Outflows can carve cavities around the envelope of a star, as seen in a number of regions. Hull et al. (2016) and Maury et al. (2018) presented a clear example in Serpens SMM1 and B335. In the SMM1 core a high-velocity jet of ionized gas and a highly collimated molecular outflow are carving a cavity around the young Class 0 protostellar source powering the jet. In B335 the east–west outflow has carved a cavity whose walls are clearly visible in their ALMA data. This scenario might explain the southernmost cavity because cores B and C are geometrically close to power the outflows. However, we have no data to search for outflow emission from the B and C MM3 cores. Furthermore, the northernmost cavity is difficult to explain in this way because we lack an explicit core detection nearby. For this clump, the core mass distribution extends from 6.6 to 59.4 M_⊙, where we used T_d = 27 K uniformly.

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The W43-MM4 (hereafter MM4) is also associated with a radio continuum source. Balser et al. (2001) suggested the presence of an UC H ii region at the center of MM4, while Zoonematkermani et al. (1990) found coincidence with strong free–free emission (∼300 mJy), typical from UC H ii regions. However, the resolution of both detections is coarse (∼9'' and 5''), which makes it difficult to correlate with our higher resolution ALMA data. This clump is also one of the closest in our sample to the W-R/OB cluster powering up W43, with a projected distance of about 2 pc. This distance is close enough to consider the clump inside the shock and the ionization fronts from the W43 giant H ii region.¹⁷ However, SiO(2–1) maps of W43-Main presented by Nguyen-Lu'o'ng et al. (2013) show insignificant emission toward MM4. Although the authors attribute the SiO emission to a low-velocity shock produced by colliding flows, we would have expected an enhancement in the SiO emission and the development of photoionized regions (PDRs) from MM4 given its proximity to the W43 H ii region.

Bally et al. (2010) estimated an MM4 clump mass between 0.9 to 1.3 × 10³ M_⊙ assuming an overall T_d = 28 K. This temperature is consistent with estimations reported by Nguyen-Lu'o'ng et al. (2013) based on the UV radiation field illuminating this clump. Figure 5 shows the ALMA map of MM4, where the emission appears distributed around the main peak with a tail toward the southeast. Source A dominates the emission with a flux of 160 mJy, although we did not resolve it, as shown in Figure 5. Another seven sources are also detected mainly around core A, the dominant source in MM4 and a likely candidate for a UC H ii region. Three additional cores are detected toward the southwest, C, G, and D. They appear to be connected to the main filament, although it is interesting to see that no sources were detected within the bridge that joins the tail with the main filament. The core mass estimates for MM4 are listed in Table 3.

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The initial mass estimate from Motte et al. (2003) places these clumps in the <1000 M_⊙ regime, where the estimates are ∼500 M_⊙ for MM6, ∼870 M_⊙ for MM7, and ∼390 M_⊙ for MM8. Current data from W43-Main suggest no radio continuum and/or infrared/far-infrared detections sources associated with these clumps. Thus, they seem to be in an early stage of evolution. As these clumps have not been extensively studied, we lack detailed SEDs for them. Therefore, we assumed a dust temperature of T_dust = 25 K for all three of them because this seems a representative value considering their fluxes and the temperatures assumed for the other clumps. The source parameters for the cores we extracted from these clumps are listed in Table 3.

The MM6 clump shows a clear filamentary structure with 10 cores detected along the major axis and 2 cores to the east. Figure 6 shows the MM6 ALMA map and the detected cores. From a total of 12 detected cores, the brightest, labeled A, has an integrated flux density of 52 mJy and and a deconvolved size of 0.02 pc. From Table 3, we see that core K has a higher integrated flux than A. However, this is because the deconvolved size from the Gaussian fit is larger and so consequently is its integrated flux. Now and by looking at the peak flux, core A is clearly the dominant source in the clump, with 20.5 mJy beam⁻¹ compared to 6.5 mJy beam⁻¹ from K. The core estimated masses are within the <25 M_⊙ regime for MM6, and and their mass distribution appears to be uniform even when we consider the most massive cores A and B. This is a departure from what is seen in the other W43-Main clumps, where the brightest cores in MM1 (see Paper I and Motte et al. 2018), MM2, MM3, and MM4 significantly dominate the core mass distribution of their respective clumps. Given the clear filamentary morphology of MM6, we can directly calculate its width,¹⁸ which on average is closer to 43 or 0.12 pc assuming 5.5 kpc as the distance to the Sun. Now, the maximum recoverable angular scale for our data is about 512 or 0.14 pc. Thus, the filament width is within the length scales that ALMA is sensitive to, and it therefore does not seem to be a cutoff given by the array configuration. Although such filament widths were initially seen toward low-mass star-forming regions (Arzoumanian et al. 2011), data obtained from single-dish mapping suggest that a similar filament length scale might also be present in high-mass star-forming regions (André et al. 2016).

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In the MM7 clump, shown in Figure 7, we detected 11 cores along the central filament, with 9 additional cores to the east and west. Cores A and B dominate the emission, but with a peak flux distribution similar to what we see in MM6 and flatter than what is seen in the other most massive clumps. In total, we extracted 20 cores from MM7, which is about a factor of two more than what we have obtained in the most massive clump from our sample (MM2). This implies a higher fragmentation level, but with a more uniform mass distribution (from 1.7 to 11.8 M_⊙). The estimated mass for core A, 11.7 M_⊙, is about a factor of six lower than the MM3 and MM4 dominant cores, and a factor 40 lower than the MM2 core A. However, this mass seems sufficient to form a high-mass star, especially if accretion is still ongoing. The MM7 clump also shows a clear filamentary structure with an average width of about 35 or 0.09 pc.

