# B-fields in Star-Forming Region Observations (BISTRO): Magnetic Fields in
the Filamentary Structures of Serpens Main

Woojin Kwon Department of Earth Science Education, Seoul National University,
1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea  SNU Astronomy Research
Center, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826,
Republic of Korea  Kate Pattle Department of Physics and Astronomy, University
College London, Gower Street, London WC1E 6BT, United Kingdom  Centre for
Astronomy, School of Physics, National University of Ireland Galway,
University Road, Galway H91 TK33, Ireland  Sarah Sadavoy  Department for
Physics, Engineering Physics and Astrophysics, Queen’s University, Kingston,
ON, K7L 3N6, Canada  Charles L. H. Hull National Astronomical Observatory of
Japan, Alonso de Córdova 3788, Office 61B, Vitacura, Santiago, Chile  Joint
ALMA Observatory, Alonso de Córdova 3107, Vitacura, Santiago, Chile  NAOJ
Fellow  Doug Johnstone NRC Herzberg Astronomy and Astrophysics, 5071 West
Saanich Road, Victoria, BC V9E 2E7, Canada  Department of Physics and
Astronomy, University of Victoria, Victoria, BC V8W 2Y2, Canada  Derek Ward-
Thompson Jeremiah Horrocks Institute, University of Central Lancashire,
Preston PR1 2HE, UK  James Di Francesco NRC Herzberg Astronomy and
Astrophysics, 5071 West Saanich Road, Victoria, BC V9E 2E7, Canada  Department
of Physics and Astronomy, University of Victoria, Victoria, BC V8W 2Y2, Canada
Patrick M. Koch Academia Sinica Institute of Astronomy and Astrophysics, No.1,
Sec. 4., Roosevelt Road, Taipei 10617, Taiwan  Ray Furuya  Tokushima
University, Minami Jousanajima-machi 1-1, Tokushima 770-8502, Japan  Institute
of Liberal Arts and Sciences Tokushima University, Minami Jousanajima-machi
1-1, Tokushima 770-8502, Japan  Yasuo Doi Department of Earth Science and
Astronomy, Graduate School of Arts and Sciences, The University of Tokyo,
3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan  Valentin J. M. Le Gouellec  SOFIA
Science Center, Universities Space Research Association, NASA Ames Research
Center, Moffett Field, California 94035, USA  Université Paris-Saclay, CNRS,
CEA, Astrophysique, Instrumentation et Modélisation de Paris-Saclay, 91191
Gif-sur-Yvette, France  Jihye Hwang Korea Astronomy and Space Science
Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea
University of Science and Technology, Korea, 217 Gajeong-ro, Yuseong-gu,
Daejeon 34113, Republic of Korea  A-Ran Lyo  Korea Astronomy and Space Science
Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea
Archana Soam SOFIA Science Center, Universities Space Research Association,
NASA Ames Research Center, Moffett Field, California 94035, USA  Xindi Tang
Xinjiang Astronomical Observatory, Chinese Academy of Sciences, 830011 Urumqi,
Peopleʼs Republic of China  Thiem Hoang  Korea Astronomy and Space Science
Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea
University of Science and Technology, Korea, 217 Gajeong-ro, Yuseong-gu,
Daejeon 34113, Republic of Korea  Florian Kirchschlager Department of Physics
and Astronomy, University College London, WC1E 6BT London, UK  Chakali
Eswaraiah CAS Key Laboratory of FAST, National Astronomical Observatories,
Chinese Academy of Sciences, Peopleʼs Republic of China  Indian Institute of
Science Education and Research (IISER) Tirupati, Rami Reddy Nagar, Karakambadi
Road, Mangalam (P.O.), Tirupati 517 507, India  Lapo Fanciullo Academia Sinica
Institute of Astronomy and Astrophysics, No.1, Sec. 4., Roosevelt Road, Taipei
10617, Taiwan  Kyoung Hee Kim Korea Astronomy and Space Science Institute, 776
Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea  Takashi Onaka
Department of Physics, Faculty of Science and Engineering, Meisei University,
2-1-1 Hodokubo, Hino, Tokyo 1191-8506, Japan  Department of Astronomy,
Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku,
Tokyo 113-0033, Japan  Vera Könyves  Jeremiah Horrocks Institute, University
of Central Lancashire, Preston PR1 2HE, UK  Ji-hyun Kang Korea Astronomy and
Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055,
Republic of Korea  Chang Won Lee (이창원) Korea Astronomy and Space Science
Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea
University of Science and Technology, Korea, 217 Gajeong-ro, Yuseong-gu,
Daejeon 34113, Republic of Korea  Motohide Tamura Department of Astronomy,
Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku,
Tokyo 113-0033, Japan  Astrobiology Center, National Institutes of Natural
Sciences, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  National Astronomical
Observatory of Japan, National Institutes of Natural Sciences, Osawa, Mitaka,
Tokyo 181-8588, Japan  Pierre Bastien Centre de recherche en astrophysique du
Québec & département de physique, Université de Montréal, C.P. 6128 Succ.
Centre-ville, Montréal, QC, H3C 3J7, Canada  Tetsuo Hasegawa (長谷川哲夫) National
Astronomical Observatory of Japan, National Institutes of Natural Sciences,
Osawa, Mitaka, Tokyo 181-8588, Japan  Shih-Ping Lai  Institute of Astronomy
and Department of Physics, National Tsing Hua University, Hsinchu 30013,
Taiwan  Academia Sinica Institute of Astronomy and Astrophysics, No.1, Sec.
4., Roosevelt Road, Taipei 10617, Taiwan  Keping Qiu School of Astronomy and
Space Science, Nanjing University, 163 Xianlin Avenue, Nanjing 210023,
Peopleʼs Republic of China  Key Laboratory of Modern Astronomy and
Astrophysics (Nanjing University), Ministry of Education, Nanjing 210023,
People’s Republic of China  David Berry East Asian Observatory, 660 N. A’ohōkū
Place, University Park, Hilo, HI 96720, USA  Doris Arzoumanian  Aix Marseille
Univ, CNRS, CNES, LAM, Marseille, France  Tyler L. Bourke SKA Organisation,
Jodrell Bank, Lower Withington, Macclesfield, SK11 9FT, UK  Jodrell Bank
Centre for Astrophysics, School of Physics and Astronomy, University of
Manchester, Manchester, M13 9PL, UK  Do-Young Byun  Korea Astronomy and Space
Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of
Korea  University of Science and Technology, Korea, 217 Gajeong-ro, Yuseong-
gu, Daejeon 34113, Republic of Korea  Wen Ping Chen Institute of Astronomy,
National Central University, Zhongli 32001, Taiwan  Huei-Ru Vivien Chen
Institute of Astronomy and Department of Physics, National Tsing Hua
University, Hsinchu 30013, Taiwan  Academia Sinica Institute of Astronomy and
Astrophysics, No.1, Sec. 4., Roosevelt Road, Taipei 10617, Taiwan  Mike Chen
Department of Physics and Astronomy, University of Victoria, Victoria, BC V8W
2Y2, Canada  Zhiwei Chen  Tao-Chung Ching (慶道沖) CAS Key Laboratory of FAST,
National Astronomical Observatories, Chinese Academy of Sciences, Peopleʼs
Republic of China  National Astronomical Observatories, Chinese Academy of
Sciences, A20 Datun Road, Chaoyang District, Beijing 100012, People’s Republic
of China  Jungyeon Cho  Department of Astronomy and Space Science, Chungnam
National University, 99 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of
Korea  Yunhee Choi  Korea Astronomy and Space Science Institute, 776
Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea  Minho Choi  Korea
Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon
34055, Republic of Korea  Antonio Chrysostomou  SKA Organisation, Jodrell
Bank, Lower Withington, Macclesfield, SK11 9FT, UK  Eun Jung Chung Department
of Astronomy and Space Science, Chungnam National University, 99 Daehak-ro,
Yuseong-gu, Daejeon 34134, Republic of Korea  Simon Coudé SOFIA Science
Center, Universities Space Research Association, NASA Ames Research Center,
Moffett Field, California 94035, USA  Sophia Dai  National Astronomical
Observatories, Chinese Academy of Sciences, A20 Datun Road, Chaoyang District,
Beijing 100012, People’s Republic of China  Pham Ngoc Diep Vietnam National
Space Center, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet,
Hanoi, Vietnam  Yan Duan  National Astronomical Observatories, Chinese Academy
of Sciences, A20 Datun Road, Chaoyang District, Beijing 100012, People’s
Republic of China  Hao-Yuan Duan  Institute of Astronomy and Department of
Physics, National Tsing Hua University, Hsinchu 30013, Taiwan  David Eden
Astrophysics Research Institute, Liverpool John Moores University, IC2,
Liverpool Science Park, 146 Brownlow Hill, Liverpool, L3 5RF, UK  Jason Fiege
Department of Physics and Astronomy, The University of Manitoba, Winnipeg,
Manitoba R3T2N2, Canada  Laura M. Fissel Department for Physics, Engineering
Physics and Astrophysics, Queen’s University, Kingston, ON, K7L 3N6, Canada
Erica Franzmann  Department of Physics and Astronomy, The University of
Manitoba, Winnipeg, Manitoba R3T2N2, Canada  Per Friberg  East Asian
Observatory, 660 N. A’ohōkū Place, University Park, Hilo, HI 96720, USA
Rachel Friesen  National Radio Astronomy Observatory, 520 Edgemont Road,
Charlottesville, VA 22903, USA  Gary Fuller  Jodrell Bank Centre for
Astrophysics, School of Physics and Astronomy, University of Manchester,
Oxford Road, Manchester, M13 9PL, UK  Tim Gledhill School of Physics,
Astronomy & Mathematics, University of Hertfordshire, College Lane, Hatfield,
Hertfordshire AL10 9AB, UK  Sarah Graves  East Asian Observatory, 660 N.
A’ohōkū Place, University Park, Hilo, HI 96720, USA  Jane Greaves  School of
Physics and Astronomy, Cardiff University, The Parade, Cardiff, CF24 3AA, UK
Matt Griffin  School of Physics and Astronomy, Cardiff University, The Parade,
Cardiff, CF24 3AA, UK  Qilao Gu  Department of Physics, The Chinese University
of Hong Kong, Shatin, N.T., Hong Kong  Ilseung Han  Korea Astronomy and Space
Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of
Korea  University of Science and Technology, Korea, 217 Gajeong-ro, Yuseong-
gu, Daejeon 34113, Republic of Korea  Jennifer Hatchell  Physics and
Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, UK  Saeko
Hayashi  Subaru Telescope, National Astronomical Observatory of Japan, 650 N.
A’ohōkū Place, Hilo, HI 96720, USA  Martin Houde  Department of Physics and
Astronomy, The University of Western Ontario, 1151 Richmond Street, London N6A
3K7, Canada  Tsuyoshi Inoue  Department of Physics, Graduate School of
Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan  Shu-
ichiro Inutsuka Department of Physics, Graduate School of Science, Nagoya
University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan  Kazunari Iwasaki
Department of Environmental Systems Science, Doshisha University, Tatara,
Miyakodani 1-3, Kyotanabe, Kyoto 610-0394, Japan  Il-Gyo Jeong Department of
Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu
41566, Republic of Korea  Korea Astronomy and Space Science Institute, 776
Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea  Miju Kang Korea
Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon
34055, Republic of Korea  Janik Karoly  Jeremiah Horrocks Institute,
University of Central Lancashire, Preston PR1 2HE, UK  Akimasa Kataoka
Division of Theoretical Astronomy, National Astronomical Observatory of Japan,
Mitaka, Tokyo 181-8588, Japan  Koji Kawabata  Hiroshima Astrophysical Science
Center, Hiroshima University, Kagamiyama 1-3-1, Higashi-Hiroshima, Hiroshima
739-8526, Japan  Department of Physics, Hiroshima University, Kagamiyama
1-3-1, Higashi-Hiroshima, Hiroshima 739-8526, Japan  Core Research for
Energetic Universe (CORE-U), Hiroshima University, Kagamiyama 1-3-1, Higashi-
Hiroshima, Hiroshima 739-8526, Japan  Francisca Kemper European Southern
Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany  Academia
Sinica Institute of Astronomy and Astrophysics, No.1, Sec. 4., Roosevelt Road,
Taipei 10617, Taiwan  Kee-Tae Kim Korea Astronomy and Space Science Institute,
776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea  University of
Science and Technology, Korea, 217 Gajeong-ro, Yuseong-gu, Daejeon 34113,
Republic of Korea  Gwanjeong Kim Nobeyama Radio Observatory, National
Astronomical Observatory of Japan, National Institutes of Natural Sciences,
Nobeyama, Minamimaki, Minamisaku, Nagano 384-1305, Japan  Mi-Ryang Kim  Korea
Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon
34055, Republic of Korea  Shinyoung Kim  Korea Astronomy and Space Science
Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea
University of Science and Technology, Korea, 217 Gajeong-ro, Yuseong-gu,
Daejeon 34113, Republic of Korea  Jongsoo Kim Korea Astronomy and Space
Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of
Korea  University of Science and Technology, Korea, 217 Gajeong-ro, Yuseong-
gu, Daejeon 34113, Republic of Korea  Jason Kirk  Jeremiah Horrocks Institute,
University of Central Lancashire, Preston PR1 2HE, UK  Masato I.N. Kobayashi
Astronomical Institute, Graduate School of Science, Tohoku University, Aoba-
ku, Sendai, Miyagi 980-8578, Japan  Takayoshi Kusune  Jungmi Kwon Department
of Astronomy, Graduate School of Science, The University of Tokyo, 7-3-1
Hongo, Bunkyo-ku, Tokyo 113-0033, Japan  Kevin Lacaille  Department of Physics
and Astronomy, McMaster University, Hamilton, ON L8S 4M1 Canada  Department of
Physics and Atmospheric Science, Dalhousie University, Halifax B3H 4R2, Canada
Chi-Yan Law  Department of Physics, The Chinese University of Hong Kong,
Shatin, N.T., Hong Kong  Department of Space, Earth & Environment, Chalmers
University of Technology, SE-412 96 Gothenburg, Sweden  Chin-Fei Lee  Academia
Sinica Institute of Astronomy and Astrophysics, No.1, Sec. 4., Roosevelt Road,
Taipei 10617, Taiwan  Yong-Hee Lee  School of Space Research, Kyung Hee
University, 1732 Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do 17104,
Republic of Korea  East Asian Observatory, 660 N. A’ohōkū Place, University
Park, Hilo, HI 96720, USA  Hyeseung Lee  Department of Astronomy and Space
Science, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon
34134, Republic of Korea  Jeong-Eun Lee  School of Space Research, Kyung Hee
University, 1732 Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do 17104,
Republic of Korea  Sang-Sung Lee  Korea Astronomy and Space Science Institute,
776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea  University of
Science and Technology, Korea, 217 Gajeong-ro, Yuseong-gu, Daejeon 34113,
Republic of Korea  Dalei Li  Xinjiang Astronomical Observatory, Chinese
Academy of Sciences, 150 Science 1-Street, Urumqi 830011, Xinjiang, Peopleʼs
Republic of China  Di Li  CAS Key Laboratory of FAST, National Astronomical
Observatories, Chinese Academy of Sciences, Peopleʼs Republic of China;
University of Chinese Academy of Sciences, Beijing 100049, People’s Republic
of China  Hua-bai Li  Department of Physics, The Chinese University of Hong
Kong, Shatin, N.T., Hong Kong  Sheng-Jun Lin (林聖鈞) Institute of Astronomy and
Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
Sheng-Yuan Liu Academia Sinica Institute of Astronomy and Astrophysics, No.1,
Sec. 4., Roosevelt Road, Taipei 10617, Taiwan  Hong-Li Liu Department of
Astronomy, Yunnan University, Kunming, 650091, PR China  Junhao Liu (刘峻豪) East
Asian Observatory, 660 N. A’ohōkū Place, University Park, Hilo, HI 96720, USA
Tie Liu (刘铁) Key Laboratory for Research in Galaxies and Cosmology, Shanghai
Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road,
Shanghai 200030, People’s Republic of China  Xing Lu  National Astronomical
Observatory of Japan, Mitaka, Tokyo 181-8588, Japan  Steve Mairs East Asian
Observatory, 660 N. A’ohōkū Place, University Park, Hilo, HI 96720, USA
Masafumi Matsumura ((松村雅文) Faculty of Education & Center for Educational
Development and Support, Kagawa University, Saiwai-cho 1-1, Takamatsu, Kagawa,
760-8522, Japan  Brenda Matthews  NRC Herzberg Astronomy and Astrophysics,
5071 West Saanich Road, Victoria, BC V9E 2E7, Canada  Department of Physics
and Astronomy, University of Victoria, Victoria, BC V8W 2Y2, Canada  Gerald
Moriarty-Schieven NRC Herzberg Astronomy and Astrophysics, 5071 West Saanich
Road, Victoria, BC V9E 2E7, Canada  Tetsuya Nagata  Department of Astronomy,
Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
Fumitaka Nakamura  Division of Theoretical Astronomy, National Astronomical
Observatory of Japan, Mitaka, Tokyo 181-8588, Japan  SOKENDAI (The Graduate
University for Advanced Studies), Hayama, Kanagawa 240-0193, Japan  Hiroyuki
Nakanishi  Department of Physics and Astronomy, Graduate School of Science and
Engineering, Kagoshima University, 1-21-35 Korimoto, Kagoshima, Kagoshima
890-0065, Japan  Nguyen Bich Ngoc Vietnam National Space Center, Vietnam
Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, Vietnam
Graduate University of Science and Technology, Vietnam Academy of Science and
Techonology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam  Nagayoshi Ohashi
Academia Sinica Institute of Astronomy and Astrophysics, No.1, Sec. 4.,
Roosevelt Road, Taipei 10617, Taiwan  Geumsook Park  Korea Astronomy and Space
Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of
Korea  Harriet Parsons  East Asian Observatory, 660 N. A’ohōkū Place,
University Park, Hilo, HI 96720, USA  Nicolas Peretto  School of Physics and
Astronomy, Cardiff University, The Parade, Cardiff, CF24 3AA, UK  Felix
Priestley  School of Physics and Astronomy, Cardiff University, The Parade,
Cardiff, CF24 3AA, UK  Tae-Soo Pyo  SOKENDAI (The Graduate University for
Advanced Studies), Hayama, Kanagawa 240-0193, Japan  Subaru Telescope,
National Astronomical Observatory of Japan, 650 N. A’ohōkū Place, Hilo, HI
96720, USA  Lei Qian  CAS Key Laboratory of FAST, National Astronomical
Observatories, Chinese Academy of Sciences, Peopleʼs Republic of China
Ramprasad Rao  Academia Sinica Institute of Astronomy and Astrophysics, No.1,
Sec. 4., Roosevelt Road, Taipei 10617, Taiwan  Jonathan Rawlings Department of
Physics and Astronomy, University College London, WC1E 6BT London, UK  Mark G.
Rawlings East Asian Observatory, 660 N. A’ohōkū Place, University Park, Hilo,
HI 96720, USA  Gemini Observatory, NSF’s NOIRLab, 670 N. A’ohōkū Place, Hilo,
HI 96720, USA  Brendan Retter  School of Physics and Astronomy, Cardiff
University, The Parade, Cardiff, CF24 3AA, UK  John Richer  Astrophysics
Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, UK
Kavli Institute for Cosmology, Institute of Astronomy, University of
Cambridge, Madingley Road, Cambridge, CB3 0HA, UK  Andrew Rigby  School of
Physics and Astronomy, Cardiff University, The Parade, Cardiff, CF24 3AA, UK
Hiro Saito  Faculty of Pure and Applied Sciences, University of Tsukuba, 1-1-1
Tennodai, Tsukuba, Ibaraki 305-8577, Japan  Giorgio Savini  OSL, Physics &
Astronomy Dept., University College London, WC1E 6BT London, UK  Masumichi
Seta  Department of Physics, School of Science and Technology, Kwansei Gakuin
University, 2-1 Gakuen, Sanda, Hyogo 669-1337, Japan  Yoshito Shimajiri
National Astronomical Observatory of Japan, National Institutes of Natural
Sciences, Osawa, Mitaka, Tokyo 181-8588, Japan  National Astronomical
Observatory of Japan, National Institutes of Natural Sciences, Osawa, Mitaka,
Tokyo 181-8588, Japan  Hiroko Shinnaga  Department of Physics and Astronomy,
Graduate School of Science and Engineering, Kagoshima University, 1-21-35
Korimoto, Kagoshima, Kagoshima 890-0065, Japan  Mehrnoosh Tahani Dominion
Radio Astrophysical Observatory, Herzberg Astronomy and Astrophysics Research
Centre, National Research Council Canada, P. O. Box 248, Penticton, BC V2A 6J9
Canada  Ya-Wen Tang  Academia Sinica Institute of Astronomy and Astrophysics,
No.1, Sec. 4., Roosevelt Road, Taipei 10617, Taiwan  Kohji Tomisaka  Division
of Theoretical Astronomy, National Astronomical Observatory of Japan, Mitaka,
Tokyo 181-8588, Japan  SOKENDAI (The Graduate University for Advanced
Studies), Hayama, Kanagawa 240-0193, Japan  Le Ngoc Tram University of Science
and Technology of Hanoi, Vietnam Academy of Science and Technology, 18 Hoang
Quoc Viet, Hanoi, Vietnam  Yusuke Tsukamoto  Department of Physics and
Astronomy, Graduate School of Science and Engineering, Kagoshima University,
1-21-35 Korimoto, Kagoshima, Kagoshima 890-0065, Japan  Serena Viti  Physics &
Astronomy Dept., University College London, WC1E 6BT London, UK  Hongchi Wang
Purple Mountain Observatory, Chinese Academy of Sciences, 2 West Beijing Road,
210008 Nanjing, Peopleʼs Republic of China  Jia-Wei Wang Academia Sinica
Institute of Astronomy and Astrophysics, No.1, Sec. 4., Roosevelt Road, Taipei
10617, Taiwan  Anthony Whitworth School of Physics and Astronomy, Cardiff
University, The Parade, Cardiff, CF24 3AA, UK  Jintai Wu  School of Astronomy
and Space Science, Nanjing University, 163 Xianlin Avenue, Nanjing 210023,
Peopleʼs Republic of China  Jinjin Xie (謝津津) National Astronomical
Observatories, Chinese Academy of Sciences, A20 Datun Road, Chaoyang District,
Beijing 100012, People’s Republic of China  Hsi-Wei Yen  Academia Sinica
Institute of Astronomy and Astrophysics, No.1, Sec. 4., Roosevelt Road, Taipei
10617, Taiwan  Hyunju Yoo Korea Astronomy and Space Science Institute, 776
Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea  Jinghua Yuan
National Astronomical Observatories, Chinese Academy of Sciences, A20 Datun
Road, Chaoyang District, Beijing 100012, People’s Republic of China  Hyeong-
Sik Yun  School of Space Research, Kyung Hee University, 1732 Deogyeong-daero,
Giheung-gu, Yongin-si, Gyeonggi-do 17104, Republic of Korea  Tetsuya Zenko
Department of Astronomy, Graduate School of Science, Kyoto University, Sakyo-
ku, Kyoto 606-8502, Japan  Yapeng Zhang Department of Astronomy, Beijing
Normal University, Beijing100875, China  Chuan-Peng Zhang  National
Astronomical Observatories, Chinese Academy of Sciences, A20 Datun Road,
Chaoyang District, Beijing 100012, People’s Republic of China  CAS Key
Laboratory of FAST, National Astronomical Observatories, Chinese Academy of
Sciences, Peopleʼs Republic of China  Guoyin Zhang  National Astronomical
Observatories, Chinese Academy of Sciences, A20 Datun Road, Chaoyang District,
Beijing 100012, People’s Republic of China  Jianjun Zhou Xinjiang Astronomical
Observatory, Chinese Academy of Sciences, 150 Science 1-Street, Urumqi 830011,
Xinjiang, Peopleʼs Republic of China  Lei Zhu  CAS Key Laboratory of FAST,
National Astronomical Observatories, Chinese Academy of Sciences, Peopleʼs
Republic of China  Ilse de Looze  Physics & Astronomy Dept., University
College London, WC1E 6BT London, UK  Philippe André  Laboratoire AIM CEA/DSM-
CNRS-Université Paris Diderot, IRFU/Service d’Astrophysique, CEA Saclay,
F-91191 Gif-sur-Yvette, France  C. Darren Dowell  Jet Propulsion Laboratory,
M/S 169-506, 4800 Oak Grove Drive, Pasadena, CA 91109, USA  Stewart Eyres
University of South Wales, Pontypridd, CF37 1DL, UK  Sam Falle Department of
Applied Mathematics, University of Leeds, Woodhouse Lane, Leeds LS2 9JT, UK
Jean-François Robitaille Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble,
France  Sven van Loo  School of Physics and Astronomy, University of Leeds,
Woodhouse Lane, Leeds LS2 9JT, UK

