On the magnetic field properties of protostellar envelopes in Orion

On the Magnetic Field Properties of Protostellar Envelopes in Orion Bo Huang (黄博) 1 , Josep M. Girart 1,2 , Ian W. Stephens 3 , Manuel Fernández López 4 , Hector G. Arce 5 , John M. Carpenter 6 , Paulo Cortes 7,8 , Erin G. Cox 9 , Rachel Friesen 10 , Valentin J. M. Le Gouellec 11,28 , Charles L. H. Hull 6,12 , Nicole Karnath 13,14,15 , Woojin Kwon 16,17 , Zhi-Yun Li 18 , Leslie W. Looney 19 , S. Thomas Megeath 20 , Philip C. Myers 15 , Nadia M. Murillo 21,22 , Jaime E. Pineda 23 , Sarah Sadavoy 24 , Álvaro Sánchez-Monge 1,2 , Patricio Sanhueza 25,26 , John J. Tobin 7 , Qizhou Zhang 15 , James M. Jackson 7 , and Dominique Segura-Cox 23,27 1 Institut de Ciències de l’Espai (ICE-CSIC), Campus UAB, Can Magrans S/N, E-08193 Cerdanyola del Vallès, Catalonia, Spain; [email protected],[email protected] 2 Institut d’Estudis Espacials de Catalunya (IEEC),c/Gran Capita, 2-4, E-08034 Barcelona, Catalonia, Spain 3 Department of Earth, Environment, and Physics, Worcester State University, Worcester, MA 01602, USA 4 Instituto Argentino de Radioastronomía (CCT-La Plata, CONICET; CICPBA), C.C. No. 5, 1894, Villa Elisa, Buenos Aires, Argentina 5 Department of Astronomy, Yale University, New Haven, CT 06511, USA 6 Joint ALMA Observatory, Av. Alonso de Córdova 3107, Vitacura, Santiago, Chile 7 National Radio Astronomy Observatory, 520 Edgemont Rd., Charlottesville, VA 22093, USA 8 Joint ALMA Observatory, Alonso de Córdova 3107, Vitacura, Santiago, Chile 9 Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), 1800 Sherman Avenue, Evanston, IL 60201, USA 10 Department of Astronomy & Astrophysics, University of Toronto, 50 St. George St., Toronto, ON M5S 3H4, Canada 11 NASA Ames Research Center, Space Science and Astrobiology Division M.S. 245-6 Moffett Field, CA 94035, USA 12 National Astronomical Observatory of Japan, Alonso de Córdova 3788, Office 61B, Vitacura, Santiago, Chile 13 SOFIA Science Center, Universities Space Research Association, NASA Ames Research Center, Moffett Field, CA 94035, USA 14 Space Science Institute, 4765 Walnut St., Suite B Boulder, CO 80301, USA 15 Center for Astrophysics|Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA 16 Department of Earth Science Education, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea 17 SNU Astronomy Research Center, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea 18 Astronomy Department, University of Virginia, Charlottesville, VA 22904, USA 19 Department of Astronomy, University of Illinois, 1002 West Green Street, Urbana, IL 61801, USA 20 Department of Physics and Astronomy, University of Toledo, Toledo, OH 43606, USA 21 Instituto de Astronomía, Universidad Nacional Autónoma de México, AP106, Ensenada CP 22830, B.C., México 22 Star and Planet Formation Laboratory, RIKEN Cluster for Pioneering Research, Wako, Saitama 351-0198, Japan 23 Center for Astrochemical Studies, Max Planck Institute for Extraterrestrial Physics, D-85748 Garching, Germany 24 Department of Physics, Engineering and Astronomy, Queenʼs University, 64 Bader Lane, Kingston, ON K7L 3N6, Canada 25 National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan 26 Astronomical Science Program, The Graduate University for Advanced Studies, SOKENDAI, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan 27 Department of Astronomy, University of Texas, 2515 Speedway, Stop C1400, Austin, TX 78712, USA Received 2023 November 6; revised 2024 February 8; accepted 2024 February 9; published 2024 February 29 Abstract 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. Selfscattering 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 ×10 2 –10 3 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 C 17 O(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. Unified Astronomy Thesaurus concepts: Star formation (1569);Magnetic fields (994);Protostars (1302) 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;Pattleetal.2023). In ideal MHD models, during the collapse phase of a prestellar core, the B-field lines are drawn The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 https://doi.org/10.3847/2041-8213/ad27d4 © 2024. The Author(s). Published by the American Astronomical Society. 28 NASA Postdoctoral Program Fellow. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s)and the title of the work, journal citation and DOI. 1 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. 2016,2020;Zhaoetal.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;Lietal.2013; Hirano & Machida 2019; Machida et al. 2020).Inanycase,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 –10 4 au; e.g., Girart et al. 1999,2013; Cox et al. 2018; Galametz et al. 2018; Hull & Zhang 2019; Le Gouellec et al. 2020; Cortés et al. 2021). Hourglass-shaped B-fields have been observed around protostellar envelopes and trace gravitationally infalling material (e.g., Girart et al. 2006,2009; Qiu et al. 2014; Beltrán et al. 2019; Le Gouellec et al. 2019; Hull et al. 2020). Building on these observations, some studies developed 3D analytical models of hourglass morphology (e.g., Myers et al. 2018, 2020), further reinforcing the prevalence of this structure. However, interferometric polarization surveys toward lowand high-mass protostars 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 hundred microns; Kataoka et al. 2015,2016; Yang et al. 2016a,2016b). 