MAGNETIC FIELDS AND MASSIVE STAR FORMATION

Twenty-one massive-star-forming regions were observed in the polarization mode with the SMA. They have masses of 10²–10³ M_☉ within a scale of <1pc, capable of forming a cluster of stars. Strong dust polarization is detected in 14 of them. During the initial survey, two objects have no detection in dust polarization at a sensitivity of 5 mJy. The remaining targets showed marginal detection at a level of 4σ, and are followed-up with additional observations to improve the signal-to-noise ratios in the map. This paper presents the sample of 14 molecular clumps with significant polarization. They have luminosities of >10³ L_☉, and are known to harbor massive protostars. Figure 1 presents the dust continuum emission overlaid with the orientation of dust polarization (E field; left panels), and the orientation of the plane-of-sky component of magnetic fields (right panels). The length of the line segments on the left panels is proportional to the percentage of polarization. The color scales show the polarized and Stokes I emission.

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The continuum emission (Stokes I) is detected strongly with signal-to-noise ratios greater than 50 for all the targets. The noise level in the Stokes I continuum is limited by the dynamic range due to a relatively sparse UV coverage. As a result, the noise level in these maps is set by the systematics in the dirty beam pattern and is higher than the noise in the Stokes Q and U maps. We classify the sample into elongated/filamentary and irregular at the parsec scale based on the morphology of the continuum emission obtained from the SMA, and the morphology of the cloud at a scale >1 pc from single dish ground-based telescope and the Herschel Space Telescope. For example, sources NGC 6334I/In/IV/V are part of the filamentary cloud seen in continuum with ground-based (Sandell 2000; Muñoz et al. 2007) and space-based Herschel observations (Russeil et al. 2013). Likewise, sources G34.4, W51E2, W51N and DR 21 (OH) are part of filamentary clouds (Rathborne et al. 2006; Tang et al. 2010; Motte et al. 2007). In addition, the continuum emission of G240, IRAS 18360 and G35.2N (Qiu et al. 2009, 2011, 2013) also appear to be elongated, and thus are included in the category of filamentary objects. Despite its filamentary appearance, we exclude NGC 2264 C1 from the list because of its linear size of 0.05 pc, which corresponds to the size of a dense core.

The polarized emission I_pol is computed from the intensity of Stokes Q and U according to $\sqrt{\vphantom{A^A}\smash{{{Q^2 + U^2 - \sigma _Q^2}}}}$. Here Q and U and σ_Q are the flux intensity and the rms noise in Q/U images, respectively. The polarization percentage is then computed from the ratio between the polarized flux and the Stokes I flux. The polarization angle θ, measured counterclockwise from the north to the east, is computed from tan2θ = U/Q. The maps of the polarized emission, polarization percentage, and polarization angle are produced using the MIRIAD task impol. We used the cutoff of 5σ_I in the Stokes I maps, and 2.5σ_Q in the Stokes Q and U maps when deriving the polarization flux, polarization percentage, and polarization angle. Here σ_I is the rms noise in the Stokes I image. The uncertainty in polarization angles follows 2865(σ_p/p), where σ_p and p are the noise and signal in polarization (Serkowski 1974; Naghizadeh-Khouei & Clarke 1993). The majority of polarization detections have signal-to-noise ratios of >5, and thus, their associated errors in polarization angles are <58.

As shown in Figure 1, the distribution of the polarized emission ranges from spatially compact in G192 to more extended in sources such as DR 21 (OH). Except for G192 and NGC 2264 C1, spatially extended polarized emission is detected in G240, NGC 6334 I/In/IV and V, G35.2N, IRAS 18360, G34.41, W51E2, W51N, and DR 21(OH). The polarized fluxes range from 10 to 50 mJy at a beam size of 15. The polarization percentage varies from 1% to as high as 10% in sources such as NGC 6334In. Among the sources with spatially resolved polarized emission, DR 21 (OH) shows polarization with large angular dispersions. The polarization segments are relatively ordered in sources G240, NGC 6334 I/In, G34.43, G35.2N and W51E2. Sources NGC 6334 IV/V, IRAS 18360, and W51E2 have moderate dispersions in the polarization angle.

