# JCMT BISTRO Observations: Magnetic Field Morphology of Bubbles Associated
with NGC 6334

Mehrnoosh Tahani Banting and KIPAC Fellowships: Kavli Institute for Particle
Astrophysics & Cosmology (KIPAC), Stanford University, Stanford, CA 94305, USA
Dominion Radio Astrophysical Observatory, Herzberg Astronomy and Astrophysics
Research Centre, National Research Council Canada, P. O. Box 248, Penticton,
BC V2A 6J9 Canada  Pierre Bastien Institut de Recherche sur les Exoplanètes
(iREx), Université de Montréal, Département de Physique, 1375, Avenue Thérèse-
Lavoie-Roux, Montréal, QC, H2V 0B3, Canada  Centre de Recherche en
Astrophysique du Québec (CRAQ), Université de Montréal, Département de
Physique, 1375, Avenue Thérèse-Lavoie-Roux, Montréal, QC, H2V 0B3, Canada  Ray
S. Furuya Institute of Liberal Arts and Sciences, Tokushima University, Minami
Jousanajima-machi 1-1, Tokushima 770-8502, Japan  Kate Pattle Department of
Physics and Astronomy, University College London, WC1E 6BT London, UK  Doug
Johnstone Department of Physics and Astronomy, University of Victoria,
Victoria, BC V8P 1A1, Canada  Herzberg Astronomy and Astrophysics Research
Centre, National Research Council of Canada, 5071 West Saanich Rd, Victoria,
BC V9E 2E7, Canada  Doris Arzoumanian  National Astronomical Observatory of
Japan, National Institutes of Natural Sciences, Osawa, Mitaka, Tokyo 181-8588,
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  Tetsuo Hasegawa National Astronomical Observatory of Japan,
National Institutes of Natural Sciences, Osawa, Mitaka, Tokyo 181-8588, Japan
Shu-ichiro Inutsuka Department of Physics, Graduate School of Science, Nagoya
University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan  Simon Coudé SOFIA
Science Center, Universities Space Research Association, NASA Ames Research
Center, M.S. N232-12, Moffett Field, CA 94035, USA  Centre de Recherche en
Astrophysique du Québec (CRAQ), Université de Montréal, Département de
Physique, C.P. 6128 Succ. Centre-ville, Montréal, QC H3C 3J7, Canada  Laura
Fissel Department of Physics, Engineering Physics and Astronomy, Queen’s
University, Kingston, ON K7L 3N6, Canada  Michael Chun-Yuan Chen Department of
Physics and Astronomy, University of Victoria, Victoria, BC V8P 1A1, Canada
Frédérick Poidevin  Instituto de Astrofisíca de Canarias, 38200 La
Laguna,Tenerife, Canary Islands, Spain  Departamento de Astrofísica,
Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain  Sarah
Sadavoy Department for Physics, Engineering Physics and Astrophysics, Queen’s
University, Kingston, ON K7L 3N6, Canada  Rachel Friesen National Radio
Astronomy Observatory, 520 Edgemont Rd., Charlottesville, VA, 22903, USA
Patrick M. Koch Institute of Astronomy and Astrophysics, Academia Sinica, 11F
of Astronomy-Mathematics Building, AS/NTU, No. 1, Sec. 4, Roosevelt Rd.,
Taipei 10617, Taiwan  James Di Francesco Department of Physics and Astronomy,
University of Victoria, Victoria, BC V8P 1A1, Canada  Herzberg Astronomy and
Astrophysics Research Centre, National Research Council of Canada, 5071 West
Saanich Rd, Victoria, BC V9E 2E7, Canada  Gerald H. Moriarty-Schieven Herzberg
Astronomy and Astrophysics Research Centre, National Research Council of
Canada, 5071 West Saanich Rd, Victoria, BC V9E 2E7, Canada  Zhiwei Chen 18
Purple Mountain Observatory, Chinese Academy of Sciences, 10 Yuanhua Road,
210023 Nanjing, PR China  Eun Jung Chung Department of Astronomy and Space
Science, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon
34134, Republic of Korea  Chakali Eswaraiah Indian Institute of Science
Education and Research (IISER) Tirupati, Rami Reddy Nagar, Karakambadi Road,
Mangalam (PO), Tirupati 517 507, India  Lapo Fanciullo Institute of Astronomy
and Astrophysics, Academia Sinica, 11F of Astronomy-Mathematics Building,
AS/NTU, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan  National Chung
Hsing University, 145 Xingda Rd., South Dist., Taichung City 402, Taiwan  Tim
Gledhill School of Physics, Astronomy & Mathematics, University of
Hertfordshire, College Lane, Hatfield, Hertfordshire AL10 9AB, UK  Valentin J.
M. Le Gouellec SOFIA Science Center, Universities Space Research Association,
NASA Ames Research Center, M.S. N232-12, Moffett Field, CA 94035, USA  Thiem
Hoang Korea Astronomy and Space Science Institute (KASI), 776 Daedeokdae-ro,
Yuseong-gu, Daejeon 34055, Republic of Korea  University of Science and
Technology, Korea, 217 Gajang-ro, Yuseong-gu, Daejeon 34113, Republic of Korea
Jihye Hwang Korea Astronomy and Space Science Institute (KASI), 776
Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea  University of
Science and Technology, Korea, 217 Gajang-ro, Yuseong-gu, Daejeon 34113,
Republic of Korea  Ji-hyun Kang Korea Astronomy and Space Science Institute
(KASI), 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea
Kyoung Hee Kim Korea Astronomy and Space Science Institute, 776 Daedeokdae-ro,
Yuseong-gu, Daejeon 34055, Republic of Korea  Basic science building 108, 50
UNIST-gil, Eonyang-eup, Ulju-gun, Ulsan 44919, Republic of Korea  Florian
Kirchschlager Department of Physics and Astronomy, University College London,
WC1E 6BT London, UK  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  Chang Won Lee Korea Astronomy and Space
Science Institute (KASI), 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055,
Republic of Korea  University of Science and Technology, Korea, 217 Gajang-ro,
Yuseong-gu, Daejeon 34113, Republic of Korea  Hong-Li Liu Department of
Physics, The Chinese University of Hong Kong, Shatin, N.T., People’s Republic
of China  Departamento de Astronomía, Universidad de Concepción, Av. Esteban
Iturra s/n, Distrito Universitario, 160-C, Chile  Takashi Onaka Department of
Astronomy, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo,
Bunkyo-ku, Tokyo 113-0033, Japan  Department of Physics, Faculty of Science
and Engineering, Meisei University, 2-1-1 Hodokubo, Hino, Tokyo 191-8506,
Japan  Mark G. Rawlings Gemini Observatory/NSF’s NOIRLab, 670 N. A‘ohōkū
Place, Hilo, HI 96720, USA  East Asian Observatory, 660 N. A‘ohōkū Place,
University Park, Hilo, HI 96720, USA  Archana Soam SOFIA Science Center,
Universities Space Research Association, NASA Ames Research Center, M.S.
N232-12, Moffett Field, CA 94035, USA  Korea Astronomy and Space Science
Institute (KASI), 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, 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, Osawa, Mitaka,
Tokyo 181-8588, Japan  Xindi Tang Xinjiang Astronomical Observatory, Chinese
Academy of Sciences, 830011 Urumqi, People’s Republic of China  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  Anthony P. Whitworth  School of
Physics and Astronomy, Cardiff University, The Parade, Cardiff, CF24 3AA, UK
Jungmi Kwon Department of Astronomy, Graduate School of Science, The
University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan  Thuong D.
Hoang Kavli Institute for the Physics and Mathematics of the Universe (Kavli
IPMU, WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
Matt Redman Centre for Astronomy, School of Physics, National University of
Ireland Galway, Galway H91 TK33, Ireland  David Berry East Asian Observatory,
660 N. A‘ohōkū Place, University Park, Hilo, HI 96720, USA  Tao-Chung Ching
CAS Key Laboratory of FAST, National Astronomical Observatories, Chinese
Academy of Sciences, People’s Republic of China  National Astronomical
Observatories, Chinese Academy of Sciences, A20 Datun Road, Chaoyang District,
Beijing 100012, China  Jia-Wei Wang Institute of Astronomy and Astrophysics,
Academia Sinica, 11F of Astronomy-Mathematics Building, AS/NTU, No. 1, Sec. 4,
Roosevelt Rd., Taipei 10617, Taiwan  Shih-Ping Lai Institute of Astronomy and
Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
Institute of Astronomy and Astrophysics, Academia Sinica, 11F of Astronomy-
Mathematics Building, AS/NTU, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617,
Taiwan  Keping Qiu School of Astronomy and Space Science, Nanjing University,
163 Xianlin Avenue, Nanjing 210023, China  Key Laboratory of Modern Astronomy
and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210023,
China  Derek Ward-Thompson Jeremiah Horrocks Institute, University of Central
Lancashire, Preston PR1 2HE, UK  Martin Houde Department of Physics and
Astronomy, The University of Western Ontario, 1151 Richmond Street, London, ON
N6A 3K7, Canada  Do-Young Byun Korea Astronomy and Space Science Institute
(KASI), 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea
University of Science and Technology, Korea, 217 Gajang-ro, Yuseong-gu,
Daejeon 34113, Republic of Korea  Huei-Ru Vivien Chen Institute of Astronomy
and Department of Physics, National Tsing Hua University, Hsinchu 30013,
Taiwan  Institute of Astronomy and Astrophysics, Academia Sinica, 11F of
Astronomy-Mathematics Building, AS/NTU, No. 1, Sec. 4, Roosevelt Rd., Taipei
10617, Taiwan  Wen Ping Chen Institute of Astronomy, National Central
University, Chung-Li 32054, Taiwan  Jungyeon Cho Department of Astronomy and
Space Science, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon
34134, Republic of Korea  Minho Choi  Korea Astronomy and Space Science
Institute (KASI), 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of
Korea  Yunhee Choi  Korea Astronomy and Space Science Institute (KASI), 776
Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea  Antonio
Chrysostomou SKA Observatory, Jodrell Bank, Lower Withington, Macclesfield
SK11 9FT, UK  Pham Ngoc Diep Vietnam National Space Center, Vietnam Academy of
Science and Technology, 18 Hoang Quoc Viet, Hanoi, Vietnam  Hao-Yuan Duan