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 (Stephens et al. 2017b; Kataoka et al. 2017; Sadavoy et al. 2018a; Bacciotti et al. 2018; 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 (Sadavoy et al. 2018b; Alves et al. 2018; Lee 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 starforming 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 owing to their early evolutionary stage that preserves information about their initial collapse. The B-field Orion Protostellar Survey (BOPS)used the Atacama Large Millimeter/submillimeter Array (ALMA)to observe 870 μm dust polarization toward 61 young, low-mass 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;Zhangetal.2014) probed sources at varying evolutionary stages and in different star-forming regions, thus resulting in samples that were biased and nonuniform. 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 2introduces 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. 2. 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. We targeted the brightest Class 0 sources using their Very Large Array, 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 starforming regions. Observations were made from 2019 November 29 to 2019 December 20, using the ALMA compact configurations C43-1 and C43-2 and an intermediate configuration of both, which provided baselines between about 14 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 were 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. 2 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al. Table 1 Source Properties for the Entire Sample Name R.A. Decl. Beam P.A. DClass L bol T bol σ I CO 12 s CO 17 s Type (h:m:s)(d:m:s)(arcsec ×arcsec)(deg)(pc)(L e )(K)(mJy)(mJy)(mJy)Stokes I HH212M 05:43:51.41 −01:02:53.25 0.95 ×0.70 −70.0 429.2 0 14.00 53.0 0.10 30.0 2.2 Extended HH270IRS 05:51:22.72 02:56:04.95 0.93 ×0.71 −79.0 460.0 I //0.13 95.0 1.8 Compact HOPS-10 05:35:09.05 −05:58:26.94 0.92 ×0.66 −68.8 388.2 0 3.33 46.2 0.09 25.0 2.7 Compact HOPS-11 05:35:13.43 −05:57:57.96 0.90 ×0.66 −70.2 388.3 0 9.00 48.8 0.11 53.0 2.7 Compact HOPS-12E 05:35:08.95 −05:55:55.04 0.82 ×0.66 −78.8 388.6 0 //0.11 35.0 2.4 Binary HOPS-12W 05:35:08.63 −05:55:54.70 0.92 ×0.66 −68.6 388.6 0 7.31 42.0 0.11 46.0 2.6 Binary HOPS-50 05:34:40.92 −05:31:44.79 0.89 ×0.66 −70.3 391.5 0 4.20 51.4 0.08 14.0 2.4 Compact HOPS-53 05:33:57.40 −05:23:30.05 0.82 ×0.66 −78.9 390.5 0 26.42 45.9 0.09 44.0 3.1 Extended HOPS-60 05:35:23.29 −05:12:03.50 0.82 ×0.66 −79.1 392.8 0 21.93 54.1 0.12 79.0 2.3 Compact HOPS-78 05:35:25.97 −05:05:43.43 0.82 ×0.66 −79.2 392.8 0 8.93 38.1 0.13 40.0 2.6 Extended HOPS-81 05:35:28.02 −05:04:57.41 0.90 ×0.67 −69.6 392.8 0 1.24 40.1 0.08 41.0 1.7 Compact HOPS-84 05:35:26.57 −05:03:55.20 0.91 ×0.66 −68.7 392.8 I 49.11 90.8 0.17 15.0 2.6 Compact HOPS-87N 05:35:23.42 −05:01:30.62 0.82 ×0.66 −79.6 392.7 0 36.49 38.1 0.36 54.0 2.4 Binary HOPS-87S 05:35:23.67 −05:01:40.32 0.82 ×0.66 −79.6 392.7 0 //0.36 54.0 2.4 Binary HOPS-88 05:35:22.47 −05:01:14.38 0.89 ×0.67 −70.9 392.7 0 15.81 42.4 0.18 119.0 2.2 Extended HOPS-96 05:35:29.72 −04:58:48.68 0.82 ×0.66 −79.0 392.7 0 6.19 35.6 0.11 15.0 1.8 Compact HOPS-124 05:39:19.91 −07:26:11.27 0.91 ×0.65 −69.5 398.0 0 58.29 44.8 0.37 59.0 3.0 Compact HOPS-153 05:37:57.03 −07:06:56.32 0.89 ×0.66 −71.0 387.9 0 4.43 39.4 0.07 22.0 2.0 Extended HOPS-164 05:37:00.43 −06:37:10.96 0.89 ×0.66 −70.6 385.0 0 0.58 50.0 0.07 36.0 2.1 Compact HOPS-168 05:36:18.95 −06:45:23.63 0.81 ×0.66 −80.2 383.3 0 48.07 54.0 0.10 64.0 2.5 Extended HOPS-169 05:36:36.17 −06:38:54.46 0.81 ×0.66 −80.1 384.0 0 3.91 32.5 0.10 49.0 2.1 Extended HOPS-182 05:36:18.80 −06:22:10.29 0.82 ×0.66 −80.2 385.1 0 71.12 51.9 0.07 74.0 2.1 Extended HOPS-203N 05:36:22.87 −06:46:06.68 0.82 ×0.66 −79.9 383.5 0 20.44 43.7 0.09 38.0 1.9 Multiple HOPS-203S 05:36:22.90 −06:46:09.59 0.91 ×0.65 −69.3 383.5 0 //0.12 36.0 2.6 Multiple HOPS-224 05:41:32.07 −08:40:09.87 0.88 ×0.66 −70.9 440.3 0 2.99 48.6 0.09 36.0 2.0 Compact HOPS-247 05:41:26.19 −07:56:51.95 0.88 ×0.66 −71.3 430.9 0 3.09 42.8 0.09 18.0 2.4 Compact HOPS-250 05:40:48.85 −08:06:57.16 0.91 ×0.65 −69.7 428.5 0 6.79 69.4 0.10 74.0 2.5 Compact HOPS-288 05:39:56.01 −07:30:27.67 0.81 ×0.66 −81.2 405.5 0 135.47 48.6 0.22 63.0 2.2 Extended HOPS-303 05:42:02.65 −02:07:45.99 0.94 ×0.70 −71.4 410.0 0 1.49 43.2 0.10 19.0 2.6 Extended HOPS-310 05:42:27.68 −01:20:01.40 0.93 ×0.69 −81.1 414.3 0 13.83 51.8 0.13 44.0 2.5 Compact HOPS-317N 05:46:08.60 −00:10:38.54 0.94 ×0.69 −81.9 427.1 0 4.76 47.5 0.23 85.0 2.1 Binary HOPS-317S 05:46:08.38 −00:10:43.64 0.94 ×0.69 −81.9 427.1 0 //0.23 75.0 2.1 Binary HOPS-325 05:46:39.20 00:01:12.25 0.96 ×0.70 −69.2 428.5 0 6.2 49.2 0.11 94.0 4.0 Extended HOPS-340 05:47:01.32 00:26:23.00 0.96 ×0.70 −68.6 430.9 0 1.85 40.6 0.08 32.0 2.4 Binary HOPS-341 05:47:00.92 00:26:21.45 0.96 ×0.70 −68.3 430.9 0 2.07 39.4 0.08 43.0 2.5 Binary HOPS-354 05:54:24.27 01:44:19.82 0.93 ×0.70 −81.2 355.4 0 6.57 34.8 0.07 19.0 1.4 Extended HOPS-358 05:46:07.26 −00:13:30.30 0.95 ×0.70 −70.2 426.8 0 24.96 41.7 0.13 44.0 2.6 Extended HOPS-359 05:47:24.85 00:20:59.34 0.94 ×0.71 −70.8 429.4 0 10.00 36.7 0.13 8.0 1.8 Extended HOPS-361N 05:47:04.64 00:21:47.77 0.94 ×0.69 −81.5 430.4 0 //0.56 70.0 3.2 Binary