(Received …; Revised …; Accepted …)

###### Abstract

We present 850 $\mu$m polarimetric observations toward the Serpens Main
molecular cloud obtained using the POL-2 polarimeter on the James Clerk
Maxwell Telescope (JCMT) as part of the B-fields In STar-forming Region
Observations (BISTRO) survey. These observations probe the magnetic field
morphology of the Serpens Main molecular cloud on about 6000 au scales, which
consists of cores and six filaments with different physical properties such as
density and star formation activity. Using the histogram of relative
orientation (HRO) technique, we find that magnetic fields are parallel to
filaments in less dense filamentary structures where $N_{H_{2}}<0.93\times
10^{22}$ cm-2 (magnetic fields perpendicular to density gradients), while
being perpendicular to filaments (magnetic fields parallel to density
gradients) in dense filamentary structures with star formation activity.
Moreover, applying the HRO technique to denser core regions, we find that
magnetic field orientations change to become perpendicular to density
gradients again at $N_{H_{2}}\approx 4.6\times 10^{22}$ cm-2. This can be
interpreted as a signature of core formation. At $N_{H_{2}}\approx 16\times
10^{22}$ cm-2 magnetic fields change back to being parallel to density
gradients once again, which can be understood to be due to magnetic fields
being dragged in by infalling material. In addition, we estimate the magnetic
field strengths of the filaments ($B_{POS}=60-300~{}\mu$G)) using the Davis-
Chandrasekhar-Fermi method and discuss whether the filaments are
gravitationally unstable based on magnetic field and turbulence energy
densities.

