On the Magnetic Field Properties of Protostellar Envelopes in Orion

We present 870 μm polarimetric observations toward 61 protostars in the Orion molecular clouds with ∼400 au (1″) resolution using the Atacama Large Millimeter/submillimeter Array. We successfully detect dust polarization and outflow emission in 56 protostars; in 16 of them the polarization is likely produced by self-scattering. Self-scattering signatures are seen in several Class 0 sources, suggesting that grain growth appears to be significant in disks at earlier protostellar phases. For the rest of the protostars, the dust polarization traces the magnetic field, whose morphology can be approximately classified into three categories: standard-hourglass, rotated-hourglass (with its axis perpendicular to outflow), and spiral-like morphology. A total of 40.0% (±3.0%) of the protostars exhibit a mean magnetic field direction approximately perpendicular to the outflow on several × 102–103 au scales. However, in the remaining sample, this relative orientation appears to be random, probably due to the complex set of morphologies observed. Furthermore, we classify the protostars into three types based on the C17O (3–2) velocity envelope’s gradient: perpendicular to outflow, nonperpendicular to outflow, and unresolved gradient (≲1.0 km s−1 arcsec−1). In protostars with a velocity gradient perpendicular to outflow, the magnetic field lines are preferentially perpendicular to outflow, with most of them exhibiting a rotated hourglass morphology, suggesting that the magnetic field has been overwhelmed by gravity and angular momentum. Spiral-like magnetic fields are associated with envelopes having large velocity gradients, indicating that the rotation motions are strong enough to twist the field lines. All of the protostars with a standard-hourglass field morphology show no significant velocity gradient due to the strong magnetic braking.

1. INTRODUCTION Magnetic fields (henceforth B-fields) are thought to play a crucial role in the star-forming processes (e.g., Maury et al. 2022;Pattle et al. 2023).In ideal MHD models, during the collapse phase of a prestellar core, the B-field lines are drawn inward into an hourglass morphology, forming a pseudo-disk.They carry away angular momentum very efficiently, which ultimately leads to catastrophic magnetic braking, preventing the formation of a centrifugally supported disk (Ciolek & Mouschovias 1994;Allen et al. 2003;Galli et al. 2006).In real astrophysical environments, various nonideal MHD effects may come into play, allowing the formation of an accretion disk around the central protostar (Dapp & Basu 2010;Hennebelle et al. 2016Hennebelle et al. , 2020;;Zhao et al. 2020).In addition, an initial misalignment between the B-field and the rotation axis leads to weaker magnetic braking of the collapsing core, enabling early disk formation (e.g., Joos et al. 2012;Li et al. 2013;Hirano & Machida 2019;Machida et al. 2020).In any case, B-fields are also thought to be important in the formation, collimation, acceleration, and regulation of outflows associated with protostellar systems (e.g., Pudritz & Ray 2019).
Polarized dust continuum emission allows us to examine the B-field morphology in star-forming regions.In the presence of B-fields, spinning and elongated dust grains with paramagnetic properties are expected to align their long axes perpendicular to the field direction (e.g., Hoang & Lazarian 2009;Andersson et al. 2015).In recent decades, dust polarization observations carried out with (sub)millimeter interferometers have increasingly demonstrated their effectiveness in mapping B-fields at the scales of cores (∼ 10 4 au) and envelopes (∼ 10 2 to 10 4 au) (e.g., Girart et al. 1999Girart et al. , 2013;;Cox et al. 2018;Galametz et al. 2018;Hull & Zhang 2019;Le Gouellec et al. 2020;Cortés et al. 2021).Hourglassshaped B-fields have been observed around protostellar envelopes and trace gravitationally infalling material (e.g., Girart et al. 2006Girart et al. , 2009;;Qiu et al. 2014;Beltrán et al. 2019;Le Gouellec et al. 2019;Hull et al. 2020).Building upon these observations, some studies developed 3D analytical models of hourglass morphology (e.g., Myers et al. 2018Myers et al. , 2020)), further reinforcing the prevalence of this structure.However, interferometric polarization surveys toward low and high-mass protostellar at core and envelope scales found that the B-field does not correlate with the axis of outflows.This suggests that the B-field may be less dynamically important than angular momentum and gravity (Hull et al. 2013;Zhang et al. 2014).
On the other hand, millimeter polarized emission in planetforming disks is dominated by self-scattering of large dust grains (∼ several hundreds of microns, Kataoka et al. 2015Kataoka et al. , 2016;;Yang et al. 2016a,b).Recent high-resolution observations of dust polarization have revealed polarization patterns that more closely align with self-scattering, rather than the signature expected from B-fields within protostellar and protoplanetary disks (Kataoka et al. 2017;Stephens et al. 2017a;Bacciotti et al. 2018;Sadavoy et al. 2018a;Cox et al. 2018;Girart et al. 2018;Hull et al. 2018;Yang et al. 2019).Only a few observations show cases where the polarization is consistent with magnetically aligned dust grains on disk scales (Lee et al. 2018;Sadavoy et al. 2018b;Alves et al. 2018;Ohashi et al. 2018).
The Orion molecular clouds (OMCs) are one of the best regions to study the role of B-fields in the star formation process.They are the closest (∼ 400 pc, Kounkel et al. 2017) high-mass/intermediate-mass star-forming regions, and have been extensively studied across multiple wavelengths, providing a wealth of ancillary data and information.Moreover, most solar-type stars, including the Sun, formed in massive, clustered star-forming regions (Lada & Lada 2003), making the OMCs a more typical representation of star-forming conditions within the Galaxy.Finally, the OMCs have the largest population of Class 0 protostars within 500 pc (Stutz et al. 2013;Furlan et al. 2016).Class 0 protostars are exceptionally well-suited for studying the role of B-fields in star formation due to their early evolutionary stage that preserves information about their initial collapse.
The B-field Orion Protostellar Survey (BOPS) used ALMA to observe 870 µm dust polarization toward 61 young lowmass protostars in the OMCs.Its main objective is to investigate the role of B-fields on spatial scales ranging from 400 to thousands of au, fully encompassing the protostellar envelope surrounding the youngest protostars.The limited sensitivity of previous surveys (e.g., Hull et al. 2014;Zhang et al. 2014) probed sources at varying evolutionary stages and in different star-forming regions, thus resulting in samples that were biased and non-uniform.To mitigate this, the BOPS observations uniformly probe B-field structures within the envelopes surrounding protostars in one star-forming region.In this paper, we present the first results of the BOPS project, organized as follows: Section 2 introduces the observations and the processes of data reduction.The main results are presented in Section 3, followed by a detailed discussion of these results in Section 4. Finally, the summary is given in Section 5.