Molecular outflows often mark the birth of protostars. During the phase of protostellar accretion, infalling gas with excess angular momenta is ejected in a wind. The detailed process involved in launching the wind is unclear for massive outflows (Qiu et al. 2007). However, it is likely related to magnetic fields, similar to outflows in low-mass protostars (Shang et al. 2007). The wind, which travels at several 100 km s⁻¹ (e.g., HH80/81 Marti et al. 1998), interacts with the ambient gas and produces molecular outflows seen in CO (Zhang et al. 2001) and other tracers (Qiu et al. 2007). Therefore, the orientation of outflows defines the axis of the accretion disk that is not spatially resolved in the SMA observations.

The right panels of Figure 1 present molecular outflows identified in the CO 3–2 transition obtained simultaneously in the SMA polarization observations. The blue and red shifted CO emission are plotted in blue and red contours. For W51E2, we use the CO 3–2 outflow data from Shi (2010). We also mark the orientation of the outflows with arrows. In many cases, blue- and redshifted outflows can be paired in a bipolar fashion. However, there are outflows that appear to be unipolar. We identified a total of 21 outflows in our sample. At the first glance, the major axis of some outflows, e.g., G240, is parallel to the magnetic fields. Other outflows, such as those in G192 and G35.2N, have major axes perpendicular to the orientation of the magnetic field. There are also outflows that are oriented between 0° and 90° with respect to the magnetic field. Some outflow pairs emanate from the same cores, but with the outflow axes more than 60° apart (e.g., DR 21(OH)).

One of the questions to be addressed in this survey is how magnetic fields at scales of ≲ 0.1 pc compare with that of the parsec-scale magnetic fields revealed by the single dish telescopes. In our sample, sources with published single dish polarization measurements are NGC 6334 I/In/VI/V, G34.43, G35.2N, DR 21(OH), W51E2, W51N, and DR 21(OH) (Matthews et al. 2009; Cortes et al. 2008; Dotson et al. 2010). These data, measured at a spatial resolution from 10'' to 20'', correspond to the average polarization direction at a linear scale of 0.1–0.6 pc for source distances from 1.5 kpc to 6 kpc. We compare the polarization position angle measured with the SMA with the position angle measured at the larger scale for the same position. The majority of the SMA data reveal polarized emission within an extent of <15''. The most extended polarization emission in the SMA observations is 20'' seen in DR 21(OH). Thus, the large-scale polarization do not vary significantly across the SMA maps.

To account for the difference in linear resolution in the SMA sample due to varying source distances, we convolved the Stokes I/Q/U images to the lowest linear resolution (0.03 pc) corresponding to the source at the farthest distance. We then compute the polarization angles using the MIRIAD task impol. This normalization is needed to remove the bias toward the nearby objects that have a better linear resolution in the images, and thus contribute more data points to the statistical analysis outlined below. For the nearest targets, the convolution degrades the angular resolution by a factor of 3.5. We note that the polarization angles in the convolved images resemble the maps at native SMA resolutions.

We use the convolved SMA images to compute |θ_clump(pol) − θ_SMA(pol)| for every independent measurement in the SMA data. Here θ_clump(pol) is the polarization position angle measured with single dish telescopes, and θ_SMA(pol) is the polarization position angle measured with the SMA at the scale of dense cores. For most of the targets, the spatial extent of the polarized emission is smaller than the single dish beam. For polarization sources that are more extended than the single dish beam, we interpolate the single dish data to compute the angular difference. To limit errors in polarization angles, we apply a cutoff of σ > 3.5σ_Q to the SMA polarization data, although the results remain the same if a lower cutoff of 3σ or 2.5σ is applied. Since the direction of magnetic field vectors is not determined in polarization measurements, we limit the angular difference |θ_clump(pol) − θ_SMA(pol)| from 0° to 90°. A 0° difference corresponds to the case where magnetic fields in the SMA image are aligned with the large-scale magnetic fields, whereas a 90° difference implies that the two are perpendicular.