Interstellar medium (847), Interstellar magnetic fields (845), Interstellar
filaments (842), Molecular clouds (1072), Star formation (1569), Polarimetry
(1278), Submillimeter astronomy (1647)

††journal: ApJ††facilities: JCMT

=200

##  1 Introduction

Magnetic fields are thought to play a key role in various stages of star
formation over a large range of scales. For example, ordered magnetic fields
have been detected in molecular clouds on 0.1 pc and larger scales (e.g.,
Palmeirim et al., 2013; Li et al., 2014), suggesting that magnetic fields play
a role in forming such structures. However, interferometric observations have
shown that the magnetic fields of young stellar objects (YSOs) vary in
morphology on about 100 au and smaller scales. Surveys of large samples of
YSOs have reported that magnetic fields are randomly oriented with respect to
bipolar outflows (e.g., Hull et al., 2013, 2014), while hourglass shaped
fields have been reported toward a few of the youngest protostellar systems
(e.g., Girart et al., 2006; Stephens et al., 2013). Recent polarimetric
observations made using the Atacama Large Millimeter/submillimeter Array
(ALMA) have been revealing various detailed polarization and magnetic field
structures on scales of 100 au and smaller toward many YSOs, with high angular
resolution and sensitivity including a clear hourglass morphology (e.g., Maury
et al., 2018; Kwon et al., 2019), magnetic field structures tracing turbulence
and/or outflow cavities (e.g., Hull et al., 2017; Sadavoy et al., 2018; Le
Gouellec et al., 2019), and polarization patterns due to scattering of
mm/submm radiation by large grains (e.g., Cox et al., 2018; Lee et al., 2018;
Sadavoy et al., 2019).

The B-fields In STar forming Region Observations (BISTRO) survey (Ward-
Thompson et al., 2017) has been studying the role of magnetic fields in star
formation at submillimeter wavelengths on about 2000–7000 au scales, using the
James Clerk Maxwell Telescope (JCMT) and its polarimeter POL-2. This project
began polarimetric observations in 2016 and was completed in early 2019,
targeting 16 fields in nearby star forming regions: e.g., Orion A (Ward-
Thompson et al., 2017; Pattle et al., 2017), Ophiuchus (Kwon et al., 2018;
Soam et al., 2018; Liu et al., 2019; Pattle et al., 2019), IC 5146 (Wang et
al., 2019), Barnard 1 (Coudé et al., 2019), NGC 1333 (Doi et al., 2020), and
Auriga (Bich Ngoc et al., 2020). In addition to studies of individual regions,
Yen et al. (2020) found using all of the BISTRO data that magnetic fields are
misaligned with outflows by about $50\arcdeg$ on 0.05-0.5 pc scales. The
BISTRO project was extended to include more distant and more massive star-
forming regions (BISTRO-2; Pattle et al., 2018; Arzoumanian et al., 2020) and
to observe a wider range of evolutionary stages and star formation
environments (BISTRO-3).

As part of the BISTRO survey, this paper focuses on the Serpens Main molecular
cloud, which is located at a distance of 415 pc (Dzib et al., 2010; Herczeg et
al., 2019). Serpens Main consists of two subclusters— North-West (hereafter
NW) and South-East (SE) — and has largely been studied as an active,
intermediate-mass star-forming region. For example, several tens of YSOs have
been detected in the region by the Spitzer Space Telescope (Harvey et al.,
2007; Evans et al., 2009), and it was found that younger YSOs (Class 0/I) are
located in the central regions of the subclusters, while older YSOs (Class
II/III) are more widely distributed, and preferentially located in the SE
subcluster (Winston et al., 2007). Furthermore, the SE subcluster shows larger
velocity gradients compared to the NW subcluster (Graves et al., 2010). Lee et
al. (2014) mapped the molecular cloud at $7\arcsec$ resolution in the 3 mm
continuum and the N2H+, HCO+, and HCN (1-0) molecular lines, using the
Combined Array for Research in Millimeter-wave Astronomy (CARMA). They
identified six filamentary structures using the N2H+ (1-0) channel maps.
Interestingly, two filaments are less dense and do not have star formation
activity, while the others are dense enough for gravitational collapse and
have YSOs. The properties of, and star formation activity within, these
filaments need to be investigated alongside their magnetic fields, and are the
main topics of this paper. Previously, Matthews et al. (2009) detected linear
polarizations toward Serpens Main using the JCMT and SCUPOL (the predecessor
to POL-2), but the polarized signal was detected only in limited regions in
the centers of the two subclusters, which made it impossible to study the
magnetic fields in the filamentary structures. Conversely, Sugitani et al.
(2010) have studied the large-scale magnetic fields around the molecular cloud
using near-infrared imaging polarimetry. The detailed magnetic fields within
the molecular cloud, however, could not be studied using such data.

In this paper, we describe how the data have been taken and reduced in Section
2. Detected polarization measurements and inferred magnetic fields are
introduced in Section 3, followed by discussions on the relationships between
the physical properties of the filaments, including their magnetic fields and
star formation activities (Section 4). We address the column densities at
which the relative directions of magnetic fields and column density structures
change, in Section 4. Finally, we summarize our results in Section 5.

##  2 Observations

We observed the Serpens Main molecular cloud using the 15m-diameter JCMT, as
part of the BISTRO survey. The POL-2 polarimeter was inserted into the ray
pathway of the Submillimeter Common-User Bolometer Array 2 (SCUBA-2; Holland
et al., 2013) camera, in order to make linear polarization measurements. Both
450 $\mu$m and 850 $\mu$m measurements are taken simultaneously, but only the
850 $\mu$m data, with an angular resolution of $14\arcsec$, are used in this
study. POL-2 observations adopt a modified version of the standard SCUBA-2
DAISY pattern, scanning the sky at a speed of $8^{\prime\prime}\textrm{
s}^{-1}$ with a half-wave plate rotation speed of 2 Hz. This mode allows each
$4^{\prime\prime}$ pixel to contain samples from a full revolution of the
half-wave plate (Friberg et al., 2016), and provides 13 arcminute-diameter
mapping coverage with a central 3 arcminute-diameter area of the best
sensitivity. Two pointings have been observed, each for 14 hours (21 repeats
of 40 minutes long observing blocks) in JCMT weather band 2 ($0.05<\tau<0.08$
at 225 GHz), in order to cover the whole Serpens Main molecular cloud to good
sensitivity. The two pointings were centered on (R.A., decl.) = (18:29:59.370,
+01:12:52.00) and (18:29:49.530, +01:16:11.10) in J2000 coordinates for the
southeast (SE) and the northwest (NW) fields, respectively. The SE field was
observed in 2016 April to May, while the NW field was observed in 2017 March
to May.

Standard POL-2 data reduction procedures were followed using the
$pol2map$111http://starlink.eao.hawaii.edu/docs/sc22.htx/sc22.html routine,
which has recently been added to the Starlink software suite (Currie et al.,
2014). The $pol2map$ routine makes Stokes I (total intensity), Stokes Q, and
Stokes U maps from POL-2 time-stream data. At the final stage of making images
using $pol2map$, the
$skyloop$222http://starlink.eao.hawaii.edu/docs/sun258.htx/sun258ss72.html
algorithm, an implementation of the SCUBA-2 iterative mapmaking algorithm
$makemap$ (Chapin et al., 2013) which improves image consistency by reducing
multiple observations simultaneously, was used. We applied the ‘August 2019’
instrumental polarization (IP)
model333https://www.eaobservatory.org/jcmt/2019/08/new-ip-models-for-
pol2-data/ to the data, with our final total intensity map serving as the
model for estimating artificial polarized emission to be corrected for. In
addition to the typical POL-2 procedures (e.g., Pattle et al., 2020a),
additional steps were taken to combine the SE and NW fields. Data from the two
pointings were initially reduced separately to make initial total intensity
maps. These maps were combined to produce an initial coadded total intensity
map, which was used to generate a signal-to-noise-based mosaic mask for use in
the next step. This mask constrains the mapmaker by defining a fixed area
containing astrophysical signal (Chapin et al., 2013). The data from each
field were again reduced separately, at this stage invoking the $skyloop$
algorithm and using the mask defined based on the initial coadded $I$ map, to
generate Stokes $Q$ and $U$ maps, and an improved Stokes $I$ map. The $Q$ and
$U$ maps were corrected for instrumental polarization using the improved
Stokes $I$ map and the August 2019 IP model. Finally, the maps of the two
fields were coadded, to produce a final mosaicked set of Stokes $I$, $Q$, and
$U$ maps from which polarization fractions and directions were calculated
using the equations: $p=PI/I$ and $\psi=0.5\tan^{-1}(U/Q)$, where $p$ is
polarization fraction and $PI$ is polarized intensity. When calculating the
polarization intensities, classical de-biasing was adopted, such that
$PI=\sqrt{Q^{2}+U^{2}-\sigma^{2}}$, where
$\sigma^{2}=(Q^{2}\sigma_{Q}^{2}+U^{2}\sigma_{U}^{2})/(Q^{2}+U^{2})$. Finally,
the raw POL-2 power unit of pW was converted to intensity units of Jy beam-1
using the POL-2 flux conversion factor (FCF) of 725 Jy beam-1 pW-1, determined
by multiplying the SCUBA-2 850 $\mu$m FCF (537 Jy beam-1 pW-1; Dempsey et al.,
2013) by a factor 1.35 to account for additional losses in POL-2 at 850 $\mu$m
(Friberg et al., 2016). All the maps were made using the default $4\arcsec$
pixels, and the noise level achieved in the final total intensity map is about
4 mJy beam-1.