HOPS-361S 05:47:04.79 00:21:42.74 0.94 ×0.69 −81.8 430.4 0 478.99 69.0 1.15 130.0 3.0 Binary HOPS-370 05:35:27.64 −05:09:34.45 0.91 ×0.66 −68.7 392.8 I 360.86 71.5 0.21 102.0 3.6 Extended HOPS-373W 05:46:30.91 −00:02:35.20 0.95 ×0.70 −69.6 428.1 0 5.32 36.9 0.12 67.0 2.4 Binary HOPS-373E 05:46:31.11 −00:02:33.10 0.95 ×0.70 −69.6 428.1 0 //0.12 67.0 /Binary HOPS-383 05:35:29.79 −04:59:50.43 0.90 ×0.67 −69.9 392.8 0 7.83 45.8 0.07 28.0 2.0 Compact HOPS-384 05:41:44.14 −01:54:46.05 0.93 ×0.69 −80.6 409.5 0 1477.95 51.9 0.30 24.0 4.2 Extended HOPS-395 05:39:17.09 −07:24:24.64 0.81 ×0.66 −79.9 397.2 0 0.5 31.7 0.09 15.0 2.8 Extended HOPS-398 05:41:29.42 −02:21:16.44 0.96 ×0.69 −70.0 408.0 0 1.01 23.0 0.11 5.0 /Extended HOPS-399 05:41:24.94 −02:18:06.71 0.93 ×0.68 −80.6 407.9 0 6.34 31.1 0.21 67.0 2.0 Extended HOPS-400 05:42:45.26 −01:16:13.94 0.93 ×0.69 −81.2 415.4 0 2.94 35.0 0.15 50.0 1.5 Extended HOPS-401 05:46:07.73 −00:12:21.36 0.95 ×0.70 −69.6 426.9 0 0.61 26.0 0.08 16.0 2.3 Extended HOPS-402 05:46:10.04 −00:12:16.97 0.94 ×0.69 −81.5 426.9 0 0.55 24.2 0.10 4.0 /Compact HOPS-403 05:46:27.91 −00:00:52.20 0.94 ×0.69 −81.7 428.2 0 4.14 43.9 0.14 60.0 1.4 Extended HOPS-404 05:48:07.72 00:33:51.76 0.94 ×0.69 −81.2 430.1 0 0.95 26.1 0.10 6.0 2.3 Compact HOPS-407 05:46:28.26 00:19:27.90 0.97 ×0.70 −68.3 419.1 0 0.71 26.8 0.08 16.0 2.2 Extended HOPS-408 05:39:30.90 −07:23:59.80 0.89 ×0.66 −71.0 398.9 0 0.52 37.9 0.06 18.0 2.1 Extended HOPS-409 05:35:21.37 −05:13:17.93 0.89 ×0.67 −71.0 392.8 0 8.18 28.4 0.13 40.0 2.0 Compact OMC1N-45-ES 05:35:15.97 −05:20:14.28 0.91 ×0.66 −68.8 392.8 ///0.19 46.0 3.5 Binary OMC1N-45-EN 05:35:16.05 −05:20:05.78 0.91 ×0.66 −68.8 392.8 ///0.19 46.0 2.6 Binary OMC1N-4-5-W 05:34:14.26 −05:20:11.65 0.91 ×0.69 −68.9 392.8 Starless //0.12 //Unresolved OMC1N-6-7 05:35:15.70 −05:20:39.35 0.91 ×0.66 −69.4 392.8 ///0.25 98.0 3.6 Extended 3 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al. 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 selfcalibration. Then, we performed three successive rounds of phase-only self-calibration for each source to improve the image quality. The Stokes Iimage was used as a model for selfcalibration, with solution intervals set to 600, 30, and 10 s 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 self-calibration. 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 −1 in both the Stokes Qand U maps. This difference arises from the total intensity image being more dynamic range limited than the polarized intensity images. The debiased polarized intensity is defined as ()PQU QU 22 212 s=+- (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 ·()UQ0.5 arctan q =, using a 3σvalue of the polarization intensity map as a threshold. For the line data, we first applied the self-calibration solutions to the entire data set. 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 u-v plane. Finally, we performed the tclean task to produce Stokes I,Q, and Uimage cubes using self-calibrated, continuum-subtracted 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 blueand redshifted 12 CO (3–2)outflow images were obtained using a velocity range starting from +/−5kms −1 with respect to V LSR and included all channels where the emission was at least 5σ. However, in some sources (HOPS-78, HOPS-88, HOPS-124, HOPS-182, HOPS-310, HOPS-340, HOPS-341, HOPS-354, HOPS-361N, HOPS-361S, HOPS370, HOPS-384, HOPS-399, and OMC1N-6-7)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 nine protostars that had companions in one field (HH270IRS, HOPS-310, HOPS-317S, HOPS-354, HOPS-399, HOPS-400, HOPS-402, HOPS-403, and HOPS-404). 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. 3. Results Figure 1shows the results for typical protostars in the sample. Plots for the entire sample are available in Appendix B. One field, OMC1N-4-5-W, does not show polarization Table 1 (Continued) Name R.A. Decl. Beam P.A. DClass L bol T bol σ I CO 12 s CO 17 s Type (h:m:s)(d:m:s)(arcsec ×arcsec)(deg)(pc)(L e )(K)(mJy)(mJy)(mJy)Stokes I OMC1N-8-N 05:35:18.20 −05:20:48.62 0.91 ×0.66 −69.5 392.8 ///0.19 31.0 3.0 Multiple OMC1N-8-S 05:35:18.01 −05:20:55.82 0.91 ×0.66 −69.5 392.8 ///0.19 31.0 3.0 Multiple Note. Columns (2)−(13)present the R.A., decl., 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 (CO 12 s ), error of C 17 O image cube (CO 17 s ), and type of Stoke I, respectively. The values D, evolutionary stage, L bol , and T bol are obtained from Tobin et al. (2020)and Federman et al. (2023). The Stokes Itypes 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,”respectively; sources are classified as either “Binary”or “Multiple”when there are a two or more well resovled components within 10″(∼4000 au)from the peak intensity. Table 2 Spectral Setup Spectral window Channels Rest Frequency Bandwidth Spectral Resolution Velocity Resolution (GHz)(MHz)(MHz)(km s −1 ) 1: CO (3–2)1920 345.79599 468.75 0.24 0.21 2: continuum 1920 348.50000 1875.00 0.98 0.84 3: continuum 1920 334.50000 1875.00 0.98 0.88 4: continuum * 1920 336.50000 1875.00 0.98 0.87 Note. The fourth spectral window includes C 17 O, which is marked by an asterisk. 