Figure 2 presents the distribution of the angular difference between the polarization measurements with the single dish and those measured with the SMA. The figure shows that there is a large number of SMA polarization segments aligned within 40° with the large-scale polarization. Among the 173 independent polarization measurements at a scale of 0.03 pc, over 60% of them are at position angles within 40° of the large-scale polarization. There is a lack of polarization segments when the angular difference lies between 40° and 80°. There is another peak at an angular difference around 90°. Overall, the angular difference of polarization segments exhibits a bimodal distribution: one group of polarization segments maintains the polarization orientation of their parental clump; the other group of polarization segments is perpendicular to the polarization orientation of their parental clump. This finding implies that magnetic fields at the core scale of 0.03 pc are organized. Otherwise, randomly oriented fields would render an equal probability of angular distribution in Figure 2. Furthermore, Figure 2 indicates that magnetic fields at the 0.03 pc scale are correlated with the mean field orientation in their parental clump. They are either aligned within 40° of the parsec-scale field or perpendicular to the parsec-scale field.

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We also examine how polarization at the 0.03 pc scale is related to the major axis of the parsec-scale clump θ_clump(maj). Sources G240, NGC 6334I/In/IV, G34.4, IRAS 18360 and G35.2N, W51E2, W51N, and DR 21 (OH) are either part of a large-scale filament, or exhibit a parsec-scale elongated morphology. NGC 2264 C1 is excluded from the list despite its elongated structure since its linear extent is 0.05 pc, much smaller than a clump. However, including it in the analysis would not change the outcome since it would contribute only one data point to the statistics. For all these elongated objects, except DR 21 (OH), we measure θ_clump(maj), the position angle of the major axis of the clump, by fitting a two dimensional elliptical Gaussian profile to the dust continuum emission from the SMA. For DR 21 (OH) whose structure in the SMA map does not have a well-defined elongation (Girart et al. 2013 suggests that the clump is nearly face-on), we use the larger scale filament (Motte et al. 2007) to define its major axis. We compare the position angle of the major axis of the clump θ_clump(maj) with θ_SMA(pol). Figure 3 presents the distribution of angular difference, |θ_clump(maj) − θ_SMA(pol)|, between the filament's major axis and the polarization from the SMA. Similar to the previous case, we limit the angular difference from 0° to 90°. As shown in Figure 3, there is a large number of segments with their polarization parallel to the major axis of filaments. Of the 197 polarization segments, over 60% of them are aligned with the major axis of the clump. There appears to be another peak of polarization segments with angular differences near 90°. In between the two peaks, there is a lack of polarization segments between the angular difference from 40° to 80°. Overall, the angular difference of the segments appears in a bimodal distribution: one group of polarization segments is aligned with the major axis of their parental clump; the other group of polarization segments is perpendicular to the major axis of their parental clump.

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We further compare the outflow axis seen in the CO J = 3–2, θ_outflow, obtained from the SMA with the position angle of magnetic fields θ_SMA(B) at the origin of the outflow. Here θ_SMA(B) is the field orientation measured within one SMA synthesized beam. When the blue- and redshifted lobes form an apparent bipolar outflow, only one position angle is reported. In cases of unipolar outflows, we measure the position angle from the single outflow lobe. A total of 21 outflows is revealed in the sample. Figure 4 presents the angular difference between the outflow axis and the position angle of the magnetic fields |θ_outflow − θ_SMA(B)|. Due to a lack of information on the direction of the magnetic field, we limit the angular difference from 0° to 90°. A 0° difference corresponds to the outflow axis being in parallel to the major axis of the outflow. Because of the small number of outflows in the statistics, we refrain from interpreting the detailed structure in the distribution. Overall, there appears to be no strong correlation between the outflow axis and the magnetic field orientation in the core from which outflows originate.

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Before we interpret the results in Figures 2–4, we investigate the projection effect of two vectors in a three-dimensional space intersecting at an angle α. We pose the following question: when the two vectors are randomly oriented in space, what is its projected angle β onto a plane? This question is relevant to the study here since the observations only provide the polarization component projected onto the plane of the sky without information along the line of sight (see also Tassis et al. 2009; Hull et al. 2013). For the majority of the vectors oriented within the 2π solid angle, one expects that the projected angle β will be smaller than α. However, certain orientations of vectors can render β greater than α. For example, if two vectors intersect at the origin of an XYZ Cartesian coordinate system, with one line being in the XZ plane, and the other line lying in the YZ plane, the angle α can vary from 0° to 90°, while the projected angle β on to the XY plane is always 90°.