##  3 Results

Figure 1 shows our Stokes I, Q, and U maps, demonstrating linear polarization
signal toward Serpens Main. The noise levels achieved are 3.8, 3.1, and 2.9
mJy beam-1 respectively. As shown in the figure, linear polarizations have
been detected well over a large region, not only in the centers of the two
subclusters. Previous JCMT/SCUPOL observations also detected clear linear
polarization signal, but these detections were limited to only the central
regions (Matthews et al., 2009) due to lack of sensitivity.

The Serpens Main molecular cloud has six filamentary structures located
predominantly in the SE subcluster, as shown in the inset panel of Figure 2.
Lee et al. (2014) observed Serpens Main in the 3 mm continuum and three J=1-0
molecular lines of N2H+, HCO+, and HCN using CARMA at $7\arcsec$ resolution.
They analyzed its structures and kinematics using the dendrogram technique
(Rosolowsky et al., 2008). In particular, they identified six filamentary
structures based on the integrated intensity and channel maps of N2H+ (1-0),
which is known to trace high density regions: e.g., $n_{crit}$(N2H+ 1-0) =
$6.1\times 10^{4}~{}cm^{-3}$ at T = 10 K (Shirley, 2015). Some properties of
the filaments selected from Lee et al. (2014) are listed in Table 1, and refer
to the filaments identified in the inset panel of Figure 2. Note that there
are two types of filaments: FN1, FC1, and FC2 have no YSOs, while the other
three filaments contain YSOs. Furthermore, filaments FN1 and FC1 are less
dense and have large velocity gradients, while the other filaments are denser
and have relatively small velocity gradients. Finally, the linear densities of
the FN1 and FC1 filaments are comparable to or lower than the critical values
for isothermal, self-gravitating cylinders without magnetic support, above
which they can gravitationally contract (Ostriker, 1964; Lee et al., 2014).

Table 1: Selected physical properties of filaments

Filament | Width | $\nabla V$ | $\langle\sigma\rangle$ | $\langle\sigma\rangle_{nt}$ | N${}_{H_{2}}$ | Mass | ML | ML,crit | YSOs
---|---|---|---|---|---|---|---|---|---
| (pc) | (km s-1 pc-1) | (km s-1) | (km s-1 | ) ($\times 10^{22}$ cm-2) | ($M_{\sun}$) | ($M_{\sun}$ pc-1) | ($M_{\sun}$ pc-1) |
FN1 | 0.03 | $3.2\pm 0.08$ | 0.27 | 0.21 | 3.6 | 3.79 | 18.0 | 23.7 | no
FC1 | 0.04 | $4.8\pm 0.14$ | 0.25 | 0.24 | 3.5 | 4.76 | 28.0 | 20.0 | no
FC2 | 0.05 | $0.7\pm 0.07$ | 0.21 | 0.20 | 5.2 | 10.57 | 52.9 | 22.4 | no
FS1 | 0.04 | $0.8\pm 0.03$ | 0.13 | 0.12 | 4.3 | 16.33 | 49.5 | 19.2 | yes
FS2 | 0.03 | $1.5\pm 0.08$ | 0.24 | 0.23 | 7.9 | 17.95 | 74.8 | 20.2 | yes
FS3 | 0.03 | $0.8\pm 0.07$ | 0.23 | 0.22 | 9.3 | 14.08 | 82.8 | 20.5 | yes

Note. — All the values and information in this table come from Lee et al.
(2014), who identified the filaments using CARMA N2H+ (1-0) observations with
an angular resolution of $7\arcsec$. The columns list filament widths,
velocity gradients along the filaments ($\nabla V$), velocity dispersions
($\langle\sigma\rangle$), non-thermal velocity dispersions
($\langle\sigma\rangle_{nt}$), column densities of molecular hydrogen
(N${}_{H_{2}}$), filament masses, filament masses per length (ML), critical
filament masses per length (ML,crit), and whether YSOs are found.

Figure 1: Stokes I, Q, and U maps (left, center, and right, respectively)
toward the Serpens Main molecular cloud obtained at 850 $\mu$m using
JCMT/POL-2 as part of the BISTRO survey. The contours indicate 12 mJy beam-1
in the total intensity map, which is approximately the $3\sigma$ level.
Figure 2: Serpens Main magnetic field directions (green segments) inferred
from 850 $\mu$m JCMT POL-2 observations by rotating polarization directions by
$90\arcdeg$. The green segment lengths indicate polarization fractions; a
polarization fraction of 10% is shown by the bar at the top left. The white
bar indicates a length scale at 415 pc, the distance of Serpens Main. The
color scale and contours show the total intensity distribution. Contour levels
are 0.042, 0.362, 0.725, 1.090, 1.450, 2.170, 3.620, and 5.800 Jy beam-1. The
inset panel identifies the six filaments discussed in the text.

###  3.1 Field morphology

Magnetic fields, and specifically the field morphology projected on the plane
of sky, can be studied using polarized thermal emission from dust grains. Non-
spherical dust grains spin around their minor axes due to radiative
anisotropic torques. Within a magnetic field, such spinning grains will have
their minor axes aligned parallel to the field (e.g., Lazarian & Hoang, 2007).
Therefore, the thermal emission of non-spherical dust grains is linearly
polarized perpendicular to the field. This allows us to infer magnetic field
directions by rotating linear polarisation angle measurements by $90\arcdeg$.
Note that in contrast, at short wavelengths such as those in the optical
regime, polarization is mainly caused by preferential absorption of
unpolarised background emission by aligned grains, rather than by the emission
from grains. Thus, at those shorter wavelengths, linear polarization and
magnetic field directions are parallel to one another.

Figure 2 shows magnetic field directions projected onto the plane of sky
across Serpens Main as green segments, inferred by rotating the linear
polarization angles by 90°, overlaid on the 850$\mu$m total intensity map.
Data points with a signal-to-noise ratio (SNR) in total intensity of greater
than 30 and a polarization fraction smaller than 15% have been selected after
binning up by a factor of 3 in pixel width. This binning yields a pixel size
of $12\arcsec$, comparable to the angular resolution of $\sim 14\arcsec$. The
lengths of the segments indicate polarization fractions, which are relatively
large (up to about 10%) in the low-intensity boundary regions, and get smaller
going into the dense core regions. The polarization fractions are discussed
quantitatively in the next subsection.

The distribution of polarization directions is shown as a histogram in Figure
3. The most common direction is P.A. = $4.5\arcdeg$, suggesting that an east-
west magnetic field dominates. This direction is somewhat consistent with that
measured by Planck toward Serpens Main. We estimate an average direction of
$P.A.=-20\arcdeg$ from the Planck polarimetric data at 353 GHz (Collaboration
et al., 2016), assuming a 10 arc-minute beam at the J2000 center position of
Serpens Main, (R.A., decl.) = (18:29:55, +01:13:00). Since the histogram shown
in Figure 3 is a distribution of polarization angles measured on smaller
scales than those of the Planck data, the means of the directions are not
expected to agree entirely, and the difference of $\sim 25\arcdeg$ can be
understood. The polarization direction of Planck data matches the direction of
elongation of the Serpens Main molecular cloud, suggesting that the large-
scale magnetic field is perpendicular to the overall elongation of the
molecular gas structures. This large-scale field has also been reported in
near-infrared polarimetric observations sensitive to the periphery of the
molecular cloud (Sugitani et al., 2010).

The magnetic field directions within individual filaments with differing
physical properties are one of the key focuses of this study. Figure 2 shows
that the southern filaments, FS1, FS2, and FS3, have magnetic fields
preferentially oriented in the east-west direction. This trend suggests that
the field directions are perpendicular to these filaments overall at the
angular resolution of our data, which is too low to separate FS2 and FS3. A
similar behavior is observed in the FC2 region. In contrast, the FN1 and FC1
filaments exhibit field directions which are mainly parallel to their major
axes. Since FN1 and FC1 are less dense than the other filaments, this
difference suggests that magnetic fields are parallel to filaments in less
dense cases but perpendicular in denser ones, a result that has been reported
in many previous studies (e.g., Collaboration et al., 2016; Ward-Thompson et
al., 2017). However, magnetic field directions change dramatically at the
locations of dense cores. For example, the magnetic field seems to surround
the core located to the south of FN1, (R.A., decl.) = (18:30:02, +01:15:10).
Field direction variations are also clearly seen in the central core regions
of both the NW and SE subclusters. A detailed quantitative analysis and
discussion of the relative orientations of magnetic fields with respect to the
filaments follows in Section 4. Comparisons between the magnetic field on the
scales resolved in these data and in interferometric observations of Serpens
Main will be undertaken in a separate paper (Tang et al. in preparation).

Figure 3: A histogram of polarization position angles (P.A.) in Serpens Main.
The orange dashed line shows a Gaussian fit to the histogram, with
$\bar{\theta}=4.5\arcdeg$ and $\sigma=38.7\arcdeg$.  Figure 4: The
relationship between polarization fraction and total intensity in Serpens
Main. The black dashed, blue solid, and red solid lines denote slopes of -1,
-0.8, and -0.634, respectively.