OBSERVATIONS AND DATA REDUCTION
The BOPS (PI: Ian Stephens, 2019.1.00086)survey used ALMA Band 7 (870 µm) to observe 57 fields, each centered on a different protostar as identified by the VLA/ALMA Nascent Disk and Multiplicity (VANDAM) Survey of Orion Protostars (Tobin et al. 2020).The vast majority of these protostars are Class 0, though a few bright Class I protostars were also included in the sample.The names and coordinates of these protostars are listed in Table 1 of Appendix D. We targeted the brightest Class 0 sources using their VLA, C-array, 9 mm fluxes (∼ 1 ′′ resolution).The sample size was selected to be approximately twice that of the TADPOL survey (Hull et al. 2014), which included 30 sources throughout different star forming regions.Observations were made from November 29, 2019, to December 20, 2019, using the ALMA compact configurations C43-1 and C43-2, and an intermediate configuration of both, which provided baselines between about 14 m and 312 m.The observations were taken in Frequency Division Mode (FDM), providing modest spectral resolutions.We used four spectral windows, two in each sideband, with the upper sideband targeting 12 CO (3-2) and continuum, and the lower sideband targeting the continuum only.The maximum bandwidth (1.875 GHz per spectral window) was selected for the continuum, while a more modest bandwidth but higher spectral resolution was used for 12 CO (3-2).Notably, C 17 O (3-2) in spectral window 4 was detected toward each protostar, which we used to trace the envelope kinematics.Other molecular transition lines were detected because of the resolution provided by the ALMA FDM mode, but are not considered here.The rest frequency, bandwidth, spectral resolution, and velocity resolution of each spectral window are listed in Table 2 of Appendix D.
The dust continuum images were produced using the tclean task in CASA (CASA Team et al. 2022), with a Briggs weighting robust parameter set to 0.5, which is a good compromise between resolution and sensitivity (Briggs 1995).The extremely bright line 12 CO (3-2) is flagged before self-calibration.Then we performed three successive rounds of phase-only self-calibration for each source to improve the image quality.The Stokes I image was used as a model for self-calibration, with solution intervals set to 600, 30, and 10 seconds for the first, second, and third iterations, respectively.To avoid the effects of bright lines on the dust continuum emission, channels exceeding 1.5 times the continuum baseline were flagged after the third round of selfcalibration.The final Stokes I, Q, U continuum maps were produced independently using line-free and self-calibrated data of all spectral windows.
The self-calibrated continuum emission (Stokes I) is strongly detected with a signal-to-noise ratio (S/N) ranging from 750 to 4200 for all targets.The average noise level in the final Stokes I image is ∼ 0.1 mJy beam −1 , which is higher than the noise level of σ QU ∼ 0.07 mJy/beam in both the Stokes Q and U maps.This difference arises from the total-intensity image being more dynamic-range-limited than the polarized intensity images.The debiased polarized in-tensity is defined as (Vaillancourt 2006;Hull & Plambeck 2015), using a 3σ QU cutoff value.The fractional polarization is derived as P frac = P/I.The polarization angle is calculated as θ = 0.5 • arctan(U/Q), using a 3σ value of the polarization intensity map as a threshold.
For the line data, we first applied the self-calibration solutions to the entire dataset.Then, the full, non-channelaveraged dirty image cubes were produced to identify the channels of continuum.The uvcontsub task was used to perform continuum fitting and subtraction in the UV plane.Finally, we performed the tclean task to produce Stokes I, Q and U image cubes using self-calibrated, continuumsubtracted data for each spectral window.
The 12 CO (3-2) and C 17 O (3-2) channel maps were used to identify the molecular outflows and the molecular emission from the envelope, respectively.The envelope's centroid velocity (V LSR ) was estimated by fitting a Gaussian to the spectrum obtained from averaging the C 17 O (3-2) emission within a scale of 1000 au around the position of the protostar.The immoments task was used to generate the outflow maps.The blue-and red-shifted 12 CO (3-2) outflow images were obtained using a velocity range starting from +/-5 km s −1 with respect to V LSR and included all channels where the emission was at least 5σ.However, in some sources , the channels near the V LSR are significantly affected by the spatial filtering of the large scale emission or by optical depth effects.In these cases we manually selected the channels.The velocity field of the envelope was traced using the C 17 O (3-2) line, specifically the moment 1 map.This map covers all channels with emission exceeding 3σ.Our sample included 9 protostars that had companions in one field (HH270IRS, HOPS-310, HOPS-317S, .Since C 17 O emission is optically thin in the envelope region (see Appendix C), we select the stronger component and carefully choose which channels to include to minimize any effects from the weaker component.

RESULTS
Figure 1 shows the results for typical protostars in the sample.Plots for the entire sample are available in Appendix E. One field, OMC1N-4-5-W, does not show polarization emission nor CO (3-2) outflow emission, and the dust peak intensity is weak (∼3 mJy beam −1 ), signifying it could be a starless core.In the remaining fields, we successfully detected both dust polarization and molecular outflows in 56 sources, and the dust polarization but no clear outflow in 3 sources (HOPS-373E, HOPS-398, HOPS-402).Additionally, we identified 2 sources (HOPS-87S and OMC1N-8-S) with outflow signature but no polarization detection, which will not be included in this paper.Among these 56 protostars, 47 clearly exhibit the usual red and blue bipolar patterns, the remaining 9 protostars only show one distinct outflow com-  4,8,16,32).The magenta segments represent the polarization.The regions of polarization intensity less than 3σ have been masked.Second column: the velocity field in color scale (obtained from the C 17 O (3-2) line) overlaid with the B-field segments (i.e., polarization rotated by 90 • ) and Stokes I contours.Third column: an enlarged perspective of 1000 au of the second column.In the second and third panels, the black segments represent the B-fields.The red and blue arrows indicate the mean direction of the red-shifted and blue-shifted outflows.For the velocity field, regions with an S/N less than 4 have been flagged.The grey arrows in the second and third columns indicate the mean B-field directions weighted by the intensity including all the polarization segments, and weighted by the uncertainty within annular region of 400-1000 au, respectively.In the first, second, and third columns, the black contour levels for the Stokes I image are 10 times the rms × (1,2,4,8,16,32,64,128,256,512).The black dotted square in the first column corresponds to 2000 au scale, while the black dashed, and solid circles correspond to scales of 1000 au, and 400 au, respectively. .Histograms of different angle's differences for the 17 protostars with compact, barely resolved polarized emission thought to be related to dust polarization caused by dust self-scattering (upper panels), and for the rest of the protostars with extended polarized emission (lower panels).Upper panels: histogram of angle's difference between the outflow direction θ Out and the mean polarization direction weighted by the intensity ⟨θ Pol ⟩ I (left), and between the disk orientation along the major axis θ Disk and the mean polarization direction ⟨θ Pol ⟩ I (right).In this right histogram, one disk, from HOPS-354, is not included because the disk is probably nearly face-on.Bottom panels: histogram of angle's difference between the outflow direction θ Out and the intensity-weighted average B-field direction using all the detected polarized emission ⟨θ B 1 ⟩ I (left), and within an annular region with an inner and outer radius of 400 and 1000 au ⟨θ B 2 ⟩ I (right), respectively.HOPS-250 is not included in the right panel because there is no 4σ polarization detection within the annular region.
ponent, with the other being very weak or overlapping with other outflow lobe.
The properties for the entire sample can be found in Table 1 in Appendix D. The position angles of polarization are determined using two different methods: the total-intensityweighted average and the uncertainty-weighted average, respectively.The position angles of polarization weighted by intensity ⟨θ Pol ⟩ I and uncertainty ⟨θ Pol ⟩ σ can be expressed as, respectively: where  (2020).We excluded the disks with a low S/N ratio (< 5σ of integrated intensity) and the almost face-on disks (with an inclination angle of <30 • ).These position angle of polarization ⟨θ Pol ⟩, B-field ⟨θ B ⟩, outflow θ Out , and disk θ Disk are listed in Table 3 and Table 4 in Appendix D.