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The MM8 clump has the lowest mass in our sample. Here, we detected a total of 18 cores with a peak flux distribution similar to that in MM7 and MM6. Three of the detected cores dominate the peak flux: cores A, B, and D. This is in line with what is seen in the MM6 and MM7 clumps (population 1). In fact, in MM8 we see an increase in the number of low-mass cores, where some of them have a mass lower than 1 M_⊙. We recall that these sources are all significant detections with fluxes that are a least 10σ higher than the noise. The ALMA map for MM8 with the identified cores is shown in Figure 8. The MM8 clump also shows a filamentary structure, but in this case, the peak of the clump emission was offset from the phase center by ∼20''. The filament width is on average about 24 or 0.06 pc, which is similar to MM7.

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In general, we find that all the clumps in the W43-Main molecular complex show a filamentary structure. Here, we define a filament as emission from the clump that shows a geometrically elongated morphology with a preferred direction. Additionally, we found that three of these clumps (MM2, MM3, and MM4) have one core that dominates the flux distributions and therefore the mass. The other three clumps (MM6, MM7, and MM8) have a flatter mass distribution with two to three cores dominating the emission. We also find in most clumps single and isolated cores that do not seem to be directly associated with the main filament (e.g., cores G in MM3 and A in MM8). Although fragmentation in these filaments is evident along the major axis, additional fragmentation is seen, sometimes in the orthogonal axis projection (such as MM4), as well as in filaments parallel to the main axis (e.g., MM7). In these cases, more than one core is detected. As we show below, this difference is also correlated with a difference in the amount of polarized emission detected from these filaments. The filaments that are dominated by a massive core are highly polarized, but the filaments with a flatter core-mass distribution are virtually unpolarized.

The magnetic field morphology onto the plane of sky for the MM2 clump is shown in Figure 2. The polarized emission covers most of the Stokes I map at the 3σ level from north to south. The inferred magnetic field pattern is quite complex, showing areas on the map where the field appears to be coherent over significant portions of the filament. Over these areas, the EVPA dispersion is small, which is suggestive of strong fields. However, we have chosen larger regions to estimate the field strength in order to obtain a sufficient number of independent points and also to derive a representative value for the ambient magnetic field around the cores in a given region.

To the west of the main filament and over the MM2-C core, the field morphology suggests continuity with the field over the main filament, despite the gap seen in the total intensity. It is important to state that most of the polarized emission used to infer the field morphology and estimate its strength in this clump is within one-third of the primary beam of the ALMA 12 m antenna (inner dotted circle in Figure 2). Within this region, ALMA meets the specification of a minimum detectable amount of linear polarization of 0.1%. Outside this region, the specification is not guaranteed, but in band 6 the performance degradation is no worse than 0.6% at the 50% level of the FWHM with an error in the EVPA no larger than 2°. Thus, we are confident that the polarization morphology over MM2-C is representative of the magnetic field morphology.

To estimate the field strength throughout the MM2 clump, we have defined four regions based on the projected field apparent connectivity (see Figure 9). Region 1 was defined over sources A and D where the field shows a well-connected radial pattern. Toward core A in region 1, the field pattern is mostly radial, which is quite similar to the morphology seen toward MM1-A (Paper I). In that case, the interpretation was that gravity dominates and the field is being dragged toward the main core. We explore this possibility in the discussion section (see Section 4). To the north and over core F, we defined region 2, where the field is also continuous, well connected, and clearly distinct from the field morphology seen in region 1. Region 3 is defined over cores B and J, where the field pattern seems isolated and with a different morphology with respect to the field pattern seen in region 2. Region 4 is defined to the west over core C, where the field is isolated from the main filament. However, at the 2.5σ level, there seems to be continuity between the field in this region and the filament main field. Figure 9 shows the regions on top of the polarized intensity map. In all the four regions, the angular scale for the 3σ polarized emission is about 5''. We used this angular scale to calculate δϕ and σ_v. Table 4 shows the estimated B_pos for all the cores belonging to the chosen region.

We obtained field estimates from 0.1 to 3.2 mG throughout the clump (see Table 4). This range of field estimates is smaller to the values obtained toward W43-MM1, where the spread and morphology the polarized emission is similar. In MM1 the emission covered the entire filament, or ∼13'', which is about the extension of MM2 (∼14'') when we consider the entire polarized emission. The differences in the field estimates here compared to Paper I come from the values of ΔV where the Kolmorogov extrapolation give smaller line widths than the 3 km s⁻¹ used there. Also, the regions used to calculate δϕ in Paper I traced field patterns with lower dispersion values in the EVPA. In MM2, the situation is more complex as the field is clearly connected throughout the filament, which complicates the definition of these regions. It is important to point out that the DCF method assumes that the EVPA dispersion is the product of perturbations in the field lines by the nonthermal motions of the gas (a more detailed discussion can be found in A). However, in region 1, over the MM2-A core, the EVPA dispersion seems to be produced by infalling gas perturbations of the field lines rather than by turbulence (see Section 3.3 for our gas infalling results). One way to see this is by noting that the northeast and northwest pseudo-vectors toward the center of MM2-A seem to be almost orthogonal to each other. It is unlikely that turbulence induces this level of change in the field lines, and therefore it has come from gravity. Although in MM1-A we have a similar situation, the geometrical distribution of the polarized emission seemed to favor a bimodal distribution between two distinct subregions, but where one of them is more extended. As both regions have small EVPA dispersion, one dominated, which decreased the overall value of δϕ (see Figure 2 in Paper I). This resulted in an increase in the estimated field strength when compared to MM2-A, although both regions have similar field morphologies. Therefore, this bias in the estimation of δϕ likely yielded magnetic field strength estimates that are lower limits of the "true" magnetic field strength around the MM2-A and D cores. The same might be said from the estimation made toward MM1-A in Paper I.