Institute of Astronomy and Department of Physics, National Tsing Hua
University, Hsinchu 30013, Taiwan  Jason Fiege  Department of Physics and
Astronomy, The University of Manitoba, Winnipeg, MB R3T 2N2, Canada  Erica
Franzmann  Department of Physics and Astronomy, The University of Manitoba,
Winnipeg, MB R3T 2N2, Canada  Per Friberg  East Asian Observatory, 660 N.
A‘ohōkū Place, University Park, Hilo, HI 96720, USA  Gary Fuller Jodrell Bank
Centre for Astrophysics, School of Physics and Astronomy, University of
Manchester, Oxford Road, Manchester, M13 9PL, UK  Sarah F. Graves East Asian
Observatory, 660 N. A‘ohōkū Place, University Park, Hilo, HI 96720, USA  Jane
S. Greaves School of Physics and Astronomy, Cardiff University, The Parade,
Cardiff, CF24 3AA, UK  Matt J. 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., People’s Republic
of China  Ilseung Han  Korea Astronomy and Space Science Institute (KASI), 776
Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea  University of
Science and Technology, Korea, 217 Gajang-ro, Yuseong-gu, Daejeon 34113,
Republic of Korea  Jennifer Hatchell Physics and Astronomy, University of
Exeter, Stocker Road, Exeter, EX4 4QL, United Kingdom  Saeko S. Hayashi
Subaru Telescope, National Astronomical Observatory of Japan, 650 N. A‘ohōkū
Place, Hilo, HI 96720, USA  Charles L. H. Hull National Astronomical
Observatory of Japan, Alonso de Córdova 3788, Office 61B, 7630422, Vitacura,
Santiago, Chile  Joint ALMA Observatory, Alonso de Córdova 3107, Vitacura,
Santiago, Chile  NAOJ Fellow  Tsuyoshi Inoue  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 Korea Astronomy and Space Science Institute (KASI), 776 Daedeokdae-ro,
Yuseong-gu, Daejeon 34055, Republic of Korea  Yoshihiro Kanamori  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  Miju Kang
Korea Astronomy and Space Science Institute (KASI), 776 Daedeokdae-ro,
Yuseong-gu, Daejeon 34055, Republic of Korea  Sung-ju Kang Korea Astronomy and
Space Science Institute (KASI), 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055,
Republic of Korea  Akimasa Kataoka Division of Theoretical Astronomy, National
Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan  Koji S.
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 Institut de Ciencies de l’Espai (ICE, CSIC), Can Magrans,
s/n, 08193 Bellaterra, Barcelona, Spain  ICREA, Pg. Lluís Companys 23,
Barcelona, Spain  Institut d’Estudis Espacials de Catalunya (IEEC), E-08034
Barcelona, Spain  Gwanjeong Kim Nobeyama Radio Observatory, National
Astronomical Observatory of Japan, National Institutes of Natural Sciences,
Nobeyama, Minamimaki, Minamisaku, Nagano 384-1305, Japan  Jongsoo Hee Kim
Korea Astronomy and Space Science Institute (KASI), 776 Daedeokdae-ro,
Yuseong-gu, Daejeon 34055, Republic of Korea  University of Science and
Technology, Korea, 217 Gajang-ro, Yuseong-gu, Daejeon 34113, Republic of Korea
Kee-Tae Kim Korea Astronomy and Space Science Institute (KASI), 776
Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea  Mi-Ryang Kim
Korea Astronomy and Space Science Institute (KASI), 776 Daedeokdae-ro,
Yuseong-gu, Daejeon 34055, Republic of Korea  Shinyoung Kim Korea Astronomy
and Space Science Institute (KASI), 776 Daedeokdae-ro, Yuseong-gu, Daejeon
34055, Republic of Korea  University of Science and Technology, Korea, 217
Gajang-ro, Yuseong-gu, Daejeon 34113, Republic of Korea  Jason M. Kirk
Jeremiah Horrocks Institute, University of Central Lancashire, Preston PR1
2HE, UK  Masato I.N. Kobayashi Department of Earth and Space Science, Graduate
School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka
Vera Konyves  Jeremiah Horrocks Institute, University of Central Lancashire,
Preston PR1 2HE, UK  Takayoshi Kusune  Division of Theoretical Astronomy,
National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan
Kevin Lacaille Department of Physics and Astronomy, McMaster University,
Hamilton, ON L8S 4M1, Canada  Department of Physics and Atmospheric Science,
Dalhousie University, Halifax, NS B3H 4R2, Canada  Chi-Yan Law  Department of
Physics, The Chinese University of Hong Kong, Shatin, N.T., People’s Republic
of China  Department of Space, Earth & Environment, Chalmers University of
Technology, SE-412 96 Gothenburg, Sweden  Chin-Fei Lee  Institute of Astronomy
and Astrophysics, Academia Sinica, 11F of Astronomy-Mathematics Building,
AS/NTU, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan  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 (KASI), 776 Daedeokdae-ro, Yuseong-gu, Daejeon
34055, Republic of Korea  University of Science and Technology, Korea, 217
Gajang-ro, Yuseong-gu, Daejeon 34113, Republic of Korea  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  Dalei Li  Xinjiang
Astronomical Observatory, Chinese Academy of Sciences, 150 Science 1-Street,
Urumqi 830011, Xinjiang, China  Di Li CAS Key Laboratory of FAST, National
Astronomical Observatories, Chinese Academy of Sciences, People’s 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., People’s Republic of China  Junhao Liu School of
Astronomy and Space Science, Nanjing University, 163 Xianlin Avenue, Nanjing
210023, China  Key Laboratory of Modern Astronomy and Astrophysics (Nanjing
University), Ministry of Education, Nanjing 210023, China  Sheng-Yuan Liu
Institute of Astronomy and Astrophysics, Academia Sinica, 11F of Astronomy-
Mathematics Building, AS/NTU, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617,
Taiwan  Tie Liu Shanghai Astronomical Observatory, Chinese Academy of
Sciences, 80 Nandan Road, Shanghai 200030, People’s Republic of China  Ilse de
Looze  Physics & Astronomy Dept., University College London, WC1E 6BT London,
UK  A-Ran Lyo Korea Astronomy and Space Science Institute (KASI), 776
Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea  Steve Mairs East
Asian Observatory, 660 N. A‘ohōkū Place, University Park, Hilo, HI 96720, USA
Masafumi Matsumura Faculty of Education, Kagawa University, Saiwai-cho 1-1,
Takamatsu, Kagawa, 760-8522, Japan  Brenda C. Matthews Department of Physics
and Astronomy, University of Victoria, Victoria, BC V8P 1A1, Canada  Herzberg
Astronomy and Astrophysics Research Centre, National Research Council of
Canada, 5071 West Saanich Rd, 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  Nagayoshi Ohashi
Institute of Astronomy and Astrophysics, Academia Sinica, 11F of Astronomy-
Mathematics Building, AS/NTU, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617,
Taiwan  Geumsook Park  Korea Astronomy and Space Science Institute (KASI), 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  Tae-Soo Pyo Subaru Telescope, National
Astronomical Observatory of Japan, 650 N. A‘ohōkū Place, Hilo, HI 96720, USA
SOKENDAI (The Graduate University for Advanced Studies), Hayama, Kanagawa
240-0193, Japan  Lei Qian CAS Key Laboratory of FAST, National Astronomical
Observatories, Chinese Academy of Sciences, People’s Republic of China
Ramprasad Rao Institute of Astronomy and Astrophysics, Academia Sinica, 11F of
Astronomy-Mathematics Building, AS/NTU, No. 1, Sec. 4, Roosevelt Rd., Taipei
10617, Taiwan  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
Department of Astronomy and Earth Sciences, Tokyo Gakugei University, Koganei,
Tokyo 184-8501, Japan  Giorgio Savini  Physics & Astronomy Dept., University
College London, WC1E 6BT London, UK  Anna M. M. Scaife Jodrell Bank Centre for
Astrophysics, School of Physics and Astronomy, University of Manchester,
Oxford Road, Manchester, M13 9PL, UK  Masumichi Seta  Department of Physics,
School of Science and Technology, Kwansei Gakuin University, 2-1 Gakuen,
Sanda, Hyogo 669-1337, Japan  Yoshito Shimajiri  Department of Physics and
Astronomy, Graduate School of Science and Engineering, Kagoshima University,
1-21-35 Korimoto, Kagoshima, Kagoshima 890-0065, 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  Ya-Wen Tang Institute of
Astronomy and Astrophysics, Academia Sinica, 11F of Astronomy-Mathematics
Building, AS/NTU, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan  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, PR China  Hsi-Wei
Yen Institute of Astronomy and Astrophysics, Academia Sinica, 11F of
Astronomy-Mathematics Building, AS/NTU, No. 1, Sec. 4, Roosevelt Rd., Taipei
10617, Taiwan  Hyunju Yoo Korea Astronomy and Space Science Institute (KASI),
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, 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  Chuan-Peng Zhang National Astronomical Observatories, Chinese
Academy of Sciences, A20 Datun Road, Chaoyang District, Beijing 100012, China
CAS Key Laboratory of FAST, National Astronomical Observatories, Chinese
Academy of Sciences, People’s Republic of China  Guoyin Zhang  CAS Key
Laboratory of FAST, National Astronomical Observatories, Chinese Academy of
Sciences, People’s Republic of China  Yapeng Zhang Department of Physics, The
Chinese University of Hong Kong, Shatin, N.T., People’s Republic of China
Jianjun Zhou Xinjiang Astronomical Observatory, Chinese Academy of Sciences,
150 Science 1-Street, Urumqi 830011, Xinjiang, China  Lei Zhu  CAS Key
Laboratory of FAST, National Astronomical Observatories, Chinese Academy of
Sciences, People’s Republic of China  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 P. S.
Eyres Jeremiah Horrocks Institute, University of Central Lancashire, Preston
PR1 2HE, UK  Sam Falle Department of Applied Mathematics, University of Leeds,
Woodhouse Lane, Leeds LS2 9JT, UK  Sven van Loo School of Physics and
Astronomy, University of Leeds, Woodhouse Lane, Leeds LS2 9JT, UK  Jean-
François Robitaille  Université Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble,
France