4 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al. emission or CO (3–2)outflow emission, and the dust peak intensity is weak (∼3 mJy beam −1 ), signifying that 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 three sources (HOPS-373E, HOPS-398, HOPS-402). Additionally, Figure 1. Example maps in the 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 indicate the 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 3σhave 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 Icontours. 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 redshifted and blueshifted outflows, respectively. For the velocity field, regions with an S/N less than 4 have been flagged. The gray 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 an annular region of 400–1000 au, respectively. In the first, second, and third columns, the black contour levels for the Stokes Iimage 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 a scale of 2000 au, while the black dashed and solid circles correspond to scales of 1000 and 400 au, respectively. Fourth column: C 17 O PV diagram perpendicular to the outflow direction. The color scale indicates the total intensity of the C 17 O line. Black solid contour levels are 3 times the intensity rms ×(1, 2, 4, 8, 16, 32, 64), while dashed contours are set at 3 times 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 and blueshifted scales, respectively. 5 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al. we identified two 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 component, with the other being very weak or overlapping with the other outflow lobe. The properties for the entire sample can be found in Table 1. The position angles of polarization are determined using two different methods: the total-intensity-weighted average, and the uncertainty-weighted average. The position angles of polarization weighted by intensity 〈θ Pol 〉 I and uncertainty 〈θ Pol 〉 σ can be expressed as, respectively, ⎛ ⎝⎞ ⎠⎛ ⎝⎞ ⎠ ·· () D N K M 0.5 arctan , 0.5 arctan , 1 IPol Pol qqáñ= áñ= s where Nand Dare intensity-weighted values of Stokes Qand U, respectively, and Mand Kare uncertainty-weighted values of Stokes Qand U, respectively (see Appendix Afor 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 (01, ∼40 au)observations as reported in Tobin et al. (2020). We excluded the disks with a low S/N (<5σof integrated intensity)and the almost face-on disks (with an inclination angle of <30°). The position angles of polarization (〈θ Pol 〉),B-field (〈θ B 〉), outflow (θ Out ), and disk (θ Disk )are listed in Tables 3and 4. 3.1. Self-scattering Self-scattering polarization is observed parallel to the minor axis of an inclined disk (e.g., Kataoka et al. 2015;Yangetal. 2016a,2016b; Kataoka et al. 2016;Stephensetal.2017a; Kataoka et al. 2017); 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 case the upper limits of the size of polarized emission are comparable to disk sizes, suggesting that the polarizationarisesfromdiskscales.The deconvolved major and minor axes from the Gaussian fits are consistent with the resolved disk sizes obtained from highangular-resolution data by Tobin et al. (2020).Thetoppanels of Figure 2show the distribution of the difference between the polarization direction and the outflow direction (top left panel)and the disk orientation along the major axis (top right panel)in compact polarized sources. In these two plots, for 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 outflow direction is 7°, and the median difference between polarization direction and the disk major axis is 86°.The fractional polarization of these 16 protostars is between 0.5% and 2.0%, suggesting that the compact polarization detected arises from self-scattering (e.g., Kataoka et al. 2016;Yang et al. 2017;Girartetal.2018). The outflow position angle, polarization direction, and disk orientation of these sources arelistedinTable4. 3.2. B-field at Envelope Scales We are left with 40 protostars associated with a molecular and envelope polarization emission. We do not expect selfscattering to be significant in the envelope because the emission is more isotropic and the grain size is smaller compared 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).Inthestandardhourglass category, eight protostars show the expected morphology (e.g.,Girartetal.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 nine protostars with well-organized or partial spiral patterns in their B-field structure (as in, e.g., Sanhueza et al. 2021).Inadditiontothesethreecategories, five protostars exhibit a B-field pattern that is complex, and five do not have enough data (see Table 3).Inthecaseofa 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 six protostars in our sample that have polarized emission that appears to be along streamer-like dust structures (HOPS-168, HOPS-182, HOPS-361N, HOPS-361S, HOPS-370, and OMC1N-8-N, as showninAppendixB).TheB-field in each of these protostars appears to follow the direction of this streamerlike structure. As shown by the peripheral vectors in all panels of Figure 1 (particularly in the HOPS-182 field),3σpolarized emission in some regions may be generated by noise in the data; we therefore performed a total-intensity-weighted average B-field using a 4σ QU threshold in our polarization emission data (see Appendix A). The bottom left panel of Figure 2shows 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 for 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). 