Although the field lines around the main core (region 1) have a clear radial pattern, the field to the north is more difficult to interpret. Here and to the east, the pattern appears remarkably smooth and uniform, with a clear direction along the major axis of the filament for the field over MM2-F, but turning to ∼45° between MM2-B and MM2-D. This uniformity strongly suggests that magnetic tension along the filament is dynamically significant. The width of this emission is about half the filament width, or 32, which is about 0.08 pc. However, to the west, the field lines deviate ∼40° and are even orthogonal to the main axis in some parts. Continuity in the field lines is present as the field smoothly changes direction. This change is significant, and it occurs across an important section of the filament. In Figure 2 we see that the width of the 5σ pseudo-vectors that change direction in region 2 is about 14, or 0.04 pc. Thus, the field appears to have a coherent and smooth direction over many core length scales, which suggests that the field is not affected by the gravitational pull of these cores. In region 3, the field lines approximate a radial pattern over core B. However, the significance of the emission is not as high as over core A, and thus this interpretation is inconclusive. To the east of core B we have almost negligible polarized emission at a Stokes I level, where we do detect polarized emission elsewhere (region 4). At the eastern edge of region 3, the field lines appear to follow the main axis, but they smoothly deviate below core B to become orthogonal to the main axis of the filament. It is not clear how the field connects from the eastern edge of region 3 with the field in region 2 given the deviation we see. In region 4 the polarized emission is not as significant, and the required number of points to estimate the field was met by considering the 2.5σ pseudo-vectors. Nevertheless, the field morphology seems consistent with the more significant points. The inferred field lines in this region appear to connect with the field in the main filament. It is clear that the field evolves from being orthogonal to the main axis of the filament to a smooth alignment with the main axis.

The magnetic field morphology over the MM3 clump, shown in Figure 3, is distributed mostly throughout the center of the filament. It shows four distinct regions that include all the detected cores in the clump, where the field appears to be well ordered. Although the polarized emission appears to be more compacted than in MM2, there is also indication of continuity from region to region in the derived field morphology. In all of these four regions, we have a sufficient number of independent points to estimate B_pos. These distinct regions are also indicated in Figure 9 and the estimates for B_pos and the parameters from the polarization map are listed in Table 4. Most of the polarized emission is located around cores A, B, and D (region 3) at the center of the filament, and over core F, where the polarized emission is the brightest in the clump. Over MM3-A, the field morphology appears similar to what we have seen in MM2 and MM1, where the field appears to be dragged by gravity. Following the discussion for the MM2 field strength estimate over region 1, the EVPA dispersion seen over region 3 in MM3 also appears to result from perturbations by infalling gas over the field lines rather than turbulence. Therefore, we also consider the estimates here to be lower limits, with estimated values for B_pos of between 0.1 and 1.4 mG.

The polarized intensity map from the MM3 clump (Figure 3) shows strong and compact emission (up to 30% of Stokes I) around and over core F. The inferred magnetic field morphology is uniform and ordered, with a small dispersion in the field lines orientation (i.e., equivalent to the EVPA dispersion, or δϕ = 103). A similar situation is seen over core C and to a lesser degree over E, where the polarized emission is compact but not as strong as what is seen over core F. However, we do not detect polarized emission over the shell associated with the UC H ii region. Given the size and flux obtained from the shell, we would have expected to detect polarization at similar levels as in the other regions in the clump (see the regions defined in Figure 9). We explore possible explanations to this in Section 4.2.

We obtained significant values for B_pos in the order of milliGauss from all three estimation methods for all the regions in MM3. The range of the fractional polarization is also significant. We obtained from 0.5% to 30.7%, where most of the emission is on-axis with the exception of region 1, which is located at the edge of the one-third of the primary beam (see the inner dotted circle in Figure 3) and slightly off-axis. The 0.5% correspond to region 3 and over core A, which is expected given the increase in the Stokes I emission due to the larger column density. This tendency of lower polarization fraction with increasing column density has been commonly observed (Fissel et al. 2016). In contrast, the highest amount of fractional polarization comes from compact and bright spots of polarized intensity. It is not clear why we see such a compact clusters of polarized emission (see also results for MM6 and MM7), but it might correspond to places where the dust its well illuminated by the radiation field produced by the protostars, or some other source, which might significantly increase the grain alignment.

In the case of the MM4, the polarized intensity is confined to the center of the clump and around core A. Polarized emission is also detected to the northwest over core E and to the southwest, but there we did not detect cores with sufficient significance. All the detections are on-axis, as indicated by the inner dotted circle in Figure 5. The inferred magnetic field morphology is remarkably uniform, suggesting almost parallel field lines over cores A and F. The extension of the detected field is about 4'', or 0.11 pc. Although it is difficult to conclude whether MM4 is a filament given its compact morphology, it is possible to define a major axis southeast to northwest (see Figure 5), which seems to be orthogonal to the main field direction. Over core E and to the southwest tail from core A (a tail that seems orthogonal to the defined main axis), the field lines are also parallel, but the number of independent points is too small to reliably estimate the field. Nonetheless, over core E, the EVPA uniformity is significant with a small dispersion estimate (δϕ ∼ 5°), which suggests a strong field. Toward cores C, G, and D, we did not detect significant polarization. Only a compact amount of polarized intensity, at a level of 10%, is detected at the edge of core C. We estimated B_pos toward the center of the MM4 clump, where we obtained strengths on the order of milliGauss (<10 mG, see Table 4).