###### Abstract

We study the Hii regions associated with the NGC 6334 molecular cloud observed
in the sub-millimeter and taken as part of the B-fields In STar-forming Region
Observations (BISTRO) Survey. In particular, we investigate the polarization
patterns and magnetic field morphologies associated with these Hii regions.
Through polarization pattern and pressure calculation analyses, several of
these bubbles indicate that the gas and magnetic field lines have been pushed
away from the bubble, toward an almost tangential (to the bubble) magnetic
field morphology. In the densest part of NGC 6334, where the magnetic field
morphology is similar to an hourglass, the polarization observations do not
exhibit observable impact from Hii regions. We detect two nested radial
polarization patterns in a bubble to the south of NGC 6334 that correspond to
the previously observed bipolar structure in this bubble. Finally, using the
results of this study, we present steps (incorporating computer vision;
circular Hough Transform) that can be used in future studies to identify
bubbles that have physically impacted magnetic field lines.

dust polarization – NGC 6334 – magnetic fields – star formation – Hii bubbles

††journal: ApJ

##  1 Introduction

Ionized atomic hydrogen (Hii) regions around massive stars are evidence of
recent star formation activity. Expansion of these Hii regions and their
interactions with molecular clouds (Tremblin et al., 2012) can also lead to
increased density (Thompson et al., 2012; Inutsuka et al., 2015) along their
edges and the initiation of a new star-formation sequence (e.g., Elmegreen,
1998; Deharveng et al., 2005; Zavagno et al., 2010a, b; Chen et al., 2022).
Conversely, stellar outflows combined with magnetic fields can reduce the
efficiency of massive star formation significantly (Nakamura & Li, 2007; Wang
et al., 2010; Koch et al., 2012a, b; Federrath, 2015; Krumholz & Federrath,
2019; Chen et al., 2022). In magnetohydrodynamic simulations, for instance,
magnetic fields enable outflows to travel farther than distances in
hydrodynamic simulations, resulting in turbulent motions and decreased star-
formation efficiency at greater distances (e.g., Offner & Liu, 2018; Krumholz
& Federrath, 2019). The initial morphology of the magnetic field in the cloud
relative to the Hii regions also influences the star-formation efficiency
(Chen et al., 2022). Before examining the star-formation activities caused by
Hii regions, it is necessary to study the magnetic field morphology of these
regions and the influence of Hii regions on the magnetic fields of the parent
molecular cloud.

The physical sizes of Hii regions range from ultra-compact ($<0.1$ pc) to
evolved ($>1$ pc; Russeil et al., 2016), enabling us to estimate their age,
ionizing flux, and density (e.g., Osterbrock & Ferland, 2006; Anderson et al.,
2014). These regions can be identified in mid-infrared (MIR) observations as
bubble- or shell-like structures, which are often asymmetrical in shape
(Comeron, 1997) and are formed as a result of winds and radiation from the
massive central stars. The stellar winds and radiation result in expanding Hii
regions, which sweep material on their shells and consequently alter the
magnetic field morphology of their environment (due to flux freezing) compared
to the rest of the parent cloud.

While Hii region age estimates are required for studying star formation, their
ages can be underestimated if magnetic fields are ignored (Chen et al., 2022).
This underestimation of age is due to the fact that strong magnetic fields
resist the Hii expansion perpendicular to the field direction (which may also
result in ovoid-shaped bubbles; Chen et al., 2022). The relative orientation
of magnetic field with the expansion of the Hii region influences not only the
density of the shell but also its fragmentation and core formation (Chen et
al., 2022). Some studies have examined the role and significance of magnetic
fields in cloud evolution and star formation and have shown that the magnetic
fields can be aligned tangential to the shells of evolved Hii regions (e.g.,
Pereyra & Magalhães, 2007; Tang et al., 2009; Chen et al., 2012; Santos et
al., 2014; Fissel et al., 2016; Soam et al., 2017; Chen et al., 2017;
Eswaraiah et al., 2017; Soam et al., 2018; Pattle et al., 2018; Dewangan et
al., 2018; Eswaraiah et al., 2020; Könyves et al., 2021; Devaraj et al., 2021;
Fernández-López et al., 2021; Hoang et al., 2022; Chung et al., 2022). This
tangential field morphology is also predicted in some theoretical simulations
(Krumholz et al., 2007; Henney et al., 2009; Arthur et al., 2011; Ntormousi et
al., 2017). However, the complete morphology and role of magnetic fields in
relation to Hii regions are not yet well understood.

If Hii regions orient and order the field lines tangential to them, this will
also appear as tangential magnetic fields when projected onto the plane of the
sky and will be accompanied by higher polarization fractions. These ordered
field lines will experience less deviation from tangential morphology, leading
to less depolarization and a higher polarization fraction. To better
understand the morphology of magnetic fields associated with Hii regions, here
we study the magnetic fields in the NGC 6334 molecular cloud and its Hii
regions. In this study, we investigate the presence or absence of tangential
magnetic field morphology in Hii regions, as well as whether the presence of
such fields is accompanied by an increase in polarization fraction.
Determining the presence of this morphology may reveal the significance of Hii
regions in the evolution of cloud’s magnetic fields. Furthermore, by
understanding how Hii regions may influence the morphology of magnetic fields
in their parental cloud, we may also be able to determine the initial magnetic
field morphology of the parental cloud prior to its evolution. Knowing this
initial magnetic field morphology allows us to compare it to the magnetic
field morphology predicted by cloud-formation scenarios.