###  3.2 Polarization fraction as a function of continuum intensity

The relationship between polarization fraction and column density (or
continuum intensity as a proxy for column density) has been used to show where
polarized dust emission originates from in star-forming clouds. Polarization
fractions depend on both grain properties and local physical conditions
(Andersson et al., 2015). In the case of linear polarization of dust thermal
emission that is used in this study, there must be a mechanism by which non-
spherical dust grains are aligned. Such mechanisms include anisotropic
radiation, subsonic or supersonic flows, and/or magnetic fields. In the
relevant case of the interstellar medium and molecular clouds whose dust
grains are still sub-micrometer to several micrometers in size, polarization
principally arises from spinning dust grains which are caused to align with
respect to the magnetic field by torques from an incident anisotropic
radiation field, i.e. both a magnetic field and an incident radiation field
are needed.

Figure 4 presents the relationship between polarization fraction and continuum
intensity in Serpens Main at 850 $\mu$m on a log-log scale. Only data points
that have a SNR in total intensity larger than 30 and a polarization fraction
smaller than 15% have been selected. The black dashed line denotes a slope of
$-1$ for reference, i.e. $p\propto I^{-1}$. The blue and red solid lines show
the trend of the highest polarization data points at each intensity ($p\propto
I^{-0.8}$; i.e., the behaviour of the upper envelope of the data points) and
the result of fitting a power law to the full sample ($p=75.6~{}I^{-0.634}$),
respectively. Note that the slopes of both the upper-envelope trend and the
fit are shallower than $-1$. If polarization were limited to the outer shell
area of the molecular cloud, the relationship between polarization fraction
and intensity would follow the reference slope of $-1$ (e.g., Jones et al.,
2015). The data points in Serpens Main, however, show a shallow slope so
polarization is not limited to the periphery of the molecular cloud; some must
originate from the dense inner regions of the cloud as well. This overall
trend of polarization fraction decreasing with intensity is well-known, and
often found in molecular clouds (e.g., Kwon et al., 2018; Soam et al., 2018;
Liu et al., 2019; Pattle et al., 2019; Wang et al., 2019; Coudé et al., 2019).
This trend is understood to result from weakening of dust grain alignment
mechanisms in high density regions, due to decreasing radiation fields and
increasing grain sizes (e.g., Hoang et al., 2020). In addition, varying
magnetic field directions along the line of sight depolarize the signal, due
to integration over multiple magnetic field components. Studies of alternative
polarization mechanisms and dust properties, which are also interesting and
important, have been carried out (e.g., Collaboration et al., 2020; Le
Gouellec et al., 2020; Pattle et al., 2020b), but are unlikely to apply on the
size scales that we consider.

We note that Pattle et al. (2019) showed that as polarization intensities are
calculated using the squared sum of Stokes Q and U values, resulting in the
noise characteristics of polarization fractions following a Ricean
distribution, an observed power-law index of $-1$ of polarization fraction as
a function of intensity may result from the non-detection of polarized
emission, raising the need for caution when interpreting such a relationship.
Our results, however, clearly show a shallower power-law index, indicating
real detections. Note that in the regime with a power-law index slope
shallower than $-1$, i.e., well-detected polarization, both the Rice
distribution and the power-law approaches are consistent with one another.

##  4 Discussion

###  4.1 Histogram of relative orientations

The relationship between magnetic fields and filamentary structures can be
studied quantitatively using the histogram of relative orientations (HRO)
technique (Soler et al., 2013; Collaboration et al., 2016), which compares
polarization directions ($\hat{E}$) against optical depth gradients
($\nabla\tau$). For the HRO technique, a histogram of relative orientations
($\phi$) between $\hat{E}$ and $\nabla\tau$ needs to be produced at each
density to be investigated. In this work, instead of using optical depth
gradients we use intensity gradients for simplicity, which is reasonable in a
small region where temperatures and dust properties are not varying
significantly. Note that in the optically thin regime, which is our case,
intensity is proportional to the product of the Planck function for blackbody
radiation and the optical depth. Thus, a 15% variation of temperature, e.g.,
between 12 K and 14 K, produces a 25% variation in intensity at 850 $\mu$m. In
addition, note that the directions of gradients are analyzed here, not the
amplitudes of gradients. Next, within the HRO the central area ($A_{c}$, where
$|\phi|<22.5\arcdeg$) and the extreme area ($A_{e}$, where
$|\phi|>67.5\arcdeg$) are calculated. Finally, the histogram shape parameter
($\xi$) is calculated:

$\xi=\frac{A_{c}-A_{e}}{A_{c}+A_{e}}.$ (1)

When the relative orientation of most data points is small, i.e., when
polarization directions are parallel to optical depth (here intensity)
gradients, $\xi$ is positive since $A_{c}>A_{e}$. In contrast, when
polarizations are perpendicular to intensity gradients, $\xi$ is negative.
Since the magnetic field direction is perpendicular to the polarization and
the filament direction is perpendicular to the intensity gradient, positive
values of the histogram shape parameter $\xi$ also imply that magnetic fields
are parallel to filaments. In the same way, negative $\xi$ values indicate
that magnetic fields are perpendicular to filaments. The uncertainties on
$\xi$ are dominated by the number of data points in each bin of the histogram
and are calculated as (Collaboration et al., 2016)

$\sigma^{2}_{\xi}=\frac{4(A_{e}^{2}\sigma_{A_{c}}^{2}+A_{c}^{2}\sigma_{A_{e}}^{2})}{(A_{c}+A_{e})^{4}}.$
(2)

Here, $\sigma_{A_{c}}$ and $\sigma_{A_{e}}$ are obtained following
$\sigma_{k}^{2}=h_{k}(1-h_{k}/h_{tot})$, where $h_{k}$ corresponds to the
number of data points in the central or extreme bin and $h_{tot}$ is the total
number of data points.

Figure 5 presents the histogram shape parameters for individual filaments as
well as for all filaments combined. The data used for the plot are gridded to
$4\arcsec$ pixels, with a SNR in total intensity larger than 3, a SNR in
polarized intensity larger than 2, a polarization angle uncertainty smaller
than $15\arcdeg$, and a polarization fraction smaller than 15%. Data points
for individual filament areas have been selected by eye based on the
identifications of Lee et al. (2014) and are presented in the left panel of
Figure 5. Note that the main trends of the HRO analysis are not changed
depending on whether a few segments are included or excluded. The column
densities ($N_{H_{2}}$) of molecular hydrogen used in this analysis are
calculated from the 850 $\mu$m dust thermal intensities ($I_{\nu}$):

$N_{H_{2}}=\frac{I_{\nu}}{\kappa_{\nu}B_{\nu}(T_{d})~{}\mu_{H_{2}}m_{H}\Omega},$
(3)

where $\kappa_{\nu}$ is the absorption coefficient at 850 $\mu$m assuming a
gas-to-dust mass ratio of 100 (0.02 cm2g-1), $T_{d}$ is the dust temperature
(12 K, Lee et al., 2014), $\mu_{H_{2}}$ is the molecular weight per hydrogen
molecule (2.8, Kauffmann et al., 2008), $m_{H}$ is the atomic hydrogen mass
($1.67\times 10^{-24}$ g), and $\Omega$ is the beam solid angle.

As shown in Figure 5 by the black solid line, the $\xi$ values using all
filament data decrease with column density. The transition from positive to
negative $\xi$ is not clear, since it happens in the first bin where the mean
intensity corresponds to $N_{H_{2}}\approx 0.93\times 10^{22}\textrm{
cm}^{-2}$. Therefore, although individual filaments reveal a range of
properties, which are addressed below, the overall transition of the magnetic
field from parallel to perpendicular within the Serpens Main filaments tends
to occur around this column density.

Individual filaments show a range of relative orientations for their
associated magnetic fields, as shown in various colors in Figure 5. First, all
the histogram shape parameters of the filament FN1 are positive (blue), which
means that the magnetic fields in FN1 are parallel to the filamentary
structure. Also, note that FN1 is the least dense-filament,
$N_{H_{2}}<3.1\times 10^{22}$ cm-2. Next, FC1 is the second least dense
filament and shows a transition from positive to negative $\xi$ values
(green), which indicates that magnetic fields are parallel to the filament in
its less dense regions but perpendicular in the relatively denser regions.
Note that the mass-per-length values of these two filaments are subcritical
(FN1) or marginally supercritical (FC1) even without considering magnetic
fields, and they have no embedded YSOs (Table 1). All the other filaments
(FC2, FS1, and FS2/3) have negative $\xi$ values, suggesting that their
magnetic fields are perpendicular to their major axes. Filaments FS2 and FS3
are not easy to separate from each other, so we consider them together.
Indeed, these two filaments are very similar in density as the densest
filaments among the sample (Table 1). We also note that there is no
significant magnetic field variation over the region in response to the
different observed filament directions.

This trend of relative magnetic field orientation changing with density has
been reported in multiple previous studies. For example, Collaboration et al.
(2016) examined the relative orientations between magnetic field directions
and column density structures by applying the HRO technique to Planck
polarimetric data at 353 GHz. Those authors found that a transition from
parallel to perpendicular orientations appears between $N_{H}\sim 0.5\times
10^{22}$ cm-2 and $\sim 5\times 10^{22}$ cm-2, consistent with our result
above.