Self-scattering
Self-scattering polarization is observed parallel to the minor axis of an inclined disk (e.g.Kataoka et al. 2015Kataoka et al. , 2016Kataoka et al. , 2017;;Yang et al. 2016a,b;Stephens et al. 2017b), thus it is expected to be aligned with the outflow direction.Within the BOPS sample with clear outflow detections, there are 17 protostars with compact polarized emission.We performed Gaussian fits to the polarized intensity and found that in each cases, the upper limits of the size of polarized emission are comparable to disk sizes, suggesting that the polarization arises from disk scales.The deconvolved major and minor axes from the Gaussian fits are consistent with the resolved disk sizes obtained from high resolution data by Tobin et al. (2020).The upper panels in Figure 2 show the distribution of the difference between the polarization direction and the outflow direction (left-upper panel), and the disk orientation along the major axis (right-upper panel) in compact polarized sources.In these two plots, almost all of the sources the polarization angle appears to be perpendicular to the disk major axis and parallel to the outflow.Only HOPS-250 shows a polarization angle perpendicular to the outflow.Excluding this source, we find that the median difference between polarization direction and the the outflow direction is 7 • , and the median difference between polarization direction and the the disk major axis is 86 • .The fractional polarization of these 16 ptotostars is between 0.5% to 2.0%, suggesting that the compact polarization detected arises from self-scattering (e.g., Kataoka et al. 2016;Yang et al. 2017;Girart et al. 2018).
The outflow position angle, polarization direction, and disk orientation of these sources are listed in Table 4.

B-field at envelope scales
We are left with 40 protostars associated with a molecular and envelope polarization emission.We do not expect self-scattering to be significant in the envelope, because the emission is more isotropic, and the grain size is smaller comparing to disk scale (Kataoka et al. 2016).Thus, for these cases (including HOPS-250 with compact polarized emission), we assume that the polarization is produced by magnetically aligned grains.Based on this, we classify each protostar based on its B-field pattern, as seen in Figure 3.We find that most of these targets can be classified into three main B-field morphologies: standard-hourglass, rotated-hourglass and spiral (note that in many sources there are significant deviations from an ideal spiral shape).In the standard-hourglass category, 8 protostars show the expected morphology (e.g., Girart et al. 2006), in which their outflow is roughly parallel to the direction of the hourglass axis.There are 13 protostars that exhibit a similar hourglass structure, but flipped by 90 • , such that its axis is perpendicular to the outflow, these are classified as rotated-hourglass.The spiral category encompasses 9 protostars with well-organized or partial spiral patterns in their B-field structure (as in, e.g., Sanhueza et al. 2021).In addition to these three categories, 5 protostars exhibit a B-field pattern that is complex, and 5 do not have enough data (see Table 3).In the case of a rotated-hourglass B-field morphology, all protostars with this shape in our sample exhibit extended polarized emission, thus the potential ambiguity with self-scattering is not important.Moveover, there are 6 protostars in our sample that have polarized emission that appears to be along streamerlike dust structures (HOPS-168, HOPS-182, HOPS-361N, HOPS-361S, HOPS-370 and OMC1N-8-N, as shown in Appendix E).The B-field in each of these protostars appears to follow the direction of this streamer-like structures.
As shown by the peripheral vectors in all panels of Figure 1 (particularly in the HOPS-182 field), 3σ polarized emission in some regions may be generated by noise in the data, we therefore performed a total-intensity-weighted average Bfield using a 4σ QU threshold in our polarization emission data (see Appendix A).The bottom-left panel of Figure 2 shows the histogram of the angle difference between the outflow and these average B-field directions.The distribution appears almost random.However, there is a slight preference to the cases where the outflow is perpendicular to the B-field direction: two-fifths of the protostars (16 out of 40) are located in the last quartile (angle difference in the 67.• 5-90 • range).