Numerous Hii regions are associated with NGC 6334, which is a massive star-
forming molecular cloud, on the inner edge of the Sagittarius-Carina arm
(Russeil et al., 2012), with core masses ranging from 200 to 2000M⊙ (Zernickel
et al., 2013) and a total mass of a few 105M⊙ (André et al., 2016). These Hii
regions have influenced the gas dynamics in NGC 6334 (Schneider et al., 2020)
and some of them are well-known and optically observed (e.g., Gum, 1955; Persi
& Tapia, 2008). The presence of numerous Hii regions along the filamentary NGC
6334 molecular cloud, which were initially detected by Rodriguez et al. (1982)
and have been extensively studied, is not unique to this region and has been
similarly observed in other molecular clouds (e.g., NGC 6357; Russeil et al.,
2010). Rodriguez et al. (1982) estimate the luminosity of the Hii regions
within NGC 6334 and identify the Zero Age Main Sequence stellar type required
to generate the estimated luminosity (see their Table 2). Subsequent studies
identify a number (or cluster) of stars that may have contributed to the
formation of the NGC 6334 Hii regions (e.g., Tapia et al., 1996).

NGC 6334 and its sub-regions have been observed with various radio,
millimeter, and sub-millimeter facilities, including the Atacama Large
Millimeter/sub-millimeter Array (ALMA; e.g., Sadaghiani et al., 2020; Cortés
et al., 2021), the Very Large Array (VLA; e.g., Rodríguez et al., 2014), and
the Sub-Millimeter Array (SMA; e.g., Zhang et al., 2014). NGC 6334 is actively
forming stars and includes a $\sim 10$ pc filament (main ridge; Loughran et
al., 1986; Russeil et al., 2010; Shimajiri et al., 2019) with an average
density significantly higher than most filaments observed in the Gould Belt
(André et al., 2016). Wu et al. (2014) determined a parallax distance of
$1.35^{+0.15}_{-0.13}$ kpc for NGC 6334, $\sim 20\%$ smaller than its near
kinematic distance of 1.7 kpc (Wu et al., 2014) and photometric distance of
$1.74\pm 0.31$ kpc (Neckel, 1978).

To investigate the magnetic field morphology of NGC 6334 and its Hii regions,
we observe polarized dust emission at 850 $\mu$m, using the James Clerk
Maxwell Telescope111https://www.eaobservatory.org/jcmt/ (JCMT) near the summit
of Mauna Kea. Probing the plane-of-sky magnetic field ($B_{\textsc{POS}}$)
morphology using polarized dust emission is possible due to the alignment of
the short axis of amorphous dust grains (e.g., Draine, 2009) with the magnetic
field, which has been observed at various wavelengths (e.g., Pattle & Fissel,
2019). This alignment is explained through radiative torques (RAT; Draine &
Weingartner, 1997; Lazarian, 2007; Lazarian & Hoang, 2007; Andersson et al.,
2015; Hoang & Lazarian, 2016).

Previously, Arzoumanian et al. (2021, hereafter Paper I) studied the magnetic
fields within NGC 6334 and the region’s filamentary nature. We focus on its
Hii regions in this study. We discuss our JCMT polarization observations and
the previously observed Hii regions associated with NGC 6334 in Section 2. In
Section 3, we discuss the methodology that we use to characterize the magnetic
field morphologies of the Hii regions and discuss their impact on the cloud’s
magnetic field. In Section 4, we compare the magnetic pressure and tension
with the gas, radiation, and dynamic pressures in these regions and further
explore techniques for identifying these Hii regions based on their dust
polarization properties. Section 5 summarizes our approach and findings.

##  2 Observational data

In this section, we first discuss the JCMT SCUBA-2/POL-2 (Bastien et al.,
2011; Holland et al., 2013; Friberg et al., 2016) polarimetric observations of
NGC 6334 at 850 $\mu$m, taken as part of the B-fields In STar-forming Region
Observations (BISTRO) survey (Ward-Thompson et al., 2017). We then present the
Hii regions of NGC 6334 as obtained from a variety of previously published
catalogs.

###  2.1 JCMT BISTRO observations

The 850 $\mu$m dust polarized emission observations were carried out under dry
weather conditions with the atmospheric opacity ranging between $0.03$ and
$0.07$ at 225 GHz. The data were reduced using the
pol2map222http://starlink.eao.hawaii.edu/docs/sc22.htx/sc22.html reduction
code. Observational and data reduction procedures are discussed in detail in
Paper I, which also includes these data.

The observations have a spatial resolution of $14\arcsec$ (Half Power Beam
Width of the JCMT at 850 $\mu$m). The maps of Stokes $I$ (the total dust
thermal continuum emission), Stokes $Q$, and Stokes $U$ are re-projected onto
Cartesian grids with pixel sizes of $4\arcsec$. The NGC 6334 molecular cloud
is depicted in Figure 1 with pixel size of $4\arcsec$. The Stokes $I$, $Q$,
and $U$ maps and their associated uncertainties are discussed in detail in
Paper I.

Figure 1: NGC 6334 at 850 $\mu$m with a pixel size of 4″. The color image
shows Stokes $I$ without any selection criteria applied. The cloud is composed
of a main ridge ($\sim 10$ pc long filament) along with dense clumps and
cores. Evidence of Hii shells is also visible in the Stokes $I$ map.

We obtain the polarization angle ($\psi$) and the initial polarized intensity
($PI_{\textsc{init}}$), using the Stokes parameters in the following
equations:

$\displaystyle\psi=0.5\,\arctan(\frac{U}{Q}),$ (1) $\displaystyle
PI_{\textsc{init}}=\sqrt{Q^{2}+U^{2}},$

where the polarization angle is determined according to the IAU convention
(from North to East in the equatorial coordinate system). The
$B_{\textsc{POS}}$ lines are perpendicular to the polarization lines, and
their orientation ($\chi_{B_{\textsc{POS}}}$) is obtained using

$\chi_{B_{\textsc{POS}}}=\psi+90^{\circ}.$ (2)

The parameter $PI_{\textsc{init}}$ is positively biased due to the squaring of
the uncertainties in $Q$ (denoted by $\delta Q$) and $U$ (denoted by $\delta
U$). We debias $PI_{\textsc{init}}$ and obtain the debiased polarization
fraction ($PF$) as follows (e.g., Serkowski, 1962; Wardle & Kronberg, 1974):

$\displaystyle PI$ $\displaystyle=\sqrt{Q^{2}+U^{2}-0.5(\delta Q^{2}+\delta
U^{2})},$ (3) $\displaystyle PF$ $\displaystyle=\frac{PI}{I}.$

This debiasing approach has been successfully used in previous studies for
signal to noise ratios (SNR) higher than three (e.g., Vaillancourt, 2006;
Plaszczynski et al., 2014; Montier et al., 2015; Hull & Plambeck, 2015; Pattle
et al., 2019; Doi et al., 2020; Pattle et al., 2021). Subsequently, we find
the uncertainties of the debiased polarization parameters as follows:

$\displaystyle\delta PI=\frac{\sqrt{(Q\delta Q)^{2}+(U\delta U)^{2}}}{PI},$
(4) $\displaystyle\delta PF=PF\,\sqrt{(\frac{\delta PI}{PI})^{2}+(\frac{\delta
I}{I})^{2}},$ $\displaystyle\delta\psi=0.5\frac{\sqrt{(U\delta Q)^{2}+(Q\delta
U)^{2}}}{PI^{2}},$

where the $\delta$ shows the uncertainty or the $\sqrt{variance}$ in each
observed parameter. In this study, we use
SNR($I$)$=\frac{{I}}{{\delta{I}}}>10$ and
SNR($PI$)$=\frac{{PI}}{{\delta{PI}}}>3$ as data selection criteria, following
Paper I. Figure 2 illustrates the overall magnetic field morphology of NGC
6334 using the line integration convolution technique (Cabral & Leedom, 1993).
The background color image illustrates the Stokes $I$ map and the drapery
lines depict the magnetic field lines. The short yellow lines represent the
plane-of-sky magnetic field orientations, every 10 pixels.

Figure 2: Magnetic field lines associated with NGC 6334 at 850 $\mu$m. The
background color image illustrates the Stokes $I$ map and the drapery lines
depict the plane-of-sky magnetic field lines in this region as obtained using
the line integration convolution technique. The short yellow lines represent
the $B_{\textsc{POS}}$ orientations (all of the same length), every ten
pixels.