The position of the associated UC H ii region in W43-MM4 is not obvious from our map. As a difference with MM3, we did not find IRAC counterparts, but nevertheless, this suggests that the MM4 clump is in a more evolved state of evolution than some of the other clumps (e.g., MM2). Given that the sizes of UC H ii regions are expected to be small and <0.1 pc (Tan et al. 2014), the UC H ii region is likely unresolved in our data. Although an H ii region will expand more easily along the field lines, it is difficult to ascertain if the UC H ii region has a significant impact in the magnetic field, as the field coherent scale is larger than the expected size of the UC H ii region. Nevertheless, here we found striking differences in the polarized emission between two clumps where UC H ii regions have been detected. In MM3, we found no polarized emission at all around the area where the UC H ii is detected, but in MM4, we found a significant amount of polarized emission. A possiblity is that in MM4 we see a still unperturbed envelope of gas and dust, while in MM3 a cavity has already been formed by the UC H ii region. Accretion from infalling motions is difficult to establish in MM4. Although the line profile from the ${\mathrm{HCO}}^{+}(3\to 2)$ suggests self-absorption, we do not have confirmation from H¹³${\mathrm{CO}}^{+}(3\to 2)$ as the line appears to be optically thick (see Figure 4 in Motte et al. 2003).

When we compare the MM4 clump to other objects, it seems similar to the W3-Main IRS 5 clump, which has been resolved into at least five cores, although the column densities are lower (∼10⁻²³ cm⁻², according to Rivera-Ingraham et al. 2013). Hull et al. (2014) imaged W3-Main in 1 mm polarization with CARMA, obtaining a sufficient magnetic field map. There map shows a field morphology over IRS 5 that resembles an hour-glass shape, which is different from the field morphology of MM4. However, to the west of IRS 5, the field morphology seems relatively smooth, with parallel field lines to the south. Hull et al. (2014) associated this emission with the free–free emission from the W3-B H ii region, which is also associated with an infrared source (IRS 3) that has been resolved into a type O6 star (IRS 3a). As free–free emission is very weakly polarized (<1%), the polarization pattern seen in both W3-Main and MM4 cannot be explained in this way. Thus, grain alignment seems the only possibility to explain the polarized emission, which might be coming from the envelope around the UC H ii region. The line of magnetic force tends to remain straight when density irregularities develop (Spitzer 1978), which might be interpreted as field lines becoming more ordered through compression (as seen in the low-mass star-forming core B335; Maury et al. 2018).

The MM6, MM7, and MM8 clumps show significantly less amount of polarized emission than the previous clumps. Although the MM6 and MM8 clumps are in the lower range of masses in our sample, the dust continuum emission from some of their cores is comparable to cores in the other clumps where we did detected polarized emission. However, the amount of polarized emission seen in their maps appears negligible (see Figures 6–8, and 18). Thus, we did not attempt to estimate B_pos for these sources. What seems to be common in all these clumps (including the whole sample), is the presence of strong and compact sources of polarized intensity. This is clearly seen in MM6 core B, where the polarized emission is confined, just, to that core. We will explore this further in the discussion (see Section 4.2). On the other hand, the MM7 clump has a sufficient number of points to estimate B_pos over core K (if we consider the 2.5σ values, see Figure 7). Here, we obtained magnetic field strengths around 1.7 mG considering the average from all three methods. The maximum fractional polarization is also high and about 19% which suggests an increase in grain alignment efficiency.

Molecular line emission from high-density tracers was also mapped toward the MM2 and MM3 clumps. Figure 10 shows the single-dish ASTE $\mathrm{HCN}(J=4\to 3)$ and ${\mathrm{HCO}}^{+}(J=4\to 3)$ spectra toward the center of MM2, along with their respective Gaussian fits. Both molecules show a dip in their line profiles at ∼91 km s⁻¹, which is suggestive of self-absorption. In the absence of molecular emission from an optically thin species tracing similar densities (e.g., H¹³CO⁺$(J=4\to 3)$), we use the published H¹³CO⁺$(J=3\to 2)$ from Motte et al. (2003) spectra to confirm the self-absorption. A line center velocity of V = 90.8 km s⁻¹ was derived from the H¹³CO⁺$(J=3\to 2)$ spectrum, which is consistent with the dip in the $\mathrm{HCN}(J=4\to 3)$ and ${\mathrm{HCO}}^{+}(J=4\to 3)$ spectra (see Figure 10 here and Table 2 in Motte et al. 2003). In fact, this velocity is used as the V_lsr of MM2. Now, our Gaussian fitting results show two components centered at 89.7 and 93.2 km s⁻¹ with amplitudes of 1.4 and 0.99 K for the HCN line; while for the HCO⁺ line, the two components are found at 88.4 and 93.4 km s⁻¹ with amplitudes of 0.7 and 0.4 K, respectively. When we compare the two components to the V_lsr, the blue asymmetry is clear because the blue component from both lines has a much higher intensity than the red component. This type of profile is suggestive of infalling motions (Leung & Brown 1977). Figure 11 shows $\mathrm{HCN}(J=4\to 3)$ spectra around the reference coordinates covering and area of 44'' × 44'' sampled every 10''. The blue asymmetry is present in all spectra throughout MM2. We explore the implications of this blue asymmetry below (see Section 3.4).

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Figure 10 also shows the $\mathrm{HCN}(J=4\to 3)$ and HCO⁺$(J=4\to 3)$ spectra toward the same coordinates we used as phase center for MM3. As with MM2, the emission is also suggestive of self-absorption, although the HCN line does not present a strong dip in between components and is also broader and noisier than the HCO⁺ spectrum. For MM3 we also used the H¹³CO⁺$(J=3\to 2)$ results from Motte et al. (2003), which yielded V_lsr = 93.5, consistent with the dip seen in the spectra. We also created a 44'' × 44'' grid around the MM3 reference coordinates to search for blue asymmetry in the spectra as was done for MM2. However, in this case, we found that only spectra δα = 0'' and δα = 10'' show a blue asymmetry, while the spectra with δα = −10'' show a red asymmetry in both $\mathrm{HCN}(J=4\to 3)$ and HCO⁺$(J=4\to 3)$ emission (see Figure 12). This may indicate rotation in the MM3 clump at large scales.