In order to simulate the projection effect, we consider a pair of randomly oriented vectors uniformly distributed in a three-dimensional space. We select all pairs with intrinsic angles α from 0° to 40° and from 80° to 90°. The probability distributions of the projected angle β are plotted in Figures 2 and 3. As expected, small projected angles imply a high probability of small intrinsic angles α. Likewise, large projected angles close to 90° imply a high probability of large intrinsic angles. A randomly oriented vector pair in a 4π solid angle gives an equal probability distribution of projected angles β from 0° to 90°.

The simulated distributions of angles described above are compared with the observed angular difference between the clump-scale and the core-scale magnetic field orientations shown in Figure 2. The simulated results are shown in Figure 2 as dashed and dotted lines for angles from 0° to 40° and from 80° to 90°, respectively. We run the Kolmogorov–Smirnov (K-S) test to determine the probability that the two distributions are drawn from the same parent population. When comparing the observed distribution with the simulated distribution of angles of 0°–40°, the probability that the two groups are drawn from the same population is 9.3 × 10⁻⁴. The probability that the observed distribution and the simulated distribution of angles from 80° to 90° are drawn from the same parent population is 4.3 × 10⁻⁹. Similarly, the probability that the observed distribution and a flat distribution of angles from 0° to 90° are drawn from the same parent population is 2.4 × 10⁻³. On the other hand, if we combine the two simulated groups of distributions, e.g., from 0° to 40° and from 80° to 90°, with a ratio of 5:3 (shown by the dashed-dotted line in Figure 2), then we find that the probability of the observed distribution and the combined distribution are drawn from the same parent population is 0.93.

In addition to the K-S test, we also use circular statistics to test the hypothesis that the observed distribution and the simulated distribution are drawn from the same distribution. Since data presented in Figure 2 deal with directions, circular statistics are more appropriate for the analysis. We performed a Watson test for two samples of directional data (Jammalamadaka & Sengupta 2001). When comparing the observed distribution and simulated distribution of angles from 0° to 40°, from 80° to 90° and a random distribution, we found a probability of 0.001–0.01, <0.001, and <0.001, respectively. Both the K-S and Watson test reject the hypothesis that the observed distribution of angles are randomly oriented. It appears that the observed distributions are likely comprised of two populations of angles: one group with intrinsic angles (|θ_clump(pol) − θ_SMA(pol)|) from 0° to 40°, and the other group with intrinsic angles (|θ_clump(pol) − θ_SMA(pol)|) distributed from 80° to 90°.

We also run the K-S test on the distribution of the angle difference |θ_clump(maj) − θ_SMA(pol)| as shown in Figure 3. The simulated results are shown by the dashed and dotted lines for angles from 0° to 40° and from 80° to 90°, respectively. We found that probabilities that the observed distribution and simulated distribution of angles from 0° to 40°, from 80° to 90°, and a flat distribution are drawn from the same parent population are 3.4 × 10⁻³, 3.8 × 10⁻¹⁰, and 6.4 × 10⁻³, respectively. If one combines the two simulated distributions of angles from 0° to 40° and from 80° to 90° at a ratio of 5:3, the probability that the observed distribution and the combined distribution are drawn from the same population is 0.96. The results of the K-S tests are summarized in Table 3.

The comparison between the outflow major axis and the orientation of magnetic fields in the core is limited by the small number of statistics. Nevertheless, there appears to be a larger number of outflows (a total of 9 out of 21) with axes within 70°–90° of the magnetic field orientation in the core. In addition, there is another peak in the distribution close to 0°. However, that peak consists of only five outflows with their major axes within 10° of the magnetic field. Overall, the distribution in Figure 4 is consistent with a scenario that outflow orientation does not correlate with the orientation of magnetic fields in the core.