###  2.2 Observed Hii regions

Hii regions are best identified and confirmed using Radio Recombination Lines
(RRL) or H$\alpha$ observations. However, surveys by Bania et al. (2010) and
Anderson et al. (2011) demonstrated that MIR observations can be used to
identify these regions, which appear as a bubble-like structure in $\sim
22\,\mu$m observations surrounded by a shell-like structure at $\sim 12\,\mu$m
wavelength. Traditionally the Hii regions in NGC 6334 were named A to E when
observed in radio (Rodriguez et al., 1982), and I to V when observed in far
infrared (FIR; McBreen et al., 1979). For a complete list of all observed Hii
regions in NGC 6334, we use the Wide-field Infrared Survey Explorer
(WISE333http://astro.phys.wvu.edu/wise/; Anderson et al., 2014) and Simpson et
al. (2012) catalogs (observed in MIR). We refer to the Hii regions identified
in the WISE and Simpson et al. (2012) catalogs as WISE and Simpson bubbles,
respectively.

The WISE catalog compiles more than 8000 confirmed and candidate Hii regions
in the Galactic disk that were observed by the WISE satellite in the
12$\,\mu$m and 22$\,\mu$m bands (Anderson et al., 2014, 2015). The Hii bubbles
in the WISE catalog are categorized as Known (K), Groups (G), Candidates (C),
and radio Quiet candidates (Q). Known regions are those that have been
observed in either RRL or H$\alpha$. When Candidate Hii regions are spatially
associated with known Hii regions they are referred to as Groups. A radio
Quiet candidate is a region that is normally undetectable by radio continuum
surveys due to their low sensitivity, but which is detected by WISE (with the
6 mJy sensitivity of WISE at 22$\,\mu$m). Candidates (C and Q) are typically
found to be Hii regions 95% of the time (Anderson et al., 2014, 2015, 2018).

Additionally, we use the Hii catalog from Simpson et al. (2012) to further
locate regions in NGC 6334. The bubbles identified by Simpson et al. (2012)
are part of the citizen science Milky Way
Project444http://www.milkywayproject.org (MWP), in which online volunteers
determined the location of the bubbles using Spitzer observations in the
8$\,\mu$m and 24$\,\mu$m bands. The WISE and Simpson catalogs identify Hii
regions with slightly different centers and radii. This is likely because
these bubbles are not perfectly spherical, and the two studies use different
methods to determine the radii and shell thickness of Hii regions (based on
their MIR characteristic morphology): Anderson et al. (2014, WISE survey) use
circles to identify the regions, whereas Simpson et al. (2012, Simpson
catalog) rely on volunteer assistance to associate elliptical objects with
these regions (after which the regions are chosen based on their selection
number555hit rate and an effective radius is determined to describe the radius
of each one).

Figure 3: Hii regions associated with NGC 6334. The background color image
shows the Stokes $I$ map. The black lines represent the plane-of-sky magnetic
field orientation for a $12\arcsec$ pixel-sized map (in order to make it
appear less crowded visually). The length of each field line is proportional
to the polarization fraction. The red circles depict the WISE bubbles, which
are numbered with a red font on their top-right side. The orange disks
represent the Simpson bubbles, which are labeled in black font on their upper-
left corner. The inset shows a zoomed-in view of W5 (and S5), which clearly
exhibits tangential field (radial polarization) lines as equal-length segments
relative to the bubble.

The WISE and Simpson bubbles associated with our observations are illustrated
in Figure 3 and listed in Tables 1 and 2. The WISE bubbles are numbered W1 to
W8, depicted with red circles in Figure 3. The Simpson bubbles are denoted by
the letter S and are numbered similarly to the corresponding WISE bubbles; if
a WISE and a Simpson bubble depict a similar bubble in the sky, they are
numbered identically (for example, W5 and S5); if a Simpson bubble is nested
within a WISE bubble (at a similar location but with a significantly smaller
radius), it is numbered identically as the WISE bubble but with the suffix “a”
(for example W7 and S7-a).

Table 1 lists the WISE bubbles along with their equatorial coordinates,
radius, distance (parallax measurements by Wu et al., 2014), category, and the
local standard of rest velocity (km s-1). We note that the mean molecular and
ionized gas velocity of NGC 6334 are $-4$ km s-1(Russeil et al., 2016) and
$-3$ km s-1(Caswell & Haynes, 1987), respectively. Bubbles W4 to W8 are
“Known” bubbles, identified by Quireza et al. (2006) using Carbon RRL (Cii) at
3.5 cm. The physical scale of Bubble W4 is comparable to that of the NGC 6334
cloud, and it likely contributed to the formation of NGC 6334 (Fukui et al.,
2018); consequently, it is not extensively discussed in our analysis of Hii
regions within the cloud. The Simpson bubbles are listed in Table 2 along with
their equatorial, effective radius (R${}_{\text{eff}}$), effective thickness
(Th${}_{\text{eff}}$), inner and outer diameters (along the $\delta$ and
$\alpha$ axes), eccentricity, and position angle of the ellipsoid bubble. Each
of the Flags 1, 2, and 0 denotes a distinct bubble type. Flag 1 denotes
bubbles with smaller bubbles on their edges, Flag 2 represents those found
within larger bubbles, and Flag 0 indicates neither of these two.

Number | Name |  $\alpha$ (∘ J2000) |  $\delta$ (∘ J2000) | Radius ($\arcsec$) | Dist (kpc) | Category | VLSR (km s-1)
---|---|---|---|---|---|---|---
W1 | G351.479+0.643 | 260.268 | $-35.734$ | 68.0 | – | Q | –
W2 | G351.424+0.65 | 260.223 | $-35.775$ | 99.0 | – | G | –
W3 | G351.42+0.637 | 260.233 | $-35.786$ | 52.0 | – | Q | –
W4 | G351.383+0.737 | 260.106 | $-35.759$ | 303.0 | 1.3 | K | $-3.4$
W5 | G351.367+0.64 | 260.193 | $-35.828$ | 107.0 | 1.3 | K | $-3.4$
W6 | G351.311+0.663 | 260.13 | $-35.86$ | 119.0 | 1.3 | K | $-3.4$
W7 | G351.246+0.673 | 260.074 | $-35.908$ | 131.0 | 1.3 | K | 0.6
W8 | G351.17+0.704 | 259.989 | $-35.953$ | 171.0 | – | K | 0.5
Table 1: Bubbles found in the WISE catalog associated with NGC 6334. The name, right ascension ($\alpha$), and declination ($\delta$) for the center of each bubble are indicated. The velocities (VLSR) are obtained from Quireza et al. (2006) and distances (dist) from Wu et al. (2014) using parallax measurements. The bubble categories are Known (K), radio Quiet (Q), and Group (G), as identified in the WISE catalog. Number |  $\alpha$(∘ J2000) |  $\delta$(∘ J2000) | R${}_{\text{eff}}$ (′) | Th${}_{\text{eff}}$ (′) | InnXDia (′) | InnYDia (′) | OutXDia (′) | $\epsilon$ | PA(∘) | Hit | Flag
---|---|---|---|---|---|---|---|---|---|---|---
S2-a | 260.214 | $-35.768$ | 0.50 | 0.61 | 0.630 | 0.871 | 1.240 | 0.691 | 97 | 0.16 | 0
S3 | 260.225 | $-35.784$ | 0.49 | 0.61 | 0.728 | 0.730 | 1.335 | 0.068 | 10 | 0.22 | 0
S5 | 260.199 | $-35.826$ | 1.44 | 1.46 | 2.212 | 2.262 | 3.676 | 0.208 | 33 | 0.16 | 1
S7-a | 260.067 | $-35.931$ | 1.33 | 1.64 | 1.936 | 1.986 | 3.574 | 0.222 | 37 | 0.11 | 0
Table 2: Bubbles identified by Simpson et al. (2012) associated with NGC 6334.
The center of each bubble is shown in equatorial coordinates with $\alpha$ and
$\delta$. R${}_{\text{eff}}$ and Th${}_{\text{eff}}$ represent the effective
radius and thickness associated with each bubble. The bubbles are first
identified as elliptical shapes (before determination of R${}_{\text{eff}}$
and Th${}_{\text{eff}}$) with inner diameters of InnXDia and InnYDia (along
the $\delta$ and $\alpha$ axes), outer diameter of OutXDia (along the $\delta$
axis), eccentricity of $\epsilon$, and ellipse position angle of PA. The “hit
rate” of a bubble represents the level of agreement among the Milky Way
project users regarding bubble detection and is the ratio of the number of
bubbles drawn that qualify as an Hii region to the number of times the bubble
was detected by the users. The final catalog includes only bubbles with a hit
rate of 0.1 or greater. Flags 1, 2, and 0 indicate bubbles: with smaller
bubbles on their edge, positionally located within a larger bubble, and
neither of the two, respectively.