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Table 1.  The Line Parameters for ASTE Molecular Line Observations

Line	Transition	Frequency	Map Size	rms-noise
		(GHz)	(arcsec2)	(K)
HCO+	$(J=4\to 3)$	356.7342880	200'' × 160''	0.83
HCN	$(J=4\to 3)$	354.5054773	200'' × 160''	0.83

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We detected 81 cores in our sample of clumps in W43-Main. Most of these cores are located along the main axis of their respective filaments, but some exceptions, corresponding to isolated cores, are seen outside the main filaments. The estimated core masses range from a few to ~426 M_⊙, where only 2 marginally subsolar cores were detected.¹⁹ The spatial distribution of cores in all clumps is suggestive of clusters or associations. However, a significant number of cores, 54 objects, or 66%, have masses below 10 M_⊙, which is suggestive of low-mass star formation. A similar situation has also been described for W43-MM1 (see Paper I and Motte et al. 2018). Additional examples from other high-mass star-forming regions have been presented in the literature (Frau et al. 2014; Zhang et al. 2015; Cyganowski et al. 2017; Sanhueza et al. 2017; Lu et al. 2018). This indicates that low-mass stars are also being formed along with high-mass stars, and therefore, low- and high-mass star formation processes might be coupled.

Understanding the dynamical equilibrium of protostellar cores is required to assess whether these cores are collapsing and forming stars or if they are still unbound. We do this by considering the contributions from thermal motions, nonthermal motions (turbulence), and magnetic fields, as the most important physical parameters against gravity. Rotation at the core scales might be relevant, especially if flattened structures (disks?) have formed. However, it has been found that in low-mass star-forming clouds, rotation does not seem to provide significant support against gravity at the length scales traced by our data (Tobin et al. 2012). Therefore, and given the lack of detailed kinematical information from our observations, we do not consider rotation here. Additionally, previous studies suggest that magnetic fields play a role in the level of fragmentation within a core, although this is still debated (Palau et al. 2013, 2015).

We understand that a core is collapsing if the estimated mass is higher than some critical mass by the application of virial equilibrium. The considerations behind determining this critical mass has been the subject of a number of works in the past (Spitzer 1978; Bertoldi & McKee 1992; Shu 1992). It is often found that the virial mass was determined by only considering the gas kinematics, thermal and nonthermal (turbulence), and sometimes, by considering "reasonable" estimates of the magnetic field strength. However, in this work we do have quantitative information about the magnetic field and can therefore include more accurate estimates of its strength in the calculation. We start by computing what in the literature is referred to as the virial mass, or M_vir. As this mass is a representation of the energy contained in both thermal and nonthermal motions, we refer to it here as the kinetic mass, which we calculate as

$$\begin{eqnarray}&&{M}_{\mathrm{kin}}=3k\displaystyle \frac{R{\sigma }_{{\rm{v}}}^{2}}{G},\end{eqnarray} \tag{ 4 }$$

where R is the core radius, σ_v is the gas velocity dispersion along the line of sight, which is derived from the molecular line width as ${\sigma }_{{\rm{v}}}={\rm{\Delta }}{V}_{\mathrm{FWHM}}/2\sqrt{2\mathrm{ln}2}$, G is the gravitational constant, and k is a correction factor introduced by MacLaren et al. (1988) to account for the a power-law density profile ρ ∼ R^−a. Assuming a constant density in the condensation, or a = 0 and k = 5/3, the kinetic mass can be rewritten as

$$\begin{eqnarray}&&{M}_{\mathrm{kin}}=1.17\left(\displaystyle \frac{R}{\mathrm{mpc}}\right){\left(\displaystyle \frac{{\sigma }_{{\rm{v}}}}{\mathrm{km}{{\rm{s}}}^{-1}}\right)}^{2}\,{M}_{\odot }.\end{eqnarray} \tag{ 5 }$$

The gas kinetic energy is represented by the nonthermal motions seen from the molecular line widths, which are here midly larger than the thermal sound speed. Here, we use the same line widths we used to estimate B_pos, but at core scales of 1'', which are about the average of our core sizes (see Section 3.2 and Appendix A). For completion, we also calculated the Jeans mass, M_J, for each core. The computed values for M_J and M_kin are shown in Table 3. The kinetic mass already includes the contributions from thermal and nonthermal energy to the balance equation. To assess the support provided by motions against gravity, we use the kinetic mass to define a kinetic virial parameter, α_kin = M_kin/M_gas (Bertoldi & McKee 1992).

To quantify the contribution from the magnetic field in the balance against gravity, we define the magnetic mass as M_Φ = Φ/2πG^1/2 (Nakano & Nakamura 1978; Crutcher et al. 2004), where Φ is the magnetic flux and G is the gravitational constant. We used this definition to be consistent with the mass-to-magnetic flux ratio definition (see paragraph below). Having defined M_kin and M_Φ, we can now calculate a total virial parameter as

$$\begin{eqnarray}&&{\alpha }_{\mathrm{total}}=\displaystyle \frac{{M}_{\mathrm{kin}}+{M}_{{\rm{\Phi }}}}{{M}_{\mathrm{gas}}}.\end{eqnarray} \tag{ 6 }$$

The α_total includes the contribution of the magnetic field in the ratio by adding the magnetic field mass. In this way, we account for all the relevant physical processes that oppose gravitational collapse.