3.3. 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 6 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al. Table 3 Parameters of the Entire Sample Name θ Out Δθ Out B I 1 q á ñB I 2 q á ñ〈θ B 〉 σ θ v |∇v abs |θ Disk θ Inc Type (deg)(deg)(deg)(deg)(deg)(deg)(km s −1 arcsec −1 )(deg)(deg)B-field Perp-Type HH270IRS 176.1 ±6.6 92.7 76.9 68.9 ±0.8 64.4 ±7.0 64.6 ±1.8 1.2 87.4 58.8 Rot-hourglass HOPS-78 81.0 ±5.6 69.6 176.3 172.3 ±0.5 175.0 ±3.5 153.4 ±6.6 1.3 171.1 71.4 Rot-hourglass HOPS-88 81.1 ±5.6 90.4 31.5 32.8 ±1.4 27.9 ±5.1 149.3 ±4.0 1.3 166.9 25.8 Complex HOPS-96 49.1 ±5.6 75.1 113.3 100.0 ±1.6 101.5 ±2.6 123.2 ±6.8 1.1 134.6 23.6 Spiral HOPS-124 75.4 ±5.7 66.6 127.1 153.7 ±3.0 155.9 ±9.5 164.0 ±3.6 2.8 3.3 44.4 Spiral HOPS-288 39.4 ±5.8 47.6 124.2 122.8 ±0.4 119.4 ±3.5 118.3 ±3.8 3.7 145.6 64.6 Rot-hourglass HOPS-409 19.0 ±5.6 51.8 113.9 102.3 ±1.0 92.3 ±2.3 115.7 ±2.9 2.0 115.8 69.3 Rot-hourglass OMC1N-4-5-ES 53.9 ±5.6 72.2 155.9 164.3 ±0.7 160.6 ±2.3 153.4 ±13.8 1.1 //Rot-hourglass Nonperp-Type HOPS-182 57.4 ±5.5 82.3 89.5 99.1 ±0.4 90.1 ±3.0 74.9 ±2.2 1.2 150.8 60.7 Spiral HOPS-310 136.5 ±5.9 75.0 48.9 49.3 ±0.7 46.6 ±2.6 116.7 ±3.9 2.2 45.7 58.9 Rot-hourglass HOPS-341 63.6 ±6.2 65.4 8.2 14.3 ±8.3 17.1 ±22.2 177.1 ±2.0 1.2 145.8 53.1 Not enough data HOPS-361N 26.1 ±6.2 59.7 42.0 53.6 ±0.7 71.2 ±6.4 166.4 ±2.0 3.3 130.1 66.2 Spiral HOPS-361S 26.6 ±8.7 79.8 170.4 178.3 ±2.3 166.4 ±6.7 147.7 ±5.0 1.2 14.4 54.8 Spiral HOPS-404 134.9 ±17.4 89.8 70.9 90.9 ±0.9 102.9 ±6.2 99.0 ±4.2 1.1 144.2 0 Spiral Unres-Type HOPS-11 137.9 ±5.6 42.7 145.6 150.6 ±2.0 151.9 ±7.9 1.0 94.4 22.6 Std-hourglass HOPS-12W 127.9 ±7.9 124.5 46.6 21.3 ±1.4 23.2 ±6.4 1.0 103.3 33.6 Complex HOPS-87N 173.4 ±7.0 62.7 37.5 36.1 ±0.1 42.5 ±2.0 1.0 11.1 13.5 Std-hourglass HOPS-164 64.2 ±5.5 56.4 170.2 168.3 ±4.3 166.0 ±5.0 1.0 150.8 50.5 Not enough data HOPS-168 168.4 ±5.5 89.4 65.0 64.0 ±0.9 51.8 ±3.6 1.0 127.1 46.2 Rot-hourglass HOPS-169 174.2 ±5.5 43.1 66.9 48.4 ±1.2 45.5 ±4.6 1.0 61.5 40.1 Rot-hourglass HOPS-224 79.7 ±6.3 62.0 65.9 71.4 ±1.7 73.3 ±5.4 1.0 170.4 51.6 Std-hourglass HOPS-303 66.5 ±5.9 68.5 95.6 118.6 ±2.4 120.4 ±10.7 1.0 164.0 37.7 Spiral HOPS-317N 39.4 ±6.3 94.3 75.4 79.7 ±3.5 80.2 ±1.3 1.0 48.3 25.8 Not enough data HOPS-317S 87.2 ±17.3 78.7 7.3 10.1 ±0.3 3.8 ±5.2 1.0 92.2 45.4 Rot-hourglass HOPS-325 17.1 ±6.1 56.4 157.3 154.9 ±2.1 146.1 ±5.9 1.0 119.0 25.8 Rot-hourglass HOPS-359 71.6 ±2.5 23.6 50.6 49.7 ±0.3 56.0 ±6.7 1.0 3.6 28.1 Std-hourglass HOPS-370 16.7 ±5.6 114.5 110.5 108.4 ±0.3 109.9 ±2.0 1.0 109.7 71.1 Rot-hourglass HOPS-373W 89.2 ±6.1 72.4 35.0 30.9 ±1.0 25.1 ±4.6 1.0 144.3 25.8 Std-hourglass HOPS-384 104.5 ±9.2 50.0 6.4 172.1 ±0.2 172.4 ±2.6 1.0 60.2 45.6 Spiral HOPS-395 1.4 ±8.0 54.4 44.3 2.6 ±1.0 1.5 ±4.1 1.0 79.9 0 Complex HOPS-399 163.9 ±5.8 78.0 101.5 96.4 ±0.1 96.3 ±3.6 1.0 143.6 37.9 Complex HOPS-400 81.1 ±6.0 83.8 90.1 93.3 ±0.2 95.4 ±2.7 1.0 18.5 21.3 Std-hourglass HOPS-401 69.7 ±4.3 30.8 144.4 148.4 ±1.7 148.5 ±6.3 1.0 176.9 40.4 Rot-hourglass HOPS-403 62.2 ±6.1 70.5 134.3 107.9 ±1.6 104.5 ±8.8 1.0 64.0 13.0 Spiral HOPS-407 98.9 ±7.5 39.0 88.8 88.2 ±0.3 82.4 ±2.3 1.0 173.6 38.9 Std-hourglass HOPS-408 85.7 ±8.2 83.5 17.3 10.5 ±1.0 10.2 ±1.5 1.0 157.5 31.0 Not enough data OMC1N-4-5-EN 113.7 ±5.6 35.9 76.4 74.5 ±0.6 71.2 ±2.8 1.0 // Complex OMC1N-6-7 72.7 ±5.6 103.4 18.7 12.8 ±1.5 17.2 ±5.8 1.0 //Rot-hourglass OMC1N-8-N 130.9 ±5.6 61.2 117.8 122.3 ±0.7 125.8 ±2.5 1.0 //Std-hourglass Other HOPS-250 134.5 ±6.1 98.6 142.2 // 1.0 43.4 53.6 Not enough data HOPS-373E //145.0 149.1 ±1.0 154.9 ±4.6 //144.3 25.8 Complex HOPS-398 //92.5 52.4 ±1.6 20.0 ±9.0 //10.6 30.3 Complex HOPS-402 //90.3 90.9 ±0.7 90.6 ±1.0 //58.7 47.6 Not enough data HOPS-87S 58.7 ±8.0 86.5 // / / / // / OMC1N-8-S 120.2 ±7.0 99.3 // / / / // / OMC1N-4-5-W //// / / / // / Note. Columns (2)–(11)present the outflow position angle (θ Out ), outflow mean open angle (Δθ Out ), intensity-weighted B-field position angle within the field of view (B I 1 q á ñ)and within 400–1000 au (B I 2 q á ñ), uncertainty-weighted B-field position angle within 400–1000 au (〈θ B 〉 σ ), position angle of velocity gradient (θ v ), absolute velocity gradient (|∇v abs |), disk orientation along the major axis (θ Disk ), the inclination angle of the disk (θ Inc ), and the type of B-field morphology, respectively. θ Disk and θ Inc are obtained from Tobin et al. (2020). The type of B-field is classified as Standard Hourglass (Std-hourglass), Rotated Hourglass (Rot-hourglass), Spiral, Complex, and Not enough data. 7 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al. 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 the 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 (PV)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 PV image by selecting the most redshifted/blueshifted emission at 5σat 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 (intensityweighted velocity)maps of the C 17 O(3–2)emission to derive the direction of the velocity gradient. To do so, we fita2D 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 3lists 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 are detected within the annular region of 400–1000 au: 1. Perp-Type: velocity gradient is perpendicular to the outflow (67°.5|θ Out −θ v |90°; 8 out of 39). 