##  3 Hii magnetic field morphologies

Hii regions can push away their surrounding interstellar medium (and the
frozen-in field lines), resulting in tangential magnetic field (radial
polarization666We use the terms radial polarization and tangential magnetic
field interchangeably in this study, as the field lines are perpendicular to
the polarization lines.) patterns. Moreover, the magnetic field lines
surrounding these bubbles are likely to have been compressed (e.g., Eswaraiah
et al., 2020) and ordered, potentially resulting in increased polarization
fractions. These effects can be seen in our observations. The plane-of-sky
magnetic field lines depicted in Figure 3 indicate tangential fields (radial
polarization) associated with some of these Hii regions. This field morphology
is evident in W5 (S5), as illustrated in the inset of Figure 3, representing
equally sized magnetic field lines in a zoomed-in view of this bubble. This
wrapping of the field lines appears as a periodic polarization angle pattern
along the circumference of each bubble, resulting in contiguous areas of
below-90∘ and above-90∘ magnetic field angles surrounding each bubble. Figure
4 illustrates signatures of this behavior in $\chi_{B_{\textsc{POS}}}$ (cyclic
orientations of $B_{\textsc{POS}}$ lines changing from blue to red to blue to
red in the figure), which is characteristic of tangential field morphologies
(wrapping of field lines around a bubble). In this figure, blue denotes a
magnetic field angle less than 90∘ and the red color shows a magnetic field
angle greater than 90∘ (in the IAU convention).

Furthermore, theoretical studies (e.g., Krumholz et al., 2007) demonstrate
that Hii regions can influence and alter the magnetic field morphology of
their parental molecular cloud. Krumholz et al. (2007) simulate the evolution
of magnetized Hii regions, resulting in tangential magnetic field lines.
Figure 5 depicts their resulting field morphology after approximately 0.53 Myr
with an initial magnetic field strength of $14.2\,\mu$G. We examine the Hii
magnetic field morphologies and their polarization fractions in this section.

Figure 4: Plane-of-sky magnetic field angles ($\chi_{B_{\textsc{POS}}}$) in
NGC 6334. The background color image shows the magnetic field angles in
degree. The angles are in the IAU convention system. The magnetic field angles
surrounding some of the bubbles (particularly W5) indicate wrapping of the
field lines (changing from blue to red to blue). WISE bubbles are shown with
black circles. Figure 5: Co-evolution of magnetic field lines and Hii regions
as studied by Krumholz et al. (2007). The black lines and the gray circle show
the magnetic field lines and the Hii region, respectively. The field lines are
pushed by the Hii region, resulting in tangential field patterns.

###  3.1 Identifying field morphologies: Methodology

To investigate the polarization patterns associated with the Hii bubbles and
determine whether they represent a tangential magnetic field pattern, we
transform the polarization frame of reference for each bubble individually and
define radial Stokes parameters $Q_{r}$ and $U_{r}$. In this reference frame,
a polarization line along the radius of the bubble has a zero polarization
angle. At each position $(\alpha,\delta)$ about the bubble center
$(\alpha_{0},\delta_{0})$, we obtain $Q_{r}$ and $U_{r}$ using:

$\displaystyle Q_{r}$ $\displaystyle=+Q\cos{2\phi}+U\sin{2\phi},$ (5)
$\displaystyle U_{r}$ $\displaystyle=-Q\sin 2\phi+U\cos 2\phi,$

where $\phi=\arctan{\frac{\alpha-\alpha_{0}}{\delta-\delta_{0}}}$ is the polar
angle of a given position with respect to the center of the bubble in
equatorial coordinates. The angle $\phi$ is zero when pointing toward North
and increases toward East. We then determine the average $Q_{r}$ and $U_{r}$
at fixed distances from the bubble center (i.e., radial profile of $<Q_{r}>$
and $<U_{r}>$, averaged within thin, two-pixel-wide annuli around the bubble).
A positive $<Q_{r}>$ value indicates that a shell demonstrates radial
polarization pattern on average, whereas a negative value hints to tangential
polarization. $U_{r}$ represents polarization at a $\pm 45^{\circ}$ angle to
the radial direction. Therefore, $<U_{r}>=0$ indicates radial or tangential
polarization at that radius.

This formalism enables us to more easily identify radial polarization
(tangential magnetic field patterns) associated with individual bubbles.
Schmid et al. (2006) previously employed this technique to study the radial
polarization associated with Uranus and Neptune. They found that the technique
was particularly effective in reducing uncertainties caused by systematic
errors in the data reduction process. Additionally, Canovas et al. (2015) used
the technique to investigate the polarization of protoplanetary disks.

To study $<Q_{r}>$ and $<U_{r}>$ more efficiently and to determine the radial
polarization patterns, we define $\theta_{r}$ as follows:

$\theta_{r}=0.5\times\arctan\big{(}\frac{<U_{r}>}{<Q_{r}>}\big{)}.$ (6)

If a shell exhibits radial polarization on average (with positive $<Q_{r}>$
and near zero $<U_{r}>$ values), then $\cos(\theta_{r})$ should be close to 1.
We look for radii with $\cos(\theta_{r})>0.95$ (allowing for 5% total
variation or uncertainty) including the error bars, to identify shells with
radial polarization patterns. Appendix A contains a discussion of the method
used to calculate the error bars.

###  3.2 Polarization pattern of Hii regions in NGC 6334: Results

Figures 6, 7, and 8 illustrate the radial profile of both $\cos(\theta_{r})$
and the mean polarization fraction for each bubble (averaged in each annulus
with a thickness of $8\arcsec$, or two pixels). In these figures, the left
panel illustrates $\cos(\theta_{r})$ and the mean polarization fraction with
blue and red marks, respectively. The right panel shows a zoomed-in view of
the magnetic field lines of each bubble overlaid on Stokes $I$. The dashed
vertical and horizontal lines indicate the radius of each bubble (the Radius
and R${}_{\text{eff}}$ columns in Tables 1 and 2, respectively) and
$\cos(\theta_{r})=0.95$, respectively. The blue markers indicate the total
number of pixels (that satisfy the selection criteria of SNR($I$)$>10$ and
SNR($PI$)$>3$) in each annulus. Some bubbles have boundaries outside of the
NGC 6334 cloud in regions with the lowest density and fewest pixels.

We find that radial polarization in bubbles is accompanied by a higher
polarization fraction, implying that Hii regions have ordered and compressed
the magnetic field lines. A statistical study involving a large number of
bubble polarization observations is necessary to determine if the amount of
increase in polarization fraction can quantitatively reveal information about
the physical properties of the bubbles (e.g., ratio of regular to random field
or Compression factor).

To facilitate discussion of these findings, we divide this section into two
subsections: bubbles that exhibit radial polarization at one or more radial
distances and bubbles that do not. Figures 6 and 7 illustrate bubbles with
radial polarization at one or more radial distances. When a bubble is
associated with a Simpson bubble, a middle panel is added to display the
results for the Simpson bubble (Figure 7). Figure 8 illustrates bubbles with
no radial polarization patterns at any radial distance.

(a) Bubble W1, WISE category Q.
(b) Bubble W6, WISE category K.
(c) Bubble W8, WISE category K.

Figure 6: Radial polarization in W1, W6, and W8. Left column: Radial profile
of $\cos(\theta_{r})$ and the mean polarization fraction in each bubble. The
dashed vertical and horizontal lines indicate the radius of each bubble and
$\cos(\theta_{r})=0.95$, respectively. The blue, red, and black markers
indicate $\cos(\theta_{r})$, the mean polarization fraction, and the total
number of pixels (which satisfy the selection criteria of SNR($I$)$>10$ and
SNR($PI$)$>3$) in each shell, respectively. The error bars in polarization
fraction represent the standard deviation of the mean. The error bars for the
blue markers are discussed in Appendix A. Right column: Zoomed-in view of each
bubble. The black lines and the background color image represent equal-sized
magnetic field lines and Stokes $I$, respectively.

(a) Bubble W5, WISE category K.
(b) Bubble W7, WISE category K.