Massive stars form predominantly in the cluster environment in association with a number of lower mass objects. The basic unit in which massive stars form is a parsec-scale molecular clump with typical masses of 10²–10³ M_☉. The collapse and fragmentation of massive clumps give rise to cores with sizes of ≲0.1 pc at higher densities. One of the outstanding questions involved in this process is the role of magnetic fields during the dynamical evolution of molecular clumps and dense cores. The SMA observations reveal polarization at a linear scale of 0.03 pc, which corresponds to scales of dense molecular cores hosting individual or multiple protostars. Therefore, the SMA data unveil the plane-of-sky magnetic field information at dense core scales. Given these considerations, the results in Figure 2 demonstrate that (1) magnetic fields on dense core scales in a cluster-forming environment are not randomly distributed, but are organized. Otherwise, one would expect a flat distribution instead of a bimodal distribution. (2) Magnetic fields on core scales tend to be parallel or perpendicular to the field orientations in their parental clumps.

Numerical simulations of magnetized molecular clouds with turbulence offer guidance on deciphering the dynamic role of magnetic fields based on the field orientation. When the magnetic field is strong, e.g., the ratio of gas pressure to magnetic pressure β = (P_th/P_B) ≪ 1, the field is less disturbed and appears to be organized. In this regime, dense gas filaments form with their long axes perpendicular to the magnetic field, while the lower density gas in the cloud forms striations connected to the dense filament, which are aligned parallel to the magnetic fields (Ostriker et al. 2001; Nakamura & Li 2008; Van Loo et al. 2014). On the contrary, the field appears to be more randomly oriented in the weak field regime (β ≫ 1). In light of theoretical and numerical works, the fact that the majority of the dense cores have their magnetic fields more or less aligned with or perpendicular to those in the clump scale indicates that the magnetic field plays a dynamically important role in core formation. The field is strong enough on the clump scale to guide the concentration of clump material along the field lines into dense cores. When cores become massive enough, gravitational contraction may become important. The contraction is expected to pinch the magnetic field inside the core, but does not necessarily lead to a large misalignment between the averaged magnetic field on the core scale (probed by our SMA observations) and that on the clump scale (probed by single dish observations). Turbulence can in principle distort the magnetic fields on both the clump and core scales. In our sample, it does not appear to be strong enough to randomize the field directions, as would be the case if the field were dynamically insignificant.

The findings in Figure 2 are further corroborated by the comparison of magnetic fields in the core scale and the major axis of their parental clumps. In the presence of a strong magnetic field, molecular gas is expected to collapse along the field lines to form filamentary structures either parallel or perpendicular to the field (Ostriker et al. 2001; Nakamura & Li 2008; Van Loo et al. 2014). Polarimetric observations in optical, infrared, and radio wavelengths also found that the relative alignment of the large-scale magnetic fields and the major axis of filaments are in a bimodal distribution (Busquet et al. 2013; Li et al. 2013) similar to that in Figure 3. For the SMA sample, those with large-scale (sub)mm polarimetric measurements, i.e., NGC 6334, G34.4, G35.2N, W51E2, W51N, and DR 21(OH) (Matthews et al. 2009; Cortes et al. 2008; Dotson et al. 2010), show that the magnetic field is roughly perpendicular to the major axis of the filaments. If the major axis of the parsec-scale clumps traces the large-scale magnetic fields, the fact that the majority of dense cores have magnetic fields perpendicular to the clumps as exhibited in Figure 3 serves as another indication that magnetic fields play an important role in the dynamic evolution of molecular clumps.

The apparent bimodal distributions seen in Figures 2 and 3 are remarkable. A distribution similar to that in Figure 3 is expected in a regime of strong magnetic fields. As suggested in simulations (Nagai et al. 1998; Nakamura & Li 2008; Li et al. 2013; Van Loo et al. 2014), the segments perpendicular to the clump-scale field could arise from lower density gas. We examined the densities derived from dust emission against |θ_clump(pol) − θ_SMA(pol)| as well as |θ_clump(maj) − θ_SMA(pol)|, and found no dominant trends between the two groups. This could be, in part, due to the fact that the projection of angles discussed in Section 4.1 mixes the two groups together. Therefore, both high density and low density cores can have the same angular difference θ_clump(pol) − θ_SMA(pol) due to the projection effect. In addition, the sensitivity in the polarization data limits detections of field lines associated with the lower density gas. Polarization studies with more sensitive interferometers such as ALMA will provide insight on this issue.