We further investigated the magnetic field orientation by applying the HRO
analysis to all of the dense region observations. Figure 6 shows the histogram
shape parameters ($\xi$) calculated from the whole of Serpens Main including
the central subcluster areas as well as the filamentary structures. In the
figure, the regime with a column density less than $N_{H_{2}}\sim 4.6\times
10^{22}$ cm-2 is mainly that of the filamentary structures, in which the $\xi$
values decrease with density. Between $N_{H_{2}}\sim 4.6\times 10^{22}$ and
$\sim 10\times 10^{22}$ cm-2, however, the $\xi$ values increase up to zero.
This increase suggests that the magnetic fields are trending parallel to
elongated structures around a column density of $N_{H_{2}}\sim 10\times
10^{22}$ cm-2. In other words, magnetic fields become perpendicular to density
gradients (where elongated spines are defined as being orthogonal to the
direction of a density gradient). The transition can be understood as a result
of the local density gradients becoming more significant than the initial
density gradients across filaments, presumably arising from mass accumulation
of neutral species crossing magnetic field lines (ambipolar diffusion; e.g.,
Mouschovias, 1979; Hennebelle & Inutsuka, 2019). Also, this regime corresponds
to the area where filaments transition into the central hub while maintaining
their initial perpendicular fields. With increasing density, the $\xi$ values
again decrease and get back to the overall decreasing trend around
$N_{H_{2}}\sim 16\times 10^{22}$ cm-2, which indicates that magnetic fields
are again parallel to density gradients (i.e., perpendicular to “filaments”).
This behavior can be understood as magnetic field lines now being dragged
along by gravitational collapse at these high column densities.

The HRO analysis toward the Serpens Main molecular cloud nicely shows the
three transitional boundaries in column density for relative orientations of
magnetic fields with respect to the physical structures of filaments and
cores. Figure 7 summarizes the four column density regimes within the Serpens
Main molecular cloud as a schematic diagram. First, magnetic fields are
parallel to the least dense filaments, particularly where $N_{H_{2}}\lesssim
0.93\times 10^{22}$ cm-2 (region 1). This column density threshold corresponds
to $n({H_{2}})\approx 1.0\times 10^{5}$ cm-3, assuming a 0.03 pc filament
width. In contrast, denser filaments ranging from $0.93\times
10^{22}<N_{H_{2}}\lesssim 4.6\times 10^{22}$ cm-2 have magnetic fields
perpendicular to their filament structure (region 2). Where the column density
becomes larger than $N_{H_{2}}\sim 4.6\times 10^{22}$ cm-2, cores form and a
significant density gradient along a filament appears (region 3). This column
density corresponds to $n(H_{2})\approx 5.0\times 10^{5}$ cm-3, assuming cores
of about 0.03 pc in size. Note that assuming a filament width of 0.03 pc, the
critical mass per length $M_{L,crit}=20~{}M_{\sun}~{}pc^{-1}$ corresponds to
$N_{H_{2}}=3.0\times 10^{22}$ cm-2. Considering the presence of magnetic
fields, it is interesting that the column density associated with cores in
Serpens Main is larger than this value. Finally, at column densities above
$N_{H_{2}}\sim 16\times 10^{22}$ cm-2, magnetic fields are also dragged in by
frequent collisions between charged and neutral species during the dynamical
contraction, resulting in magnetic fields that are again parallel to the
density gradient (region 4). When assuming the same size scale for cores as
previously (0.03 pc), this column density threshold corresponds to
$n(H_{2})\approx 18\times 10^{5}$ cm-3 or higher.

In addition to the transition of magnetic field relative orientations between
less dense and more dense filamentary structures, this further transition
occurring at a higher density, which we recover, has recently been reported by
multiple other studies. Pillai et al. (2020) showed that magnetic fields
become parallel to filaments at a visual extinction $A_{v}\approx 20-30$
magnitude in the Serpens South cloud. That extinction is equivalent to
$N_{H}\approx 4.5\times 10^{22}-6.6\times 10^{22}$ cm-2 ($N_{H_{2}}\approx
1.6\times 10^{22}-2.4\times 10^{22}$ cm-2), based on the relation between
visual extinction and column density (Guver & Ozel, 2009). Although their
column density threshold differs from ours by a factor of 2, the transition
likely corresponds with our boundary between regions 2 and 3 (Figure 7). Also,
Wang et al. (2020) found that the filament and hub system G33.92+0.11 has a
magnetic field parallel to the gravity vector and the gas motion within the
central hub region. Since a gravity direction is comparable to a density
gradient, it appears that the hub region corresponds to region 4 of our
scenario.

Figure 5:  The left panel shows individual filament regions (Lee et al., 2014)
used in the HRO analysis, and the black contour indicates a level of 0.042 Jy
beam-1. The right panel shows the histogram shape parameter ($\xi$) for these
filaments, with the black line indicating the result using all filaments
combined.  Figure 6: Histogram shape parameters ($\xi$) of the Serpens Main
molecular cloud including both the filament and the core regions. Note that
the least dense regions have an almost positive value of $\xi$, and there is a
bump at moderate column density: $\xi$ becoming positive and decreasing again.
Refer to the text for discussion. The region numbers correspond to those in
Figure 7 and in the text.  Figure 7: Schematic diagram showing four regions
with different relationships between the magnetic field and density gradient.
Note that the green lines are magnetic field lines and the darker gray colors
indicate denser regions. The yellow vectors are polarization directions that
are perpendicular to the magnetic field lines, and the black vectors are
optical depth gradients that correspond to density gradients. The four regions
are (1) less dense filaments, (2) dense filaments, (3) core-forming regions,
and (4) regions in which the field is dragged in.

###  4.2 Field strength and star formation

Magnetic field strength, specifically the component projected on the plane of
the sky, can be estimated from linearly polarized dust thermal emission using
the Davis-Chandrasekhar-Fermi (DCF) method (Davis, 1951; Chandrasekhar &
Fermi, 1953). The DCF method estimates a field strength at a given gas density
and turbulence from the scatter of the magnetic field orientation around a
mean value. This scatter decreases in a stronger field such that:

$B_{POS}=Q\sqrt{4\pi\rho}\frac{\delta V}{\delta\phi}\approx
9.3\sqrt{n(H_{2})}\frac{\Delta V}{\delta\phi},$ (4)

where Q is a a factor of order unity, here taken to be 0.5, $\rho$ is the
density, $\delta V$ is the turbulent velocity dispersion, and $\delta\phi$ is
the magnetic field position-angle dispersion. In the rightmost expression,
$n(H_{2})$ is a number density of hydrogen molecules in cm-3, $\Delta V$ is a
FWHM linewidth in km s-1, and $\delta\phi$ is the magnetic field position-
angle dispersion in degrees, which results in a field strength measured in
$\mu$G (e.g., Ostriker et al., 2001; Crutcher et al., 2004).

Table 2 lists our estimates for the magnetic field strength within each of the
filaments in Serpens Main, using the DCF technique. The number densities are
calculated from the mean column density of the individual filaments (Fig. 5)
divided by the filament widths listed in Table 1 (Lee et al., 2014), assuming
no additional line of sight modification. Non-thermal velocity dispersions are
adopted from spectral-line observations of N2H+ made by Lee et al. (2014),
also as shown in Table 1. The model of ordered background magnetic field
morphology that is required in order to accurately calculate a field
dispersion is obtained from the Stokes Q and U maps smoothed to a resolution
of $28\arcsec$, which is equivalent to the $2\times$ larger beam. This
$28\arcsec$ resolution corresponds to 0.056 pc at the target distance, which
is reasonable for the background ordered fields of filamentary structures with
a width $\approx 0.03-0.05$ pc. The field dispersions we measure are
distributed from $14.3\arcdeg$ to $29.4\arcdeg$ and are plotted in Figure 8.
These values provide magnetic field strengths on the plane of the sky ranging
from $64-300~{}\mu$G. When estimating the uncertainty on the magnetic field
strength we assume a 50% error for the densities and use the fitting error for
the field position-angle dispersion. Combined, this results in 25–42%
uncertainty in magnetic field strength.