To explore the magnetic-only contribution, we compute the mass-to-magnetic flux ratio, as done before in W43-MM1 (Paper I). We do this to compare the relevance of the magnetic field with respect to gravity. The mass-to-magnetic flux ratio is defined following Crutcher et al. (2004)

$$\begin{eqnarray}&&{\lambda }_{B}=\displaystyle \frac{\left\langle {\left(M/{\rm{\Phi }}\right)}_{\mathrm{observed}}\right\rangle }{{\left(M/{\rm{\Phi }}\right)}_{\mathrm{crit}}}=7.6\times {10}^{-21}\displaystyle \frac{N({{\rm{H}}}_{2})}{3{B}_{\mathrm{pos}}},\end{eqnarray} \tag{ 7 }$$

where N(H₂) is the molecular hydrogen column density in cm⁻² calculated for each source independently, B_pos is the magnetic field strength in μG assumed to be a global physical parameter for a given region (see Section 3.2 for a description of the chosen regions), where the factor of 3 in the denominator corresponds to an statistical geometrical correction for (M/Φ)_observed. The geometrical shape of a core depends on the strength of the magnetic field, which will tend to flatten the core along its minor axis. In the limit case of a strong magnetic field, the core might converge to a pseudo-disk (Mouschovias 1987). Table 4 presents the derived values for λ_B using all three B_pos estimations. Although the nomenclature might appear confusing as λ_B is essentially M_gas/M_Φ, which is the inverse of a magnetic α parameter, we have decided to keep it in order to be consistent with the literature.

Before stating the result of our computations, it is necessary to factor in the uncertainties in the calculation. We derive velocity dispersions by assuming a Kolmogorov-like power spectrum, which we believe is representative of the nonthermal motions induced by the turbulence cascade from the large scales, although its nature is uncertain. Furthermore, this assumption makes the calculation of the kinematic mass (see Section 4.1.3) independent of the temperature. However, turbulence can be injected at smaller scales by outflows, shocks, and ionization fronts, and winds coming from the newly born stars, none which we consider in this analysis. Nevertheless, magnetic fields have a dampening effect on turbulence at small scales, which might decrease the contribution to the turbulent energy close to the core scales. This is also suggested by magnetohydroynamcis (MHD) simulations, where the velocity dispersion in gravitationally bounded cores was found to be sonic or mildly supersonic (Hennebelle 2018). Therefore, the injection of additional energy into the turbulence at these length scales should happen continuously to alter the energy cascade and to modify the velocity dispersion significantly. Also of importance are the uncertainties in the mass estimation. The mass estimates depend on the dust temperature, a proxy for the gas temperature, which is not well constrained for these clumps. High-mass protostellar cores are seen to develop hot cores quite early in their evolution, although the exact process is unclear. In W43-Main, the binary in MM1-A has already developed a hot core (Sridharan et al. 2014). An increase in the inner core temperature will decrease the mass estimate and therefore increase the α_total ratio, which might alter the conclusions. However, this is difficult to address without better spectroscopic millimeter or submillimeter data from these cores. Additionally, all three B_pos estimations require the volume number density as an input, which we computed by assuming spherical geometry. This assumption might bias the B_pos computation toward higher values, especially if the geometry in the line of sight has a flatter shape.

We first compare turbulence and magnetic fields independently against gravity. For thermal energy, all cores in our sample show Jeans masses that are orders of magnitude lower than the core estimated mass, as shown in Table 3. It is clear at this point that thermal pressure on its own does not contribute significantly as a support mechanism against gravitational collapse at this stage in the evolution of our cores.

When considering support from kinetic energy alone, we found that 43 out of 81 cores have α_kin < 1 (as shown in Figure 14). This corresponds to most of the cores from MM2, MM3, and MM4, and with some additional cores from the other clumps. Values of α_kin < 1 suggests that turbulence alone cannot support these cores against gravity. An extreme case is MM2-A, which is 2 orders of magnitude away from virial equilibrium. In contrast, the cores with α_kin > 1 belong mostly to MM6, MM7, and MM8 with just one core from MM2, suggesting that these cores are gravitationally unbound. This set of cores belong to the low-end range of the mass distribution and also to the clumps with the highest degree of fragmentation (clumps MM7 and MM8).

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Considering that we have detected large-scale infalling motions, we would have expected to see most of these cores with α_kin < 1. However, in ∼47% of our cores the energy from turbulence alone seems sufficient to support the cores against gravity. Although transient cores, due to the turbulence energy cascade, cannot be immediately ruled out, the high column densities obtained (mostly in excess of 10²⁴ cm⁻²) suggest that these cores are likely pressure confined, and thus the most likely scenario is that these cores are still accreting gas, but have not yet reached a critical mass to ensure gravitational collapse.

To consider the magnetic-only contribution to the virial analysis, we calculated λ_B only for the cores with associated B_pos estimates (see Figure 14 and Table 4). We computed λ_B using the average of all three B_pos estimates. Our results show that most of the cores from MM2, MM3, MM4, and MM7 with B_pos estimates are supercritical, particularly MM2-A, B, and MM3-A, B. Two cores from MM3 (MM3-E and MM3-F) are sightly subcritical, and two from MM7 appear to be subcritical (MM7-H and MM7-K). However, for MM2-A, MM2-D, MM3-A, MM3-B, and MM3-D, the values for λ_B are upper limits given that the magnetic field estimates are lower limits (see Section 3.2). For the supercritical cores, the interpretation is that the magnetic field by itself does not provide sufficient support against gravity, and therefore they should be out of virial equilibrium unless additional sources of energy (turbulence) can further contribute to the core support. For the subcritical cores, the results suggest that the magnetic field alone might be supporting these cores against gravity. Although the two cores in MM3 have large differences in the mass estimates, the magnetic field morphology that surrounds them shows almost no dispersion in the EVPA, resulting in strong B_pos estimates (of $\langle {B}_{{\rm{p}}{\rm{o}}{\rm{s}}}^{{\rm{F}}} \rangle =4.2$ mG and $\langle {B}_{{\rm{p}}{\rm{o}}{\rm{s}}}^{{\rm{E}}} \rangle \,=5.5$ mG). Frau et al. (2014) investigated NGC 7538, IRS 1-3, with the SMA, where they found a number of low-mass cores along the spiral arms of the filament that also appear to be subcritical. These cores are also at the low-end of their mass distribution.