2. Nonperp-Type: velocity gradient is not perpendicular to the outflow (|θ Out −θ v |<67°.5; 6 out of 39). 3. Unres-Type: velocity gradient is unresolved (|∇v abs | 1.0 km s −1 arcsec −1 ; 25 out of 39). We use the uncertainty-weighted position angles of the B-field on scales of 400–1000 au (represented as 〈θ B 〉 σ )for the following analysis, which are listed in Column (6)of Table 3. The left panel of Figure 4shows 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. However, in Perp-Type sources, a correlation between the B-field 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 Figure 4, due to the small sample size in each group, it is difficult to characterize the correlation between the B-field 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. 3.4. 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 (CDF)of the observed angle difference (Hull et al. 2013,2014; Stephens et al. 2017a)and compare it with 2D simulated intersecting angles uniformly projected from a 3D space. The parallel case uses the angles randomly selected within 0 and 22°.5 in 3D and then projected onto the plane of the sky in the simulation, while the ranges 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 all 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 the probability that it is drawn from a perpendicular model is 0.615. Though the probability is higher for the perpendicular case, each model could be possible for the distribution. 4. 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 Table 4 Self-scattering Sources Name θ Out Δθ Out 〈θ Pol 〉 I θ Disk θ Inc (deg)(deg)(deg)(deg)(deg) HH212M 23.5 ±6.1 51.2 27.9 ±0.4 118.6 63.0 HOPS-10 37.6 ±5.6 75.2 30.6 ±2.3 116.6 60.0 HOPS-12E 152.5 ±5.6 41.7 147.7 ±2.9 76.6 38.9 HOPS-50 164.1 ±7.9 115.5 147.3 ±0.8 68.3 58.7 HOPS-53 14.4 ±5.6 69.9 37.5 ±2.1 128.7 44.4 HOPS-60 61.1 ±5.6 86.3 74.7 ±0.6 159.0 54.6 HOPS-81 30.0 ±5.6 72.8 52.7 ±3.1 122.0 53.1 HOPS-84 83.7 ±5.6 62.4 78.1 ±0.4 167.5 62.5 HOPS-153 127.0 ±5.6 44.6 120.8 ±0.6 32.4 75.1 HOPS-203N 139.2 ±5.5 50.6 141.1 ±0.6 50.2 67.1 HOPS-203S 97.3 ±7.8 50.2 92.9 ±1.5 175.4 53.1 HOPS-247 110.0 ±7.7 91.9 105.3 ±0.5 17.9 45.9 HOPS-340 7.2 ±6.2 55.6 24.9 ±3.6 99.7 50.5 HOPS-354 52.4 ±5.1 100.3 57.2 ±3.2 158.6 29.0 HOPS-358 156.2 ±6.1 57.5 171.5 ±0.7 81.2 74.7 HOPS-383 139.2 ±5.6 52.0 130.3 ±1.2 49.7 48.2 Note. Columns (2)–(6)present the outflow position angle (θ Out ), outflow mean open angle (Δθ Out ), intensity-weighted position angle of polarization within the 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). 8 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al. 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 thousand au. Subsequently, Zhang et al. (2014)presented SMA observations of 14 massive clumps. They also found that the B-fields, on a 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 sample 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 B-field 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 B-field axes depend on the initial angle difference between the angular momentum and the B-field axes, as well as 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 a 1000 au scale. We find similar results for 7 out of 14 sources with strong velocity gradients (the Perp-Type and the Nonperp-Type): their B-field direction is perpendicular to the outflow axis. Several BOPS protostars shows the expected hourglass B-field 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 Figure 2. Histograms of 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 (top panels)and for the rest of the protostars with extended polarized emission (bottom panels). Top panels: histogram of the angle 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 the histogram in the top right panel, one disk, from HOPS-354, is not included because the disk is probably nearly face-on. Bottom panels: histogram of the angle difference between the outflow direction θ Out and the intensity-weighted average B-field direction using all the detected polarized emission B I 1 q á ñ(left)and within an annular region with inner and outer radii of 400 and 1000 au B I 2 q á ñ(right), respectively. HOPS-250 is not included in the bottom right panel because there is no 4σpolarization detection within the annular region. 9 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al. 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 indicate the 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 3σhave 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 Icontours. 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 redshifted and blueshifted outflows, respectively. For the velocity field, regions with an S/N less than 4 have been flagged. The gray 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 an annular region of 400–1000 au, respectively. In all panels, the black contour levels for the Stokes Iimage 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 a scale of 2000 au, while the black dashed and solid circles correspond to scales of 1000 and 400 au, respectively. 16 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al. 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 indicate the 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 3σhave 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 Icontours. 