Protostellar outflows observed in CO mark the ambient gas accelerated by the wind ejected during the accretion and mass assembly of a protostar. Outflows from massive protostars have been the subject of intense observational studies with both single dish telescopes (Zhang et al. 2001, 2005; Beuther et al. 2002c) and interferometers (e.g., Cesaroni et al. 1999; Beuther et al. 2002a; Sollins et al. 2004; Su et al. 2004, 2007; Qiu et al. 2007, 2008, 2009, 2011; Qiu & Zhang 2009; Wang et al. 2012; Duarte-Cabral et al. 2013). These molecular outflows are often one to two orders of magnitude more massive and energetic in mass, momentum, and energy than outflows from lower mass protostars (Zhang et al. 2005). While the launch process is still unknown, these energetic outflows are believed to be driven by a magnetohydrodynamic wind in the disk, perhaps analogous to the disk-wind or X-wind (Shang et al. 2007) that operates in low-mass protostars. Regardless of the driving process, molecular outflows offer insights into the accretion process that occurs at a scale of ≲1000 AU within a dense core. While massive (10² M_☉) rotating structures known as toroids have been reported widely in the literature (Zhang 2005; Cesaroni et al. 2007), they represent the envelope of dense cores (Keto & Zhang 2010) that likely further fragment (Wang et al. 2011, 2014). In some cases where a massive protostar is relatively isolated, a rotationally supported accretion disk may have a diameter as large as 6000 AU, as reported by Keto & Zhang (2010) in a radiative transfer modeling of multiple spectral line data in the massive protostar IRAS 20126+4104. However, in a highly clustered environment where massive stars are predominantly formed, the size of an accretion disk can be much smaller due to dynamical interactions. Therefore, the axis of an outflow provides an indirect measure of disk orientation, which normally lies in a perpendicular direction.

The comparison between the outflow axis and the position angle of the magnetic field in the core from which the outflow is launched suggests that there is no preferred alignment between the two axes. This finding implies that magnetic fields in the accretion disk do not maintain the field direction of the core. For example, in the DR 21(OH) region, two outflows appear to originate from the same core, but have position angles as far apart as 60°. Our results indicate that disk orientation is not controlled by the magnetic field that we probe with the SMA on the core scale. This is in contrast to the simplest expectation where the component of the angular momentum perpendicular to the magnetic field is removed more efficiently by magnetic braking than the parallel component, which would tend to drive the angular momentum vector (and hence the outflow direction) to align with the field direction. There are several possible explanations for this misalignment. (1) The misalignment may indicate that the field on the disk formation scale is not strong enough to brake the angular momentum/rotation perpendicular to the field, or the field and gas are decoupled in the dense region so that magnetic braking is weakened (e.g., Mellon & Li 2009; Padovani et al. 2013). (2) The disk orientation is controlled by some other dynamical processes, such as angular momentum redistribution and gravitational interactions in binary or multiple systems. In any case, the dynamical importance of the magnetic field appears to weaken from the core to the disk scale.

Recently, a polarization survey of low-mass protostellar cores with CARMA (Hull et al. 2013) found that outflow axes do not correlate with the magnetic field orientation in the dense envelope surrounding accretion disks. This result appears to contradict a similar survey carried out with the SHARP polarimeter on CSO by Chapman et al. (2013) who reported good alignment between protostellar outflows and magnetic field orientation in the core. As proposed by Li et al. (2013), these two results can be reconciled in that at the scale probed by CARMA, magnetic fields are dragged and twisted by rotation in disks and envelopes. Another difference is that the majority of the sources in Chapman et al.'s (small) sample have outflows close to the plane of the sky. This minimizes the projection effect in the magnetic field orientation which could be considerable in Hull et al.'s sample. However, as Hull et al. (2013) pointed out, the projection effect may not explain the difference since it becomes significant only for outflows that are nearly along the line of sight, which are rare.

Although our result appears to be in agreement with Hull et al. (2013), the interpretation may not be the same. Since our sample is at a distance of an order of magnitude larger than the Hull et al.'s sample, rotation in general does not produce appreciable effect on magnetic fields over the linear scale that SMA probes, except for nearby targets such as G192 (Liu et al. 2013). For our sample, it is likely that dynamic interactions in binaries or close multiples change the disk and thus the outflow orientation relative to the magnetic direction.