B-field at scales of 400-1000 au
The use of the intensity-weighted average B-field direction, as used by Hull et al. (2014), favors the polarization signal around the dust peak intensity, which may have significant contributions from both total and polarized emission in the circumstellar disk.In the BOPS sample, the disks have radii between 30 and 250 au (0. ′′ 08 and 0. ′′ 63) (Tobin et al. 2020).
To avoid possible contamination from disk self-scattering polarization (see Section 3.1), we select an annular region from 1 ′′ (∼400 au) to 2. ′′ 5 (∼1000 au).Within this region the difference between the outflow and the intensity-weighted average B-field direction appears to be very similar to the one obtained using all polarization data (as shown in bottom panels of Figure 2).The envelope kinematics are traced by optically thin C 17 O emission (see Appendix C).The envelope's angular momentum is expected to be parallel to the outflow (Pudritz & Ray 2019).We generated position-velocity (P-V) cuts from the C 17 O (3-2) channel maps centered at the dust peak intensity and perpendicular to the outflow axis.We calculated the absolute velocity gradient (|∇v abs |) in the P-V image by selecting the most red-/blue-shifted emission at 5σ at a distance of 400 au from the protostar position (as shown in column 8 of Table 3).We found significant velocity gradients (i.e., |∇v abs | ≳ 1.0 km s −1 arcsec −1 ) toward 14 protostars, which is probably indicative of rotation.However, most of the sources do not show a clear gradient, which may due to the limited spectral resolution of the observations (∼0.9 km s −1 ).In addition, we use the moment 1 (intensity-weighted velocity maps) of the C 17 O (3-2) emission to derive the direction of the velocity gradient.To do so, we fit a 2D linear regression fit to the moment 1 map following Goodman et al. (1993) and Tobin et al. (2011).Further details regarding envelope kinematics are discussed in Appendix C. Column 7 in Table 3 lists the velocity gradient position angle.In cases without a significant velocity gradient, we use the spectral resolution divided by the angular resolution as an upper limit.We use the velocity gradient position angle θ v and outflow direction θ Out (as depicted in Figure 1) to classify the protostars into three types.This is done for 39 protostars where significant polarization data is detected within the annular region of 400 to 1000 au: 1. Perp-Type: velocity gradient is perpendicular to the outflow (67.We use the uncertainty-weighted position angles of the Bfield on scales of 400-1000 au (represented as ⟨θ B ⟩ σ ) for the following analysis, which are listed in the sixth column of Table 3.The left panel in Figure 4 shows the distribution of the B-field and outflow direction for the three source types.We find no significant relation between the average B-field and the outflow directions in Nonperp-Type and Unres-Type.4, due to the small sample size in each group, it is difficult to characterize the correlation between the B-field and and the disk orientation.Globally, there seems to be random alignment between the B-field and the disk orientation within the 20 sources.However, we find some trends for the Perp-Type sources with almost all showing parallel alignment between the mean B-field and disk orientation, with a correlation coefficient of 0.96.

Geometric projection effect
The position angles of the outflow and B-field we measured are projected onto the plane of the sky.To investigate the influence of projection effects on our results, we plot the cumulative distribution function of the observed angle difference (CDF, Hull et al. 2013Hull et al. , 2014;;Stephens et al. 2017b) and compare it with 2D simulated intersecting angles uniformly projected from a three-dimensional space.The parallel case uses the angles randomly selected within 0 and 22. • 5 in 3D, and then project onto the plane of the sky in the simulation, while the range of 3D angles used in random and perpendicular cases are 0 • -90 • and 67.• 5-90 • , respectively.For simplicity, it is prudent to exclusively employ the 3D projection analysis on the entire sample only (i.e., not in any of the other subsamples analyzed in this work), represented in Figure 5.
We run the Kolmogorov-Smirnov (K-S) test on the angle difference distribution of our sample.When considering the difference between the B-fields and outflow directions in the entire 39 sources, we compared the observed distribution with the simulated models.The probability of our results being drawn from parallel models is <0.001, ruling out this scenario.The probability that the distribution is drawn from a random model is 0.325, and from a perpendicular model is 0.615.Though the probability is higher for the perpendicular case, each model could be possible for the distribution.

DISCUSSION
The polarization properties in approximately one-third of the sample, 16, strongly suggest that they are tracing selfscattering in disks.Most of these targets are Class 0 (except for the Class I source of HOPS-84), and their bolometric temperature is similar to protostars without self-scattering (see Table 1), indicating that self-scattering is independent of evolutionary stages.This result suggests that grain growth has already occurred in the disks in the earliest stages of the protostellar phase.It is possible that other sources in the sample also have polarized emission from self-scattering, but this would only be apparent around the intensity peak.Higher angular resolution observations are needed to properly quantify disk self-scattering in the full sample (see Liu et al. 2023).
Past interferometric polarization surveys using CARMA probed 16 protostars (Hull et al. 2013) and 30 star-forming cores (Hull et al. 2014) and showed that the B-fields are randomly oriented with outflows on a scale of a few thousands au.Subsequently, Zhang et al. (2014) presented SMA observations of 14 massive clumps.They also found that the B-fields, on core scale of 0.01-0.1 pc, do not correlate with the outflow direction.Arce-Tord et al. (2020) found the same results using 1 mm ALMA observations toward 29 protostellar dense cores in high-mass star-forming regions at a scale of 2700 au.In our study, both, the histogram of the difference between the outflow and the averaged B-field direction (bottom panels of Figure 2) and the CDF of these angle differences (Figure 5) show that the B-field is almost perpendicular to the outflow axis in a significant number of protostars.However, there is also a large fraction of protostars where the distribution of the angle difference appears random.These results of relative orientation probably depend on the sam-ple of observed B-field morphologies.Other causes may also explain the differences with previous results in the comparison between the mean B-field and the outflow axis.The objects in Zhang et al. (2014) are at much greater distances, so they trace much larger linear scales of the B-fields.Hull et al. (2013) had a smaller sample of protostars that spanned multiple cores and lacked sensitivity, thus mapping fewer Bfield vectors.Nevertheless, our results are in agreement with the recent numerical study done by Machida et al. (2020).They found that angular momentum, outflow and local Bfield axes depend on the initial angle difference between the angular momentum and the B-field axes, as well at which scales these directions are measured.Galametz et al. (2020) found, in a sample of 20 Class 0 protostars, that the misalignment angle of the B-field orientation with the outflow is strongly correlated with the amount of angular momentum on 1000 au scale.We find similar results for the sources with strong velocity gradients, 7 of 14 (the Perp-Type and the Nonperp-Type) the B-field direction is perpendicular to the outflow axis.
Several BOPS protostars shows the expected hourglass Bfield along the outflow axis.This morphology is predicted in the classical models of star formation where the core is initially threaded with a uniform B-field, and turbulence and angular momentum are not dynamically important (e.g., Galli et al. 2006).All the protostars with the standard-hourglass shape in our sample are observed in the Unres-Type, possibly because the B-field is strong enough to slow down the rotation in this case, or because the core's initial angular velocity was energetically less important than the B-field.Most of the protostars with strong envelope velocity gradients (Perp-Type and Nonperp-Type) appear to have a rotated-hourglass or a spiral B-field morphology.The rotated-hourglass shape tends to have field lines parallel to the velocity gradients and perpendicular to the outflows, however, in most cases of the spiral shape, the envelope B-field does not align with either the velocity gradient or the outflow.In the case of the spiral morphology, this shape could be due to an initial misalignment between B-fields and rotation.MHD simulations show that this shape generates magnetic torques, which creates two inflowing spirals aligned with the B-field (Wang et al. 2022).This is what is observed in HOPS-182, HOPS-361S, and possibly in HOPS-361N (and previously in IRAS 18089-1732: Sanhueza et al. 2021).The rotated-hourglass could be the extreme case of the standard hourglass, where gravity is so strong (i.e., with a relatively high initial mass-to-flux ratio, see Maury et al. 2018) that the bending of the lines appear perpendicular to the outflow axis, but this may happen only in the innermost part of the envelope as seen in B335 (Maury et al. 2018) and L1448 IRS 2 (Kwon et al. 2019).Alternatively, this could trace the transition from the standard poloidal hourglass to a toroidal B-field due the effect of an initially large angular momentum (e.g., Machida et al. 2007).