Figure 7: Radial polarization in W5 and W7. Left column: The radial profile of
$\cos(\theta_{r})$ and the mean polarization fraction in each bubble are
shown. The vertical and horizontal dashed lines represent the radius of each
bubble and $\cos(\theta_{r})=0.95$, respectively. The $\cos(\theta_{r})$
values, the mean polarization fraction, and the total number of pixels (which
satisfy the selection criteria of SNR($I$)$>10$ and SNR($PI$)$>3$) in each
shell are indicated by the blue, red, and black markers, respectively. The
polarization fraction error bars represent the standard deviation of the mean
(see Appendix A for $\cos(\theta_{r})$ error bars). Middle column: Radial
polarization of S5 and S7-a, with the same description as the left column.
Right column: Zoomed-in view of each bubble is shown where the magnetic field
lines (of identical size) are overlaid on the Stokes $I$ map.

(a) Bubble W2, WISE category G.
(b) Bubble W3, WISE category Q.

Figure 8: Absence of radial polarization in W2 and W3. Left column: Radial
profile of $\cos(\theta_{r})$ (blue marker) and the mean polarization fraction
(red marker) in each bubble are shown. The radius of each bubble and
$\cos(\theta_{r})=0.95$ are represented by the vertical and horizontal dashed
lines, respectively. In polarization fraction, the error bars represent the
standard deviation of the mean. Appendix A discusses the error bars for the
blue markers. Middle column: Radial polarization of S2-a and S3, with the same
description as the left column. Right column: Zoomed-in view of each bubble,
representing the observed magnetic field lines (of same size).

####  3.2.1 Bubbles with radial polarization signatures

Radial polarization at one or more radial distances can be seen in bubbles W1
and W5 to W8, with W5 and W7 having corresponding Simpson bubbles (S5 and
S7-2). W1, W6, and W8 (with no corresponding Simpson bubbles) are illustrated
in Figure 6, while W5 and W7 are depicted in Figure 7.

Bubble W1 is classified as a Radio Quiet Hii region in the WISE catalog, with
an unidentified distance by the WISE catalog or Wu et al. (2014). However, its
dust morphology indicates that W1 is associated with NGC 6334. When the
location of W1 is compared with the morphology of sub-millimeter dust
observations shown in Figure 3, it appears as though the center of this
bubble, as identified in the WISE catalog, is slightly shifted relative to the
center location where the effects of bubble expansion on dust can be observed.
At $45\arcsec$ radial distance, the polarization exhibits a radial pattern,
with a peak in polarization fraction (around 7%), as illustrated in the upper-
left panel of Figure 6. Following that at greater distances, polarization
lines diverge from radial angle and the polarization fraction decreases.

Bubble W6 is categorized as a Known bubble, and it is approximately the same
distance away from us as NGC 6334. When projected onto the plane of the sky,
W6 appears to contain a $\sim 1$ pc-long filament. The middle-left panel of
Figure 6 indicates tangential polarization near the center of the bubble
(along the filament) and radial polarization between radii of $\sim 60\arcsec$
to $110\arcsec$. This radial polarization range also exhibits higher
polarization fractions ($6-7\%)$. As depicted in Figure 3, W6 appears in
contact with W5 to the northwest and W7 to the southeast (when projected onto
the plane of the sky). Therefore, at greater distances beyond the radius of W6
the effects of radial polarization associated with W5 and W7 (higher
polarization fractions) can be seen.

Although Bubble W8 is classified as a Known bubble, neither the WISE catalog
nor the study by Wu et al. (2014) indicate its distance. However, the dust
morphology suggests that W8 should be directly associated with NGC 6334. The
lower-left panel of Figure 6 indicates radial polarization in the radius range
of $160\arcsec$ to $180\arcsec$, along with locally maximal polarization
fraction ($\sim 9\%$).

Bubble W5, a Known bubble, has the same distance from us as NGC 6334. The
magnetic field lines associated with this bubble clearly demonstrate the
impact of the Hii region, as illustrated in the inset of Figure 3. The upper-
left panel of Figure 7 shows radial polarization in the radius range of $\sim
60\arcsec$ to $90\arcsec$ with on-average higher polarization fraction ($\sim
6-8\%$). This is similar to the values in the upper-middle panel of Figure 7
for S5 (radii of $\sim 50\arcsec$ to $85\arcsec$ and $PF$ of $\sim 6-10\%$),
where the small difference is due to the slight difference in radius and
center for W5 and S5. The observed field lines appear to be more consistent
with S5 than W5. At radial distances greater than the radius of the bubble,
the polarization pattern becomes non-radial and the polarization fraction
decreases by a factor of $\sim 2$, indicating that the field lines are less-
ordered.

Bubble W7 is at the same distance as NGC 6334 and in the Known category. The
presence of radial polarization and an increase in the polarization fraction
can be seen in this bubble at $r\simeq 90\arcsec-100\arcsec$. Additionally, at
distances greater than the radius of W7, the polarization lines exhibit a
higher polarization fraction or radial polarization due to the influences of
W6 and W8.

W7 has a bipolar morphology (suggested by Harvey & Gatley, 1983, based on the
dust temperature studies of the two lobes) and on its south side is associated
with S7-a, which is part of a Herbig-Haro object (southern lobe; Bohigas,
1992). This bipolar morphology is likely caused by the confinement of an Hii
region within a flattened-like (or torus-like) molecular gas structure
(Kraemer & Jackson, 1999), which allows the ionized gas to escape only in the
north and south directions (extending $2\arcmin$; Rodriguez et al., 1988).
This bipolar structure is also visible in our observations; the magnetic field
morphology of W7 resembles a radial polarization pattern for two lobes (to the
north and south of its center), with their radial polarization features
coinciding near the center of W7, as illustrated in the lower-right panel of
Figure 7.

The southern lobe of W7 can be studied using the S7-a bubble. S7-a exhibits a
radial polarization pattern at $r\simeq 80\arcsec$, as illustrated in the
lower-middle panel of Figure 7. However, the polarization fraction increases
at radii greater than this value, as the polarization fraction is also
influenced by W8 at these radii.

No distinct Hii region has been identified in the WISE or Simpson catalogs as
being directly associated with the northern lobe of W7. We approximate the
bipolar structure (shown with black circles in Figure 9) based on the 6 cm
observations of Rodriguez et al. (1988), in which the northern lobe appears
slightly shifted to the south in comparison to the tangential field lines
(radial polarization) visible in our data. As a result, we perform our radial
polarization analysis on a bubble with a central location of
$(\alpha,\delta)=(260.07^{\circ},-35.89^{\circ})$ and a radius of $\sim
40\arcsec$, as estimated by the location of our observed polarization lines.
The absence of a distinct Hii region for the northern lobe in the catalogs
emphasizes the importance of polarization studies in identifying and examining
molecular cloud substructures. We discuss this in more detail in Section 4.2,
where we investigate the possibility of using polarization properties to
identify bubbles that have impacted the field lines.

Figure 9: Radial polarization study of W7. The mean polarization fraction, the
total number of pixels in each annulus, and $\cos(\theta_{r})$ are all shown
by the red, black, and blue markers.

####  3.2.2 Bubbles without radial polarization

Bubble W2 is classified as Group in the WISE catalog, with an undetermined
distance (to our knowledge). As illustrated in the upper-left panel of Figure
8, the bubble has polarization angles of $\sim
55^{\circ}(\cos{\theta_{r}}\simeq 0.6)$ relative to radial direction and is
therefore closer to tangential than to radial lines. These fields are oriented
in a single direction (perpendicular to the main ridge) and are likely
dominated by the region’s high density cores and/or clumps. This bubble
demonstrates a nearly constant polarization fraction of $\sim 2.5\%$.
Similarly, compared to other bubbles the averaged polarization fraction is
lower in S2-a (maximum 4% as illustrated in the upper-middle panel of Figure
8), which is nested within W2. We note a small increase in polarization
fraction just behind the radius of S2-a, followed by a slight decrease beyond
the radius. While the polarization lines appear to have an average
$\cos{\theta_{r}}\simeq 0.95$ at $20\arcsec$ and $30\arcsec$, their large
error bars indicate a non-radial polarization pattern. The large error bars
for $\cos{\theta_{r}}$ are due to the fact that the field lines are mostly in
one orientation, and thus have different radial angles (relative to radial
direction) at various points on the circle.