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 redshifted and blueshifted outflows, respectively. For the velocity field, regions with an S/N less than 4 have been flagged. The gray 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 an annular region of 400–1000 au, respectively. In all panels, the black contour levels for the Stokes Iimage 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 a scale of 2000 au, while the black dashed and solid circles correspond to scales of 1000 and 400 au, respectively. 17 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al. 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 indicate the 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 3σhave 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 Icontours. 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 redshifted and blueshifted outflows, respectively. For the velocity field, regions with an S/N less than 4 have been flagged. The gray 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 an annular region of 400–1000 au, respectively. In all panels, the black contour levels for the Stokes Iimage 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 a scale of 2000 au, while the black dashed and solid circles correspond to scales of 1000 and 400 au, respectively. 18 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al. Figure 10. (Continued.) 19 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al. Figure 10. (Continued.) 20 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al. Figure 11. Other: protostars without clear outflows and without 3σpolarization 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 indicate the 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 3σhave 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 Icontours. 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 redshifted and blueshifted outflows, respectively. For the velocity field, regions with an S/N less than 4 have been flagged. The gray 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 an annular region of 400–1000 au, respectively. In all panels, the black contour levels for the Stokes Iimage 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 a scale of 2000 au, while the black dashed and solid circles correspond to scales of 1000 and 400 au, respectively. 21 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al. Appendix C C 17 O Opacity and Velocity Gradient The opacity of C 17 O(3–2)is calculated by ⎜⎟ ⎛ ⎝⎞ ⎠ () ( ) () T JT JT ln 1 , C1 R EX cmb t=- - - n nn where T cmb =2.722 K is the cosmic microwave background temperature, and J ν (T)is the Rayleigh–Jeans equivalent temperature of a blackbody at temperature T: ()[] [] [] ·()JT h ke Kmkgs mkgs K 1 1.C2 hkT 22 221 n =- nn - -- Assuming that the Rayleigh–Jeans approximation is accurate, the observable source radiation temperature T R is estimated as ·· [] [· ] ()TI 1222 mJy beam GHz arcsec ,C3 R2maj min 1 22 nq q = - where θ maj and min q are the major and minor axes of the restoring beam, respectively, and Iis the peak of the C 17 O spectral line. The excitation temperature for an optically thick molecular line is estimated by ⎜⎟ ⎛ ⎝⎞ ⎠ ·() ()Th k hk TJT ln . C4 R EX cmb nn =+n 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 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 0.04–0.26, 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): ()vv v v,C5 lsr 0 ad=D+D+ ad where Δαand Δδare the offsets in R.A. and decl., respectively, and v α and v δ are the projections of the velocity gradient onto the αand δaxes. 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 () ()vvarctan . C6 v q=da The uncertainty is from a least-squares fit of Equation (C5)to the observed velocity field. ORCID iDs Bo Huang (黄博)https://orcid.org/0000-0001-7393-8583 Josep M. Girart https://orcid.org/0000-0002-3829-5591 Ian W. Stephens https://orcid.org/0000-0003-3017-4418 Manuel Fernández López https://orcid.org/0000-00015811-0454 Hector G. Arce https://orcid.org/0000-0001-5653-7817 John M. Carpenter https://orcid.org/0000-0003-2251-0602 Paulo Cortes https://orcid.org/0000-0002-3583-780X Erin G. Cox https://orcid.org/0000-0002-5216-8062 Rachel Friesen https://orcid.org/0000-0001-7594-8128 Valentin J. M. Le Gouellec https://orcid.org/0000-00025714-799X Charles L. H. Hull https://orcid.org/0000-0002-8975-7573 Nicole Karnath https://orcid.org/0000-0003-3682-854X Woojin Kwon https://orcid.org/0000-0003-4022-4132 Zhi-Yun Li https://orcid.org/0000-0002-7402-6487 Leslie W. Looney https://orcid.org/0000-0002-4540-6587 S. Thomas Megeath https://orcid.org/0000-0001-7629-3573 Philip C. Myers https://orcid.org/0000-0002-2885-1806 Jaime E. Pineda https://orcid.org/0000-0002-3972-1978 Sarah Sadavoy https://orcid.org/0000-0001-7474-6874 Álvaro Sánchez-Monge https://orcid.org/0000-00023078-9482 Patricio Sanhueza https://orcid.org/0000-0002-7125-7685 John J. Tobin https://orcid.org/0000-0002-6195-0152 Qizhou Zhang https://orcid.org/0000-0003-2384-6589 James M. Jackson https://orcid.org/0000-0002-3466-6164 Dominique Segura-Cox https://orcid.org/0000-00033172-6763 References Allen, A., Li, Z.