SUMMARY
We have presented the first results of the BOPS survey, which targets 61 protostars in the OMCs star-forming complex.The outflow structure was traced using 12 CO (3-2), while the velocity field in the dense region was mapped using C 17 O (3-2).We detect 870 µm dust polarization emission and outflows around 56 protostars.The main results are: 1. Self-scattering is observed in 16 sources, most of them are Class 0, indicating that grain growth in disks occurs in the very early stages of the disk evolution.
2. Dust polarization traces the B-field in 40 protostars at envelope scales (up to ∼ 3000 au).Most of these targets can be classified into three major B-field morphologies: the standard-hourglass, rotated-hourglass (which may be a highly pinched, standard hourglass), and a spiral configuration.These morphologies are the result of the complex interplay between gravitational collapse, B-fields and rotational motions during the star formation process.The B-fields aligned with the filament-or streamer-like structure could be related with accretion streamers, but high spectral resolution observations are needed to confirm this scenario.
3. Two-fifths of our sample exhibit an averaged B-field that is perpendicular to the outflow, however the remaining three-fifths of our sample have a random relative orientation.On scales of 400 to 1000 au, the sources with a strong velocity gradient perpendicular to the outflow axis (Perp-Type) have a B-field that is also perpendicular to the outflow axis.
4. Most of the protostars with strong velocity gradients |∇v abs | ≥ 1.0 km s −1 arcsec −1 (Perp-Type and Nonperp-Type) tend to have a rotated-hourglass or spiral Bfield morphology.In rotated-hourglass B-field morphologies, the B-field strength is probably less significant with regard to gravity and angular momentum.While in spiral structures, the rotation motions seem to be strong enough to twist the field lines, contributing to a helical B-field morphology.Notably, all of the sources with B-field patterns showing a standardhourglass structure of B-field are in the Unres-Type, i.e., sources without strong velocity gradients probably due to the magnetic braking.
In summary, three main B-field configurations are observed in our study, the rotated-hourglass field shape is more prevalent when the B-field strength is less significant compared to gravity and angular momentum, while strong rotation tends to give rise to spiral field structures.In contrast, standard-hourglass field patterns are more commonly observed in sources lacking strong velocity gradients.
We thank Jacob Labonte for early analysis of the BOPS data.

WEIGHTED MEAN B-FIELD POSITION ANGLE
To trace the mean orientation of polarization for these protostars, we extract the size ranging from several hundreds to several thousands of au, encompassing all polarization measurements toward the targeted source, i.e. all Stokes Q and U pixels larger than 4σ are enclosed.We then calculate its position angle ⟨θ⟩ by performing a total-intensity-weighted average, giving more weight to polarization directions in higher-density regions (Hull et al. 2013(Hull et al. , 2014)).To guarantee adequate sampling of the derivatives in each pixel, the pixel size used here falls within a region of one-third to half of the beam FWHM (e.g., Soler et al. 2017).For example, in the case of HH212M, with major and minor axes of 0. ′′ 95 and 0. ′′ 70 respectively, and a beam FWHM of ∼ 0. ′′ 83, the pixel size should be within the range of 0. ′′ 28 ∼ 0. ′′ 42.The calculation of intensity-weighted position angle of polarization ⟨θ Pol ⟩ I is expressed as: N and D are averaged values of Stokes Q and U weighted by the intensity: where i and j are pixel numbers, I(i, j), Q(i, j), and U(i, j) indicate the corresponding values in the (i, j) pixel of the Stokes I, Q, U images, respectively.The error is estimated through error propagation: where Here ∆I, ∆Q and ∆U indicate the rms noise of the Stokes I, Q and U maps, respectively.Then the Equation A3 can be expressed as: The intensity-weighted method always makes sense when applied to point sources, but it may lead to misjudgment in certain extended cases, as the position angle in the extended regions also significantly contributes to the estimation, despite having much lower density.For comparison, we also follow the approach discussed by Galametz et al. (2020) and average the position angle of polarization by weighting it with its uncertainty σ.The value of σ is calculated by error propagation and described as: where θ Pol (i, j) = 0.5 • arctan(U(i, j)/Q(i, j)), and the averaging position of polarization angle weighted by the uncertainty ⟨θ Pol ⟩ σ is expressed by: where M and K are average values of Stokes Q and U weighted by the uncertainty of the polarization position angle: The error of uncertainty-weighted angle ∆⟨θ Pol ⟩ σ is estimated by multiplying the internal uncertainty iu derived from error propagation by the the square-root of the reduced chi-squared: where n is the total number of pixels, and Note that the weighted polarization angle ⟨θ Pol ⟩ should be rotated by 90 • to infer the mean direction of the B-field ⟨θ B ⟩.The B-field position angles weighted by intensity ⟨θ B ⟩ I and uncertainty ⟨θ B ⟩ σ are available in Table 3. B. OUTFLOW PARAMETERS In many cases (47 protostars), blue-and red-shifted outflows can be clearly paired in a bipolar fashion.However, there are 9 protostars that only have one clear outflow component, while the other is either very weak or overlaps with other emission from e.g.other outflows.It should be mentioned that HOPS-373E, HOPS-398, and HOPS-402 do not exhibit clear outflows.
To estimate the outflow direction, we measure its position angle using the following steps (see Figure 6): First, we connect the source center with the edges of the red-/blueshifted outflow lobe, and then we take the bisector of the open angle as the red-/blueshifted outflow position angle.The outflow direction is determined by averaging the position angles of the redshifted and blueshifted components.The edges of the lobes are defined using the 5σ level of the emission.For the monopolar cases, we take the position angle of the clear lobe as the outflow direction.Uniformly, the radius from center to lobe edge is set to R = 1000 au, as most sources have clear outflows at this scale.The outflow position angle θ Out and its corresponding mean open angle ∆θ Out for each source are listed in Table 3 and Table 4.
We define the position angle for each of the outflow edges as θ edge = arctan(y/x), where x 2 + y 2 = R 2 .Assuming x and y have an error of half beamsize u 3 , i.e. ∆x = ∆y = u 3 , then the error of θ edge is estimated by error propagation: which is related to the location of the source within the OMCs region.For monopolar and bipolar outflows, there are two (one lobe) and four (two lobes) independent measurements, thus the error of θ Out can be expressed: for the cases with one clear lobe, and for the cases with two clear lobes.
C. C 17 O OPACITY AND VELOCITY GRADIENT The opacity of C 17 O (3-2) is calculated by: where T cmb =2.722K is the cosmic microwave background Temperature, J ν (T ) is the Rayleigh-Jeans equivalent temperature of a black body at temperature T : Assuming the Rayleigh-Jeans approximation is accurate, then the observable source radiation temperature T R is estimated as: where θ maj and θ min are the major and minor axes of the restoring beam, and I is the peak of the C 17 O spectral line.The excitation temperature for an optically thick molecular line is estimated by: We have 12 CO detection, which is usually optically thick in the OMCs (e.g., Shimajiri et al. 2013;Eisner et al. 2016).T EX ( 12 CO) ranges from 15.3 K to 50.4 K at envelope scales of 400 au.Assuming T EX (C 17 O) ≈ 50 K, we then obtained the opacity of C 17 O for each source, with a range of 0.04 to 0.26, which is considered to be optically thin.
We estimate the velocity gradient by fitting the following function (Goodman et al. 1993;Tobin et al. 2011): here ∆α and ∆δ are the offsets in right ascension and declination, and v α and v δ are the projections of the velocity gradient onto the α and δ axes.The parameter v 0 represents the systemic velocity with respect to the local standard of rest.Then the direction of velocity gradient θ v is calculated by The uncertainty is from a least-squares fit of Eqation C19 to the observed velocity field.2020) and Federman et al. (2023).The Stokes I type are classified by comparing the ratio (R) of the area enclosed by the intensity contour at 0.2 times the maximum to the restoring beam size.Sources with R < 1, 1 ≤ R ≤ 3, and R > 3 are categorized as "Unresolved", "Compact", and "Extended", sources are classified as either "Binary" or "Multiple" when there are two or more well-resolved components within 10 ′′ (∼ 4000 au) from the peak intensity.Name R.A. Dec. Beam P.A.     , 2, 4, 8, 16, 32, 64, 128, 256, 512).The black dotted square in the first column corresponds to 2000 au scale, while the black dashed, and solid circles correspond to scales of 1000 au, and 400 au, respectively., 2, 4, 8, 16, 32, 64, 128, 256, 512).The black dotted square in the first column corresponds to 2000 au scale, while the black dashed, and solid circles correspond to scales of 1000 au, and 400 au, respectively.4,8,16,32,64,128,256,512). The black dotted square in the first column corresponds to 2000 au scale, while the black dashed, and solid circles correspond to scales of 1000 au, and 400 au, respectively.4,8,16,32,64,128,256,512). The black dotted square in the first column corresponds to 2000 au scale, while the black dashed, and solid circles correspond to scales of 1000 au, and 400 au, respectively.