Finally, we consider both turbulence and magnetic energy in the dynamical equilibrium of the cores in W43-Main by computing the total virial parameter α_total as a function of the estimated core mass (see the left panel in Figure 15). From a total of 17 cores, we found 5 objects, or 29%, with α_total > 1. The remaining 12 cores, or 71% of the total, have α_total < 1 and should be out of virial equilibrium. Here, out of virial equilibrium implies that as we are accounting for all the relevant physical parameters at these length scales, these cores should be self-gravitating and forming stars. The final multiplicity inside each core is unclear from these data, and only observations with higher resolution might provide answers to this question. Although the number of bound cores dominates the distribution, the evidence from B_pos estimates coming from real data as well as reasonable velocity dispersions strongly suggests that the unbound cores are real. As previously stated, we also note that all of these cores are likely to be pressure confined given the high column densities observed toward these clumps. Thus, it is highly unlikely that the unbound cores are transient structures due to the turbulent cascade, and the more likely explanation is that these cores are still accreting and have not yet accumulated sufficient mass to become self-gravitating.

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To increase our statistics, we estimated α_total for the totality of our cores by assuming "reasonable" B_pos values. We did this using proximity to regions with B_pos estimates, and in the case of MM6 and MM8, we used the average obtained from MM7 given the similarities in their fragmentation. The result of adding all of our cores is shown in Figure 15 (right panel). The figure shows two distinctive populations of bound and unbound cores. The bound cores belong to the population of the most massive clumps with direct evidence for infalling motions from large scales, although there a number of cores in a "critical" state. The unbound cores correspond to 70% of our sample, which although quite uncertain, strongly suggests that there is a population of cores that are not gravitationally bound. For this population of cores, the support against gravity comes from a combination of magnetic and turbulent energy. Although it is quite possible that the "reasonable" B_pos estimate used for MM7 and MM8 is large (we discuss this possibility in Section 4.2), any additional source of support will increase the unbound state of the cores that we have already seen from turbulence alone.

As previously discussed, a main uncertainty in our calculations might come from the temperature assumptions. Although the temperature we used to estimate the column density at each clump comes from SED derivations, these represent the large-scale structure within the clump (given the resolution of the single-dish telescopes used to derive these SEDs). Thus, the internal core structure, particularly in the most massive sources, might have temperatures that are higher than the nominal ones used here. To account for variation in the core temperatures, we calculated error bars for the mass, α_kin, λ_B, and α_total, using a ±5 K temperature deviation relative to the nominal SED temperature of the clump. The temperature ±5 K is a reasonable assumption for the bulk of the cores in our sample, although the more massive cores might have higher temperatures (as previously discussed). The spread shown by the uncertainty in the temperature slightly move the values, but the overall trend remains, as shown in Figures 14 and 15.

From ALMA observations of IRDC G28.34, Zhang et al. (2015) found 10 gravitationally bound cores and one clump, G28-P1, was found to be unbound. However, they did not have observational information about the magnetic field and thus, they assumed a value for B = 270 μG in their analysis. Zhang et al. (2015) stated correctly that magnetic fields can substantially increase the value of the virial mass, which is exactly what we see in W43-Main. The values that we have estimated for the magnetic field are at maximum close to 2 orders of magnitude higher than the values used for G28.34, but biased toward the lower end because we used the region number density, which is lower than the core density (see Appendix A). The column densities derived toward the G28.34 cores, though not listed, appear to approach our results because the number density values are between 10⁶ and 10⁷ cm⁻³. Given that density regime, it is likely that the field strength will be on the order of milliGauss for G28.34, as expected from observations (Crutcher 2012). This will certainly increase the virial mass for those cores, which might resemble what we see in W43-Main.

Having uncovered these two populations of cores in W43-Main, it should be noted that these populations will likely produce low- and high-mass stars. Thus, as some of these cores are gravitationally bound while the others are not, the timescale for star formation in these two populations has to be different. For the bound cores, collapse cannot proceed faster than the freefall time, which sets a lower limit. However, the unbound cores might be accreting at timescales set by the infall rate, which is substantially lower. This essentially suggests that the evolutionary timescale for star formation in high-mass filaments is not uniform.

Bertoldi & McKee (1992) derived a power law for the virial parameter in the form of $\alpha =b{\left(\tfrac{{M}_{o}}{{M}_{\mathrm{obs}}}\right)}^{a}$ for magnetized star-forming cores. To compare, we fitted our data with such a power law, obtaining b = 1.06 and a = −0.92 for the initial 17 cores and b = 1.04 and a = −0.88 for the whole sample (see Figure 15). Bertoldi & McKee (1992) derive b = 2.12 and a = 2/3 for magnetized critical clumps, and b = 2.9 and a = 2/3 for pressure-confined clumps. However, in their analysis they considered M_O = M_J, which is different from what we use in α_total. In our case, M_O = M_Φ + M_kin, which might explain the difference. Frau et al. (2014) also fit a power law to their data, finding b = 2.26 and a = −0.68, in agreement with Bertoldi & McKee (1992), but they did not comment about the usage of the Jeans mass.