We also estimate the mass-to-flux ratios ($\lambda$) with respect to their
critical values, which measure whether the structures are supported by
magnetic fields or if they are expected to gravitationally contract:

$\lambda=\frac{(M/\Phi)_{obs}}{(M/\Phi)_{crit}}=7.6\times
10^{-21}\frac{N(H_{2})}{B},$ (5)

where $N(H_{2})$ is a column density of hydrogen molecules in units of
$cm^{-2}$ and $B$ is a magnetic field strength in $\mu$G (e.g., Crutcher et
al., 2004). Regions with $\lambda>1$ can gravitationally contract. The
uncertainties on $\lambda$ are calculated as
$\sigma_{\lambda}=\sqrt{(\sigma_{N}/N(H_{2}))^{2}+(\sigma_{B}/B)^{2}}$, so
they are in the range of 56–65% when adopting the uncertainties used in the
previous paragraph. Note that this measure of uncertainty provides only a
rough estimate, as we assume Gaussian distributions for the uncertainties on
column density and the magnetic field strength, which may in fact not be
independent of each other. Table 2 shows the $\lambda$ values for each
filament. Note that the values are based on only the projected magnetic field
component. Therefore, depending on the three dimensional (3D) orientation of
the magnetic fields, $\lambda$ may be smaller. We also compare the magnetic
field energy density ($P_{B}$) and the turbulence energy density ($P_{turb}$)
of individual filaments, which are respectively calculated as

$\displaystyle P_{B}$ $\displaystyle=$ $\displaystyle\frac{B^{2}}{8\pi},$ (6)
$\displaystyle P_{turb}$ $\displaystyle=$
$\displaystyle\frac{3}{2}\rho\sigma_{nt}^{2}.$ (7)

Here $\sigma_{nt}$ is non-thermal velocity dispersion. Finally, the last
column of Table 2 presents the ratio of mass-per-length to the critical value
for a cylindrical structure ignoring magnetic fields, as reported by Lee et
al. (2014) (Table 1). Values greater than 1 indicate that such a structure can
gravitationally contract.

From these measurements, we classify the filaments into three groups: {FN1,
FC1}, {FC2, FS1}, and {FS2/3}. In FN1 and FC1, the magnetic and turbulent
energy densities are comparable to each other. Note that the $\lambda$ and the
magnetic field energy density are calculated from partial components of the
fields, specifically the component projected on the plane of the sky. When the
3D orientation of the structure is considered, the total magnetic field may be
significantly larger. For example, if the 3D magnetic field strength is larger
than the plane-of-the-sky component by a factor of 2, $\lambda$ and the
magnetic field energy density become halved and quadrupled, respectively. The
FN1 and FC1 filaments both have $\lambda$ and line mass ratios either smaller
than or close to 1, which suggests that these filaments may not be able to
contract gravitationally. It is noteworthy that these filaments have no star
formation activity (no YSOs) and that they have large velocity gradients, of
3–5 km s-1 pc-1 (Table 1).

FC2 and FS1 also have magnetic field and turbulence energy densities
comparable to one another. These filaments, however, have both $\lambda$ and
mass ratios larger than 2, which suggests that they are likely to
gravitationally contract. Indeed, there are YSOs found in FS1 (Lee et al.,
2014). In the FC2 filament, there are no YSOs found, but it seems to be
gravitationally unstable. If FC2 is in fact not gravitationally unstable, our
results suggest that significant magnetic support would be required in order
to stabilize the structure. For such support to exist, based on the plane-of-
sky values of $\lambda$ that we measure, the filament would require a
significant fraction of its magnetic field to be directed along the line of
sight.

Lastly, FS2/3, which is the combined region of FS2 and FS3, has the strongest
magnetic field among the filaments. The magnetic field energy density is also
twice as large as the turbulence energy density. Therefore, magnetic fields
dominate over turbulence in this combined structure. Even with the relatively
strong magnetic field compared to turbulence, the filaments have $\lambda>1$
and evidence for YSOs, indicating that the regions remain gravitationally
unstable.

Figure 8:  Magnetic field dispersion for individual filaments and all
filaments combined. In each panel, the horizontal axis is position-angle
difference in degrees between the magnetic field direction of the non-smoothed
and smoothed data. The orange dashed lines are Gaussian functions fitted to
the histograms, whose mean and sigma values are listed in the panels.  Table
2: Magnetic field strength measures for filaments

Filament | $N_{H_{2}}$ | $n(H_{2})$ | $\delta\phi$ | $B_{POS}$ | $\lambda$ | P${}_{B_{POS}}$ | Pturb | ML/ML,crit
---|---|---|---|---|---|---|---|---
| [$\times 10^{22}~{}cm^{-2}$] | [$\times 10^{5}~{}cm^{-3}$] | [$\arcdeg$] | [$\mu$G] |  | [$\times 10^{-10}$ erg cm-3] | [$\times 10^{-10}$ erg cm-3] |
FN1 | 2.6 | 2.8 | 29.4 | $83\pm 35$ | $2.4\pm 1.6$ | 2.73 | 6.21 | 0.76
FC1 | 2.2 | 1.8 | 22.9 | $97\pm 32$ | $1.7\pm 1.0$ | 3.74 | 5.14 | 1.4
FC2 | 4.4 | 2.9 | 28.0 | $84\pm 26$ | $4.0\pm 2.4$ | 2.78 | 5.72 | 2.4
FS1 | 3.0 | 2.4 | 20.1 | $64\pm 17$ | $3.5\pm 2.0$ | 1.65 | 1.75 | 2.6
FS2/3 | 6.5 | 7.0 | 14.3 | $300\pm 75$ | $1.7\pm 0.95$ | 34.7 | 18.6 | 3.9

Note. — Only the component of the magnetic field on the plane of the sky has
been considered for the $\lambda$ and $P_{B_{POS}}$ measures.

##  5 Conclusions

We have studied the physical conditions associated with the magnetic field
within the Serpens Main molecular cloud using JCMT POL-2 850 $\mu$m
polarimetric data, with a $14\arcsec$ resolution, taken as part of the BISTRO
survey. Serpens Main consists of two subclusters containing in total of six
filamentary structures (FN1, FC1/2, FS1/2/3) encompassing a variety of
physical properties.

The most common direction of the linear polarization in Serpens Main, on $\sim
6000$ au scales, has P.A. = $4.5\arcdeg$ which suggests that the overall
magnetic fields are East-West on the plane of sky. The submillimeter
polarization fraction across Serpens Main decreases with the total intensity
as $p\propto I^{-0.634}$. A power-law index shallower than $-1$ implies that
the polarized emission is not limited to the surface of the molecular cloud.
The observed polarization fraction decrease can be understood as being the
result of weakening alignment mechanisms and/or magnetic field variations as a
function of increasing density within the cloud.

Using the HRO technique, we find that the magnetic fields are predominantly
perpendicular to the filament structures for all filaments except FN1 and FC1,
which are the least dense and have no YSOs. The field orientation transitions
from parallel ($\xi>0$) to perpendicular ($\xi<0$) with respect to the
filaments when $N_{H_{2}}\approx 0.93\times 10^{22}$ cm-2. We extend the
typical HRO analysis to explore the magnetic field within the entire cloud and
find that $\xi$ again increases at $N_{H_{2}}\approx 4.6\times 10^{22}$ cm-2,
which can be understood as the result of a density gradient along elongated
structures becoming significant (e.g., via core formation). Furthermore, $\xi$
again becomes negative at $N_{H_{2}}\approx 16\times 10^{22}$ cm-2, which is
interpreted as resulting from the magnetic field being dragged along with
increasing density.

We estimate magnetic field strengths in the filaments ranging from
$B_{POS}=60-300~{}\mu$G, using the DCF method. The magnetic field energy
density is comparable to or larger than the turbulent energy in all filaments.
The starless filaments FN1 and FC1 might be supported by either the magnetic
field or turbulence, while the other filaments appear to be gravitationally
unstable. The combined filaments FS2/3, with the strongest magnetic field,
also seem to be gravitationally unstable.

We are grateful to the anonymous referee for helpful comments. W.K. is
supported by the New Faculty Startup Fund from Seoul National University. K.P.
is a Royal Society University Research Fellow, supported by grant number
URF\R1\211322. D.J. is supported by NRC Canada and by an NSERC Discovery
Grant. C.L.H.H. acknowledges support from the NAOJ Fellowship and JSPS KAKENHI
grants 18K13586 and 20K14527. M.T. is supported by JSPS KAKENHI grant
Nos.18H05442,15H02063,and 22000005. K.Q. is partially supported by National
Key R&D Program of China No. 2017YFA0402600, and acknowledges the National
Natural Science Foundation of China (NSFC) grant U1731237. C.W.L. is supported
by the Basic Science Research Program through the NRF funded by the Ministry
of Education, Science and Technology (NRF-2019R1A2C1010851). C.E. acknowledges
the financial support from grant RJF/2020/000071 as a part of Ramanujan
Fellowship awarded by Science and Engineering Research Board (SERB),
Department of Science and Technology (DST), Govt. of India. L.F. acknowledges
the support of the Ministry of Science and Technology of Taiwan under grant
MOST107-2119-M-001-031-MY3 and Academia Sinica under grant AS-IA-106-M03. This
study is part of the JCMT Large Program BISTRO observed under the project code
M16AL004. The James Clerk Maxwell Telescope is operated by the East Asian
Observatory on behalf of The National Astronomical Observatory of Japan;
Academia Sinica Institute of Astronomy and Astrophysics; the Korea Astronomy
and Space Science Institute; Center for Astronomical Mega-Science (as well as
the National Key R&D Program of China with No. 2017YFA0402700). Additional
funding support is provided by the Science and Technology Facilities Council
of the United Kingdom and participating universities and organizations in the
United Kingdom and Canada. Additional funds for the construction of SCUBA-2
were provided by the Canada Foundation for Innovation. The authors wish to
recognize and acknowledge the very significant cultural role and reverence
that the summit of Maunakea has always had within the indigenous Hawaiian
community. We are most fortunate to have the opportunity to conduct
observations from this mountain.

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