Protostars without clear outflows
Protostars without 3σ polarization detection Figure 1.Example maps in BOPS survey.First column: 870 µm dust polarization intensity in color scale overlaid with the redshifted and blueshifted outflow lobes (obtained from the 12 CO (3-2) line), polarization segments, and dust continuum emission (Stokes I) contours.Blue contours indicate the blueshifted outflow, while red contours are redshifted outflow, with counter levels set at 5 times the outflow rms × (1, 2, 4, 8, 16, 32).The magenta segments represent the polarization.The regions of polarization intensity less than 3σ have been masked.Second column: the velocity field in color scale (obtained from the C 17 O (3-2) line) overlaid with the B-field segments (i.e., polarization rotated by 90 • ) and Stokes I contours.Third column: an enlarged perspective of 1000 au of the second column.In the second and third panels, the black segments represent the B-fields.The red and blue arrows indicate the mean direction of the red-shifted and blue-shifted outflows.For the velocity field, regions with an S/N less than 4 have been flagged.The grey arrows in the second and third columns indicate the mean B-field directions weighted by the intensity including all the polarization segments, and weighted by the uncertainty within annular region of 400-1000 au, respectively.In the first, second, and third columns, the black contour levels for the Stokes I image are 10 times the rms × (1, 2, 4, 8, 16,  32, 64, 128, 256, 512).The black dotted square in the first column corresponds to 2000 au scale, while the black dashed, and solid circles correspond to scales of 1000 au, and 400 au, respectively.Fourth column: C 17 O position-velocity (PV) diagram perpendicular to the outflow direction.The color scale indicates the total intensity of C 17 O line.Black solid contour levels are 3 times of the intensity rms × (1, 2, 4, 8, 16, 32, 64), while dashed contours are set at 3 times of the intensity rms × (-1, -2, -4).Vertical dashed lines represent a scale of 400 au, with a blue line indicating a blueshifted offset of 200 au and a red line indicating a redshifted offset of 200 au.The red and blue horizontal lines indicate the velocity values corresponding to the positions with the highest intensity on the 200 au redshifted blueshifted scales, respectively.
Figure 1.Example maps in BOPS survey.First column: 870 µm dust polarization intensity in color scale overlaid with the redshifted and blueshifted outflow lobes (obtained from the 12 CO (3-2) line), polarization segments, and dust continuum emission (Stokes I) contours.Blue contours indicate the blueshifted outflow, while red contours are redshifted outflow, with counter levels set at 5 times the outflow rms × (1, 2, 4, 8, 16, 32).The magenta segments represent the polarization.The regions of polarization intensity less than 3σ have been masked.Second column: the velocity field in color scale (obtained from the C 17 O (3-2) line) overlaid with the B-field segments (i.e., polarization rotated by 90 • ) and Stokes I contours.Third column: an enlarged perspective of 1000 au of the second column.In the second and third panels, the black segments represent the B-fields.The red and blue arrows indicate the mean direction of the red-shifted and blue-shifted outflows.For the velocity field, regions with an S/N less than 4 have been flagged.The grey arrows in the second and third columns indicate the mean B-field directions weighted by the intensity including all the polarization segments, and weighted by the uncertainty within annular region of 400-1000 au, respectively.In the first, second, and third columns, the black contour levels for the Stokes I image are 10 times the rms × (1, 2, 4, 8, 16,  32, 64, 128, 256, 512).The black dotted square in the first column corresponds to 2000 au scale, while the black dashed, and solid circles correspond to scales of 1000 au, and 400 au, respectively.Fourth column: C 17 O position-velocity (PV) diagram perpendicular to the outflow direction.The color scale indicates the total intensity of C 17 O line.Black solid contour levels are 3 times of the intensity rms × (1, 2, 4, 8, 16, 32, 64), while dashed contours are set at 3 times of the intensity rms × (-1, -2, -4).Vertical dashed lines represent a scale of 400 au, with a blue line indicating a blueshifted offset of 200 au and a red line indicating a redshifted offset of 200 au.The red and blue horizontal lines indicate the velocity values corresponding to the positions with the highest intensity on the 200 au redshifted blueshifted scales, respectively.