The virial parameter α_total, provides an assessment of the core equilibrium, but not information about the relevance of each of the parameters that counteract gravity. To explore the relative importance of kinetic energy and magnetic energy, we computed the ratio between the kinetic mass and the magnetic field mass (see Figure 16). The mean value for the ratio of the turbulent to magnetic field mass is $\left\langle {M}_{\mathrm{kin}}/{M}_{{\rm{\Phi }}}\right\rangle =1.43$, which suggests that turbulent energy dominates magnetic energy. Now, the Alfvén speed, ${V}_{{\rm{a}}}=B/\sqrt{4\pi \rho }$, has a range between 0.19 < V_a < 2.9 km s⁻¹, which is higher on average than the velocity dispersion, σ_B, as $\left\langle {V}_{{\rm{a}}}\right\rangle =1.1\gt \left\langle {\sigma }_{B}\right\rangle =0.9$ km s⁻¹, if our assumptions are correct. This also suggests that magnetic tension in these filaments is strong and might dampen the turbulent cascade at these scales, unless turbulence is replenished. One way in which turbulence can be replenished is through outflow feedback. Figure 13 shows extracted ¹³$\mathrm{CO}(J=2\to 1)$ and C¹⁸O $(J=2\to 1)$ spectra from the W43-Main large-scale CO mapping by Carlhoff et al. (2013). Each spectrum was extracted from the clump phase center position and using pencil beam regions at the resolution of the IRAM telescope (∼10''). The spectra shown in Figure 13 suggest that the ¹³CO emission is optically thick at 1 mm, where there is also substantial structure in velocity for the points considered. Gaussian fits were made to the C¹⁸O spectra (shown in red in Figure 13), which also suggests that in some clumps, C¹⁸O might be optically thick. The emission at the line wings from ¹³CO strongly suggests the presence of outflows in some of these clumps, and it is particularly clear in MM8 and MM6. Although ¹³CO and C¹⁸O trace more diffuse gas at 1 mm (the ¹²$\mathrm{CO},J=2\to 1,$ has a critical density ∼10⁴ cm⁻³) than our dust emission, they are still a sufficient proxy for outflows.

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The MM2-A core accounts for 73% of the total estimated mass for all cores in MM2. MM3-A corresponds to 30%, and MM4-A contributes 44% of the total mass for all the cores in both clumps. Although these are the most massive cores in our sample, MM2-A is by far the most massive core. In fact, MM2-A might be the most massive protostellar core in W43-Main now that MM1-A has been resolved into a binary (Motte et al. 2018). Because of this, and given that at the 0.01 pc scales MM2-A appears to be an unresolved and round protostellar core despite the elongated beam shape, it becomes interesting to understand how massive the resulting star might be. To estimate the final mass for a star in MM2-A, we follow Sanhueza et al. (2017), who made use of the Larson (2003) relation between the maximum stellar mass and the mass of the whole cluster, or

$$\begin{eqnarray}&&\left(\displaystyle \frac{{M}_{\max }}{{M}_{\odot }}\right)=1.2{\left(\displaystyle \frac{{M}_{\mathrm{cluster}}}{{M}_{\odot }}\right)}^{0.45},\end{eqnarray} \tag{ 8 }$$

here we derive the M_cluster from the MM2 total mass by making use of the current W43-Main star formation rate. For the MM2 mass, the current best estimate is $\left\langle {M}_{\mathrm{MM}2}\right\rangle =4.4\times {10}^{3}$ M_⊙ (Bally et al. 2010). Thus and assuming a star formation efficiency of 25% (Motte et al. 2003), we obtain M_cluster =1.1 × 10³ M_⊙, which gives M_max = 28 ± 14 M_⊙. The uncertainty in the mass estimates comes mostly from the temperature determination, which can introduce a 50% error in the estimation. Given the mini-starburst nature of W43-Main, the star formation rate may be higher than 25%, as estimated in other high-mass star-forming regions (Lada & Lada 2003; Alves et al. 2007). Thus, for a conservative increase to 30% in the star formation rate, we obtain M_max = 30 ± 15 M_⊙. A 30 M_⊙ star will likely correspond to an O7 star, which is consistent with the spectral type of most of the stars in the W43 H ii region (Blum et al. 1999; Heap et al. 2006). However, and as previously stated, the main caveat in the MM2-A mass estimation is the temperature assumption. As with MM1-A, it is possible that MM2-A has already developed a hot core inside, which will certainly increase the temperature and also decrease the mass estimate. Following Paper I, we also consider here T = 70 K to estimate the mass for MM2-A, which yields M_A = 118 M_⊙. This mass estimate corresponds to 27% of the original estimate. Thus if we assume the same decrease in the maximum mass as previously obtained, we derive a M_max ∼ 8 M_⊙. Although an 8 M_⊙ star is still a massive star, it is unlikely that MM2-A is a star like this. The current evidence suggests that accretion is still ongoing, and despite the temperature uncertainty, the final mass of the star might be close to the original estimate, or 30 M_⊙. It may very well be that the accretion timescale is longer than previously considered given the presence of strong magnetic fields.

Prestellar cores are the smoking gun for the core accretion model in high-mass star formation (McKee & Tan 2003). These cores should be massive, cold condensations (T < 20 K), where the emission is purely thermal. Thus, a high-mass prestellar core has not developed hot cores or outflows, and corresponds to the initial stage for high-mass star formation in the core accretion model. The MM2-A does not have a counterpart at 24 μm emission and radio continuum, which indicates a protostellar core in its earliest stages of evolution. Its massive gravitational potential well seems to be dragging the field throughout the clump and into core. We elaborate this proposal further by sketching the magnetic field connection in Figure 17. The red arrows indicate clump-scale field lines as they are dragged into MM2-A. It is unlikely that a massive core that can drag the field is in a prestellar phase. Although at a coarse resolution and lower sensitivity, the SMA has detected perturbed magnetic fields in both high and intermediate star-forming regions. Juárez et al. (2017) obtained a bimodal magnetic field distribution toward NGC 6334 V, which seems to converge toward a massive hot core. A similar situation is also seen in the DR21(OH) core, where the field also seemed dragged by gravity toward the core, although in this case the field appears to have a toroidal morphology as traced by SMA. Additionally, outflow emission from MM2-A can be explored from the ¹³CO and C¹⁸O spectra shown in Figure 13. The ¹³CO spectrum from MM2-A at 0.27 pc scales (10'' angular scales) appears to show excess emission in both line wings, which resembles an outflow. The C¹⁸O spectrum shows no excess emission in the line wings, but the line shape is not Gaussian and suggests some self-absorption, which makes the emission likely optically thick. Therefore, it is likely that MM2-A is not prestellar, but it might still be quite early in its evolution, and further studies at higher resolution will therefore hopefully uncover its nature.

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