-Y., & Shu, F. H. 2003, ApJ,599, 363 Alves, F. O., Cleeves, L. I., Girart, J. M., et al. 2020, ApJL,904, L6 Alves, F. O., Girart, J. M., Padovani, M., et al. 2018, A&A,616, A56 Andersson, B. G., Lazarian, A., & Vaillancourt, J. E. 2015, ARA&A,53, 501 Arce-Tord, C., Louvet, F., Cortes, P. C., et al. 2020, A&A,640, A111 Bacciotti, F., Girart, J. M., Padovani, M., et al. 2018, ApJL,865, L12 Beltrán, M. T., Padovani, M., Girart, J. M., et al. 2019, A&A,630, A54 Briggs, D. S. 1995, PhD thesis, New Mexico Institute of Mining and Technology CASA Team, Bean, B., Bhatnagar, S., et al. 2022, PASP,134, 114501 Ciolek, G. E., & Mouschovias, T. C. 1994, ApJ,425, 142 Cortés, P. C., Sanhueza, P., Houde, M., et al. 2021, ApJ,923, 204 Cox, E. G., Harris, R. J., Looney, L. W., et al. 2018, ApJ,855, 92 Dapp, W. B., & Basu, S. 2010, A&A,521, L56 Eisner, J. A., Bally, J. M., Ginsburg, A., & Sheehan, P. D. 2016, ApJ,826, 16 Federman, S., Megeath, S. T., Tobin, J. J., et al. 2023, ApJ,944, 49 Fernández-López, M., Girart, J. M., López-Vázquez, J. A., et al. 2023, ApJ, 956, 82 Figure 12. Starless core. Color scale indicates the total intensity. 22 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al. Furlan, E., Fischer, W., Ali, B., et al. 2016, ApJS,224, 5 Galametz, M., Maury, A., Girart, J. M., et al. 2018, A&A,616, A139 Galametz, M., Maury, A., Girart, J. M., et al. 2020, A&A,644, A47 Galli, D., Lizano, S., Shu, F. H., & Allen, A. 2006, ApJ,647, 374 Girart, J. M., Beltrán, M. T., Zhang, Q., Rao, R., & Estalella, R. 2009, Sci, 324, 1408 Girart, J. M., Crutcher, R. M., & Rao, R. 1999, ApJL,525, L109 Girart, J. M., Fernández-López, M., Li, Z. Y., et al. 2018, ApJL,856, L27 Girart, J. M., Frau, P., Zhang, Q., et al. 2013, ApJ,772, 69 Girart, J. M., Rao, R., & Marrone, D. P. 2006, Sci,313, 812 Goodman, A. A., Benson, P. J., Fuller, G. A., & Myers, P. C. 1993, ApJ,406, 528 Hennebelle, P., Commerçon, B., Chabrier, G., & Marchand, P. 2016, ApJL, 830, L8 Hennebelle, P., Commerçon, B., Lee, Y.-N., & Charnoz, S. 2020, A&A, 635, A67 Hirano, S., & Machida, M. N. 2019, MNRAS,485, 4667 Hoang, T., & Lazarian, A. 2009, ApJ,697, 1316 Hull, C. L. H., Le Gouellec, V. J. M., Girart, J. M., Tobin, J. J., & Bourke, T. L. 2020, ApJ,892, 152 Hull, C. L. H., & Plambeck, R. L. 2015, JAI,4, 1550005 Hull, C. L. H., Plambeck, R. L., Bolatto, A. D., et al. 2013, ApJ,768, 159 Hull, C. L. H., Plambeck, R. L., Kwon, W., et al. 2014, ApJS,213, 13 Hull, C. L. H., Yang, H., Li, Z.-Y., et al. 2018, ApJ,860, 82 Hull, C. L. H., & Zhang, Q. 2019, FrASS,6, 3 Joos, M., Hennebelle, P., & Ciardi, A. 2012, A&A,543, A128 Kataoka, A., Muto, T., Momose, M., Tsukagoshi, T., & Dullemond, C. P. 2016, ApJ,820, 54 Kataoka, A., Muto, T., Momose, M., et al. 2015, ApJ,809, 78 Kataoka, A., Tsukagoshi, T., Pohl, A., et al. 2017, ApJL,844, L5 Kounkel, M., Hartmann, L., Loinard, L., et al. 2017, ApJ,834, 142 Kwon, W., Stephens, I. W., Tobin, J. J., et al. 2019, ApJ,879, 25 Lada, C. J., & Lada, E. A. 2003, ARA&A,41, 57 Le Gouellec, V. J. M., Hull, C. L. H., Maury, A. J., et al. 2019, ApJ,885, 106 Le Gouellec, V. J. M., Maury, A. J., Guillet, V., et al. 2020, A&A,644, A11 Lee, C.-F., Li, Z.-Y., Ching, T.-C., Lai, S.-P., & Yang, H. 2018, ApJ,854, 56 Li, Z.-Y., Krasnopolsky, R., & Shang, H. 2013, ApJ,774, 82 Liu, Y., Takahashi, S., Machida, M., et al. 2023, arXiv:2312.13573 Machida, M. N., Hirano, S., & Kitta, H. 2020, MNRAS,491, 2180 Machida, M. N., Inutsuka, S.-i., & Matsumoto, T. 2007, ApJ,670, 1198 Maury, A., Hennebelle, P., & Girart, J. M. 2022, FrASS,9, 949223 Maury, A. J., Girart, J. M., Zhang, Q., et al. 2018, MNRAS,477, 2760 Myers, P. C., Basu, S., & Auddy, S. 2018, ApJ,868, 51 Myers, P. C., Stephens, I. W., Auddy, S., et al. 2020, ApJ,896, 163 Ohashi, S., Kataoka, A., Nagai, H., et al. 2018, ApJ,864, 81 Pattle, K., Fissel, L., Tahani, M., Liu, T., & Ntormousi, E. 2023, in ASP Conf. Ser. 534, Protostars and Planets VII, ed. S. Inutsuka et al. (San Francisco, CA: ASP),193 Pineda, J. E., Segura-Cox, D., Caselli, P., et al. 2020, NatAs,4, 1158 Pudritz, R. E., & Ray, T. P. 2019, FrASS,6, 54 Qiu, K., Zhang, Q., Menten, K. M., et al. 2014, ApJL,794, L18 Sadavoy, S. I., Myers, P. C., Stephens, I. W., et al. 2018a, ApJ,859, 165 Sadavoy, S. I., Myers, P. C., Stephens, I. W., et al. 2018b, ApJ,869, 115 Sanhueza, P., Girart, J. M., Padovani, M., et al. 2021, ApJL,915, L10 Shimajiri, Y., Sakai, T., Tsukagoshi, T., et al. 2013, ApJL,774, L20 Soler, J. D., Ade, P. A. R., Angilè, F. E., et al. 2017, A&A,603, A64 Stephens, I. W., Dunham, M. M., Myers, P. C., et al. 2017a, ApJ,846, 16 Stephens, I. W., Yang, H., Li, Z.-Y., et al. 2017b, ApJ,851, 55 Stutz, A., Tobin, J., Stanke, T., et al. 2013, in Protostars and Planets VI Posters, ed. H. Beuther, R. S. Klessen, C. P. Dullemond, & T. Henning (Tucson, AZ: Univ. of Arizona Press) Tobin, J. J., Hartmann, L., Chiang, H.-F., et al. 2011, ApJ,740, 45 Tobin, J. J., Sheehan, P. D., Megeath, S. T., et al. 2020, ApJ,890, 130 Vaillancourt, J. E. 2006, PASP,118, 1340 Wang, W., Väisälä, M. S., Shang, H., et al. 2022, ApJ,928, 85 Yang, H., Li, Z.-Y., Looney, L., & Stephens, I. 2016a, MNRAS,456, 2794 Yang, H., Li, Z.-Y., Looney, L. W., Girart, J. M., & Stephens, I. W. 2017, MNRAS,472, 373 Yang, H., Li, Z.-Y., Looney, L. W., et al. 2016b, MNRAS,460, 4109 Yang, H., Li, Z.-Y., Stephens, I. W., Kataoka, A., & Looney, L. 2019, MNRAS,483, 2371 Zhang, Q., Qiu, K., Girart, J. M., et al. 2014, ApJ,792, 116 Zhao, B., Caselli, P., Li, Z.-Y., et al. 2020, MNRAS,492, 3375 23 The Astrophysical Journal Letters, 963:L31 (23pp), 2024 March 1 Huang et al.