Figure 3 .
Figure 3. Number of protostars for different types of B-field morphology.In the first column, green rings indicate protoplanetary envelope (disk for self-scattering), star symbols located at the center indicate protostars.Red and blue arrows indicate the outflow directions.Black curves and segments indicate the B-field orientation, while magenta segments indicate polarization direction.HOPS-250, does not have 4σ polarization detection within annular region from 400 to 1000 au scale, is included in the type of Not enough data, which is marked by the asterisk symbol.

Figure 4 .
Figure 4. Distribution between the uncertainty-weighted mean B-field direction ⟨θ B ⟩ σ and outflow direction θ Out (left panel), and between the mean B-field ⟨θ B ⟩ σ and disk orientation θ Disk (right panel).In both panels, yellow stripes indicate cases where the two vectors are perpendicular to each other (67.• 5 ≤ |θ Diff | ≤ 90 • ), while green stripes represent cases where the two vectors are aligned (|θ Diff | ≤ 22. • 5).Blue dots and red crosses indicate protostars with and without clear disk orientation, respectively.However, in Perp-Type sources, a correlation between the Bfield and outflow is evident, with a correlation coefficient of 0.83 between |⟨θ B ⟩ σ − 90 • | and outflow position angle θ Out .Specifically, 75.0%(±12.5%) of the sources show a trend that the B-field is perpendicular to the outflow.We obtained the disk orientation of 20 sources from Tobin et al. (2020), 5 in Perp-Type, 5 in Nonperp-Type, and 10 in Unres-Type.As shown in the right panel of Figure4, due to the small sample size in each group, it is difficult to

Figure 5 .
Figure 5. Cumulative distribution function of the projected angles.The red polyline is the observed angle difference between the outflow direction θ Out and uncertainty-weighted mean B-field direction ⟨θ B ⟩ σ .The black solid line, dashed curve, and dotted-dashed curve indicate Monte Carlo simulations of the expected projected angle for two vectors that are 3D random (difference angle of two vector is between 0 • and 90 • ), parallel (0 • -22.• 5), and perpendicular (67.• 5-90 • ), respectively.
B.H., J.M.G. and A.S.-M.acknowledge support by the grant PID2020-117710GB-I00 (MCI-AEI-FEDER, UE).B.H. also acknowledges financial support from the China Scholarship Council (CSC) under grant No. 202006660008.This work is also partially supported by the program Unidad de Excelencia María de Maeztu CEX2020-001058-M.A.S.-M.acknowledges support from the RyC2021-032892-I grant funded by MCIN/AEI/10.13039/501100011033and by the European Union 'Next GenerationEU'/PRTR.E.G.C. acknowledges support from the National Science Foundation through the NSF MPS Ascend Fellowship Grant number 2213275.L.W.L. acknowledges support by NSF AST-1910364 and NSF AST-2307844.P.S. was partially supported by a Grant-in-Aid for Scientific Research (KAK-ENHI Number JP22H01271 and JP23H01221) of JSPS.W.K. was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2021R1F1A1061794).Z.Y.L. acknowledges support in part by NASA 80NSSC20K0533 and NSF AST-2307199.This paper makes use of the following ALMA data: ADS/JAO.ALMA#2019.1.00086.ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile.The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ.APPENDIX A.

Figure 6 .
Figure 6.Diagram to identify the position angle of outflows.

Figure 7 .
Figure 7. Self-scattering dominated protostars.First column: 870 µm dust polarization intensity in color scale overlaid with redshifted and blueshifted outflow lobes (obtained from the 12 CO (3-2) line), the polarization segments, and the dust continuum emission (Stokes I) contours.Blue contours indicate the blueshifted outflow, while red contours are redshifted outflow, with counter levels set at 5 times the outflow rms × (1,2, 4, 8, 16, 32).The magenta segments represent the polarization.The regions of polarization intensity less than 3σ have been masked.Second column: the velocity field in color scale (obtained from the C 17 O (3-2) line) overlaid with the polarization segments and Stokes I contours.Third column: an enlarged perspective of 1000 au of the second column.The magenta arrow indicates the mean polarization direction weighted by the intensity within inner region of 400 au.In the second and third panels, the red and blue arrows indicate the mean direction of the redshifted and blue-shifted outflows.For the velocity field, regions with an S/N less than 4 have been flagged.In all panels, the black contour levels for the Stokes I image are 10 times the rms ×(1, 2, 4, 8, 16, 32, 64, 128, 256, 512).The black dotted square in the first column corresponds to 2000 au scale, while the black dashed circles correspond to scales of 1000 au, respectively.Black solid circle indicates the disk size of the protostars, obtained fromTobin et al. (2020).

Figure 8 .
Figure 8. Perp-Type: velocity gradient direction ⊥ outflow direction (67.5 • ≤ |θ Out − θ v | ≤ 90 • ).First column: 870 µm dust polarization intensity in color scale overlaid with the redshifted and blueshifted outflow lobes (obtained from the 12 CO (3-2) line), polarization segments, and dust continuum emission (Stokes I) contours.Blue contours indicate the blueshifted outflow, while red contours are redshifted outflow, with counter levels set at 5 times the outflow rms × (1, 2, 4, 8, 16, 32).The magenta segments represent the polarization.The regions of polarization intensity less than 3σ have been masked.Second column: the velocity field in color scale (obtained from the C 17 O (3-2) line) overlaid with the B-field segments (i.e., polarization rotated by 90 • ) and Stokes I contours.Third column: an enlarged perspective of 1000 au of the second column.In the second and third panels, the black segments represent the B-fields.The red and blue arrows indicate the mean direction of the red-shifted and blue-shifted outflows.For the velocity field, regions with an S/N less than 4 have been flagged.The grey arrows in the second and third columns indicate the mean B-field directions weighted by the intensity including all the polarization segments, and weighted by the uncertainty within annular region of 400-1000 au, respectively.In all panels, the black contour levels for the Stokes I image are 10 times the rms ×(1, 2, 4, 8, 16, 32, 64, 128, 256, 512).The black dotted square in the first column corresponds to 2000 au scale, while the black dashed, and solid circles correspond to scales of 1000 au, and 400 au, respectively.