One of the key findings in this paper (e.g., Figure 2) is derived from the comparison of polarization measurements between the single dish telescopes and the SMA. Figure 2 reveals that magnetic fields at core scales tend to maintain the mean field orientation measured by the single dish telescopes. Can the SMA data be dominated by the smooth structure seen in single dish telescopes, and hence, create a false alignment between the clump-scale and the core-scale magnetic fields? The answer is negative.

While polarization angles measured by a single dish telescope represent the mean orientation within the telescope beam, the SMA observations, like any interferometers, probe the spatially compact structures within, while filtering out extended emission. The SMA images reveal spatial structures from 20'' down to 1'', the synthesized beam of the observations. The typical densities in dense cores inferred from the Stokes I dust continuum are >10⁵ cm⁻³, at least one order of magnitude higher than the average density of their molecular clumps. The combined effect of high resolution and high density ensures that the SMA polarization data probe the gas at ≲0.1 pc scales closely associated with star formation. One clear example is DR 21(OH). The SMA observations at high angular resolution reveal disordered polarization structure oriented in the east–west and north–south directions (Girart et al. 2013). In contrast, the polarization image obtained at the same frequency band from the JCMT and CSO exhibits east–west magnetic field lines (Vallée & Fiege 2006; Matthews et al. 2009). We test the possibility that an ordered field from single dish observations is a result of either spatial filtering or spatial smoothing, the latter of which tends to render a more uniform field orientation. We tapered the SMA images to 20'' and reconstructed the polarization map. Figure 5 presents a comparison of the JCMT SCUBA map with the convolved SMA image to 20''. As one can see, the convolved SMA image remains similar to the higher resolution SMA maps. Therefore, the single dish data probes the larger scale magnetic field, whereas interferometer maps presented here probe the underlying structures at smaller spatial scales.

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The polarization study of a large sample of massive-star-forming regions reveals important clues to the role of magnetic fields during the collapse and fragmentation of massive molecular clumps. Figure 6 presents a schematic picture summarizing the key findings in this paper. At the clump scale, gas at densities of >10⁴ cm⁻² is threaded by magnetic fields typically probed by single dish telescopes. The parsec-scale clump can be elongated and/or be part of a larger scale filament, with the major axis perpendicular to the magnetic field. The collapse of the clump leads to the formation of cores at higher densities. The magnetic field in the higher density gas appears to be either aligned with or perpendicular to the clump-scale field. As the gas in dense cores continues to condense to form accretion disks that drive molecular outflows, the major axis of the disk does not appear to be aligned with the magnetic field in the parental core.

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While this study represents the largest sample thus far of massive-star-forming regions imaged in polarization with a (sub)mm interferometer, the sample included in the statistical analysis contains only ten massive molecular clumps. Therefore, results could be biased by the collection of targets that by chance have organized magnetic fields at core scales. Among most of the sources imaged, the detected polarized emission extends to a fraction of the Stokes I image. The statistical analysis does not take into account these cores with no polarization detections. Limited studies suggest that polarization can be distorted by stellar feedback. For example, radiation and ionization from H ii regions can influence magnetic field orientation (Tang et al. 2009a). The sample in this paper is mostly at an earlier stage of evolution prior to the H ii region phase. Therefore, the effect of feedback from an H ii region is minimal in our sample. At the sensitivity of the SMA, detecting dust polarization in massive IRDC (infrared dark cloud) clumps is still difficult due to the faintness of the sources. However, these objects may contain the pristine physical conditions of massive star formation with little influence from stellar feedback. Measuring polarization in these objects will be possible with more sensitive telescopes such as ALMA.

While the results presented here are limited by the sample size, it is apparent that the technique of comparing magnetic fields at different spatial scales shows great promise in constraining the relative role of magnetic fields versus turbulence and gravity/rotation. Such a technique can be applied when polarization measurements of a much larger sample become feasible. Interferometers such as SMA and CARMA that are currently equipped with polarimeters are on the verge of their capability to undertake large observing programs. The scientific return of such programs is apparent as demonstrated in the progress made in studying magnetic fields in low- and high-mass star formation (e.g., Hull et al. 2013, and this work). While these instruments will continue to play a role in polarimetric studies, they pave the way for further studies of much larger samples with ALMA as its polarimetric capability continues to mature. It is hopeful that more statistically robust studies based on much larger samples will come to fruition in the next decade.