Figure 9 .
Figure 9. Nonperp-Type: velocity gradient direction is not perpendicular to outflow direction (|θ Out − θ v | < 67.5 • ).First column: 870 µm dust polarization intensity in color scale overlaid with the redshifted and blueshifted outflow lobes (obtained from the 12 CO (3-2) line), polarization segments, and dust continuum emission (Stokes I) contours.Blue contours indicate the blueshifted outflow, while red contours are redshifted outflow, with counter levels set at 5 times the outflow rms × (1, 2, 4, 8, 16, 32).The magenta segments represent the polarization.The regions of polarization intensity less than 3σ have been masked.Second column: the velocity field in color scale (obtained from the C 17 O (3-2) line) overlaid with the B-field segments (i.e., polarization rotated by 90 • ) and Stokes I contours.Third column: an enlarged perspective of 1000 au of the second column.In the second and third panels, the black segments represent the B-fields.The red and blue arrows indicate the mean direction of the red-shifted and blue-shifted outflows.For the velocity field, regions with an S/N less than 4 have been flagged.The grey arrows in the second and third columns indicate the mean B-field directions weighted by the intensity including all the polarization segments, and weighted by the uncertainty within annular region of 400-1000 au, respectively.In all panels, the black contour levels for the Stokes I image are 10 times the rms ×(1, 2, 4, 8, 16, 32, 64, 128, 256, 512).The black dotted square in the first column corresponds to 2000 au scale, while the black dashed, and solid circles correspond to scales of 1000 au, and 400 au, respectively.

Figure 10 .
Figure 10.Unres-Type (26 including HOPS-250): velocity gradient is unresolved.First column: 870 µm dust polarization intensity in color scale overlaid with the redshifted and blueshifted outflow lobes (obtained from the 12 CO (3-2) line), polarization segments, and dust continuum emission (Stokes I) contours.Blue contours indicate the blueshifted outflow, while red contours are redshifted outflow, with counter levels set at 5 times the outflow rms × (1, 2, 4, 8, 16, 32).The magenta segments represent the polarization.The regions of polarization intensity less than 3σ have been masked.Second column: the velocity field in color scale (obtained from the C 17 O (3-2) line) overlaid with the B-field segments (i.e., polarization rotated by 90 • ) and Stokes I contours.Third column: an enlarged perspective of 1000 au of the second column.In the second and third panels, the black segments represent the B-fields.The red and blue arrows indicate the mean direction of the red-shifted and blue-shifted outflows.For the velocity field, regions with an S/N less than 4 have been flagged.The grey arrows in the second and third columns indicate the mean B-field directions weighted by the intensity including all the polarization segments, and weighted by the uncertainty within annular region of 400-1000 au, respectively.In all panels, the black contour levels for the Stokes I image are 10 times the rms ×(1, 2,  4, 8, 16, 32, 64, 128, 256, 512).The black dotted square in the first column corresponds to 2000 au scale, while the black dashed, and solid circles correspond to scales of 1000 au, and 400 au, respectively.

Figure 11 .
Figure 11.Other: protostars without clear outflows and without 3σ polarization detection.First column: 870 µm dust polarization intensity in color scale overlaid with the redshifted and blueshifted outflow lobes (obtained from the 12 CO (3-2) line), polarization segments, and dust continuum emission (Stokes I) contours.Blue contours indicate the blueshifted outflow, while red contours are redshifted outflow, with counter levels set at 5 times the outflow rms × (1, 2, 4, 8, 16, 32).The magenta segments represent the polarization.The regions of polarization intensity less than 3σ have been masked.Second column: the velocity field in color scale (obtained from the C 17 O (3-2) line) overlaid with the B-field segments (i.e., polarization rotated by 90 • ) and Stokes I contours.Third column: an enlarged perspective of 1000 au of the second column.In the second and third panels, the black segments represent the B-fields.The red and blue arrows indicate the mean direction of the red-shifted and blue-shifted outflows.For the velocity field, regions with an S/N less than 4 have been flagged.The grey arrows in the second and third columns indicate the mean B-field directions weighted by the intensity including all the polarization segments, and weighted by the uncertainty within annular region of 400-1000 au, respectively.In all panels, the black contour levels for the Stokes I image are 10 times the rms ×(1, 2,  4, 8, 16, 32, 64, 128, 256, 512).The black dotted square in the first column corresponds to 2000 au scale, while the black dashed, and solid circles correspond to scales of 1000 au, and 400 au, respectively.

Figure 12 .
Figure 12.Starless core.Color scale indicates the total intensity.
and D are intensity-weighted values of Stokes Q and U, M and K are uncertainty-weighted values of Stokes Q and U, respectively (see Appendix A for details).Note that the weighted polarization angle ⟨θ Pol ⟩ should be rotated by 90 • to infer the mean direction of B-field ⟨θ B ⟩ if the polarization arises from B-field aligned grains.The outflow direction is estimated by averaging the position angles of the redshifted and blueshifted emission, as discussed in Appendix B. The disk's major axis angles are derived from high resolution (0. ′′ 1, ∼40 au) observations as reported inTobin et al.

Table 1 .
Source properties for the entire sample.Column 2 to 13 present the Right Ascension (R.A.), Declination (Dec.),Beam Size, Position Angle (P.A.), Distance (D), Evolutionary Stage, Bolometric Luminosity (L bol ), Bolometric Temperature (T bol ), error of total intensity map (σ I ), error of 12 CO image cube (σ12 CO ), error of C 17 O image cube (σ C 17 O ), and Type of Stoke I, respectively.The values D, evolutionary stage, L bol , and T bol are obtained from Tobin et al. (

Table 1 .
Source properties for the entire sample.

Table 2 .
Spectral setup.The fourth spectral window includes C 17 O, which is marked by an asterisk symbol.

Table 4 .
Self-scattering sources.Column 2 to 6 present the outflow position angle (θ Out ), outflow mean open angle (∆θ Out ), intensity-weighted position angle of polarization within inner 400 au scale (⟨θ Pol ⟩ I ), disk orientation along the major axis (θ Disk ), and the inclination angle of the disk (θ Inc ), respectively.θ Disk and θ Inc are obtained from Tobin et al. (2020).