Bubble W3 is classified as a radio Quiet bubble and appears within W2, with an
undetermined distance in the WISE catalog. W3 and its corresponding Simpson
bubble, S3, do not indicate radial polarization, as illustrated in the lower-
left and lower-middle panels of Figure 8. At $r\simeq 35\arcsec$, it appears
as though the polarization in W3 is approaching radial. However, because the
error bars fall below $\cos(\theta_{r})=0.95$, this bubble does not pass our
criteria for radial polarization and further analysis is required. As with W2,
the polarization lines in W3 appear to be unaffected by the Hii region, with a
nearly constant polarization fraction ($\sim 2$%) inside the bubble and a
slight increase near the radius of the bubble (up to $\sim 3\%$). W3 (and S3)
belong to a dense region of NGC 6334 with active star formation.

While W2 and W3 have unidentified distances in the WISE catalog and do not
exhibit radial polarization, observations indicate that they (or their
corresponding Simpson bubbles) are associated with NGC 6334. S3 and S2-a are
both compact Hii regions in the dense part of NGC 6334. A cluster of B0-B$0.5$
Zero Age Main Sequence stars likely ionize the S2 region (Tapia et al., 1996).
S3 is associated with the strongest maser in NGC 6334, H2O, OH, and CH3OH
masers (Moran & Rodriguez, 1980; Batrla et al., 1987; Forster & Caswell, 1989;
Menten & Batrla, 1989; Kraemer & Jackson, 1999), and a young molecular outflow
(Bachiller & Cernicharo, 1990).

Finally, we note that as illustrated in Figure 8, bubbles with no evidence of
radial polarization have larger error bars (indicating a greater dispersion of
$Q_{r}$ and $U_{r}$ values within each annulus). As the angle changes with
respect to the radius of the bubble, a uniform magnetic field morphology
results in greater dispersion, whereas tangential field lines result in small
dispersion and error bars.

##  4 Discussion

All bubbles, except for W2 (and S2-a) and W3 (and S3) exhibit some degree of
radial polarization. Table 3 summarizes our findings regarding the magnetic
field morphology of Hii regions within NGC 6334 as discussed in Section 3.
Examining the energy balance associated with these regions is required to
better understand magnetic field geometries. Additionally, the polarization
patterns of the cloud from small to large scales can reveal important
information about substructures within the cloud and the cloud’s evolution
and/or formation. We discuss these in the following subsections.

###  4.1 Field strengths and energy comparisons

Bubble | radius ($\arcsec$) | sourceγ |  $B_{\textsc{LOS}}^{\dagger}$ ($\mu$G) |  $\langle B_{\textsc{POS}}\rangle^{\star}$ ($\mu$G) | RP evidence
---|---|---|---|---|---
W1 | 68.0 |  |  | 42 | at $45\arcsec$
W2 | 99.0 | E |  | 360 | –
S2-a | 30 | E |  $-263\pm 78$ at 1665 MHz (OH) $-340\pm 78$ at 1667 MHz (OH) $-169\pm 33$ at 1420 MHz (Hi) | – | –
W3 | 52.0 | F |  | 415 | –
S3 | 29.4 | F |  | 351 | –
W5 | 107.0 | D |  $-60\pm 46$ at 1665 MHz (OH) $-69\pm 58$ at 1667 MHz (OH) $-93\pm 13$ at 1420 MHz (Hi) | 99 |  $60\arcsec$ to $90\arcsec$
S5 | 86.4 | D |  | 92 |  $50\arcsec$ to $85\arcsec$
W6 | 119.0 | C |  | 144 |  $60\arcsec$ up to $110\arcsec$
W7 | 131.0 | A |  $+148\pm 20$ at 1665 MHz (OH) $+162\pm 33$ at 1667 MHz (OH) $+47\pm 15$ at 1420 MHz (Hi) | 132 |  $85\arcsec$ to $110\arcsec$
S7-a | 79.8 | A |  | 114 | at $75\arcsec$
W8 | 171.0 | V |  | – | at $160\arcsec$ and $160\arcsec$ to $180\arcsec$
Table 3: Summary of radial polarization detection in bubbles. The first,
second, and fourth columns show bubble numbers, bubble radius, and magnetic
field strength obtained from literature, respectively. The $\gamma$ represents
sources identified by Rodriguez et al. (1982) that were used by Sarma et al.
(2000) and Balser et al. (2016) for Zeeman measurements. The $\dagger$ denotes
VLA Zeeman measurements by Sarma et al. (2000), with the negative and positive
signs indicating directions toward and away from us, respectively. We note
that the opposite sign convention of Zeeman measurements is used in Faraday
measurements. The fifth column denoted by $\star$ indicates the approximate
plane-of-sky magnetic field strength in the molecular gas surrounding the
bubble, using strengths obtained by Paper I. The values listed are the
weighted means of the magnetic field strengths estimated by Paper I in
filaments overlapping with the bubbles. The final column displays the regions
within each bubble that exhibit radial polarization. Balser et al. (2016)
determine magnetic strength of source A to be $190\pm 96\,\mu$G and the
strength of source D to be approximately 180 to 1200 $\mu$G for Source D.

We employ established equations and observations from the literature to
determine the energetic significance of the Hii regions in comparison to
magnetic fields. These are discussed in greater detail in the following two
subsections.

####  4.1.1 Energy balance relations

To estimate the gas thermal pressure ($P_{\rm{gas}}$), radiation pressure
($P_{rad}$), dynamic pressure ($P_{dyn};$ e.g., Pavel & Clemens, 2012, due to
bubble expansion), magnetic pressure ($P_{B}$; e.g., Pattle et al., 2022), and
magnetic tension ($T_{B}$; e.g., Boulares & Cox, 1990) per unit area (due to
curved field lines) of bubbles, we use the following equations (for tangential
field lines):

$\displaystyle P_{\rm{gas}}=nk_{B}T,$ (7) $\displaystyle P_{rad}=\frac{L}{4\pi
r^{2}c},$ $\displaystyle P_{dyn}=0.5\rho v_{ex}^{2},$ $\displaystyle
P_{B}=\frac{B^{2}}{8\pi},$ $\displaystyle T_{B}=\frac{B^{2}}{4\pi},$

where $n=n_{e}$, $k_{B}$, $T$, $c$, $r$, $L$, $\rho$, $v_{ex}$, and $B$ are
the electron volume density, Boltzmann constant, gas temperature, speed of
light, distance to the center of the bubble, luminosity, mass density,
expansion velocity, and magnetic field strength (perpendicular to gas motion),
respectively.

While the above-mentioned $P_{rad}$ is used for optically thick regions,
studies (Reissl et al., 2018) show that radiation pressure is generally small
(or negligible) compared to gravity or gas pressure. We can estimate the
magnetic field strength ($B_{\rm{resist}}$) required to resist the combined
effects of gas, radiation, and dynamic pressures, using:

$P_{\rm{B,resist}}+T_{\rm{B,resist}}=\frac{3B_{\rm{resist}}^{2}}{8\pi}=P_{gas}+P_{rad}+P_{dyn}.$
(8)

Magnetic fields significantly less than this $B_{\rm{resist}}$ value indicate
that the field lines are altered by the Hii regions.

####  4.1.2 Parameter estimates

Except for W1, all of these bubbles have been previously identified in various
observations (e.g., Rodriguez et al., 1982, sources denoted as A to E and
source V shown in Figure 10) and their magnetic fields were studied using
Zeeman measurements (Sarma et al., 2000; Balser et al., 2016, see Table 3). We
note that Kraemer & Jackson (1999) found an anti-correlation between the
presence of dense gas and the 6 cm radio flux, which they attribute to gas
dispersion by the feedback from the hottest stars. This gas and dust
dispersion is also visible in our $850\,\mu$m dust observations.

Figure 10: Sources identified by Kraemer & Jackson (1999). The background
color image shows the Stokes $I$ map. The orange and red circles show the Hii
regions identified in the WISE and Simpson et al. (2012) catalogs,
respectively. The x marks show the sources in Kraemer & Jackson (1999) and
used in Sarma et al. (2000) to perform Zeeman measurements.

We also employ the parameters listed in Table 4 obtained from Rodriguez et al.
(1982) and Russeil et al. (2016). Rodriguez et al. (1982) assumed a
temperature of 104 K and found the electron volume densities and the Hii
masses of these sources. Russeil et al. (2016) provide the expansion
velocities ($v_{ex}$; see their Table 1). Using the $L$ and $n_{e}$ values
from Rodriguez et al. (1982), a temperature of $10^{4}$ K, and the $v_{ex}$
values, we determine the $B_{\rm{resist}}$ magnetic field strengths as listed
in Table 4 for sources A, C, D, E, and F. These values (except for sources F
and E) exceed the observed magnetic field strengths (see Table 3) determined
using Zeeman observations (Sarma et al., 2000; Balser et al., 2016) and the
Davis-Chandrasekhar-Fermi technique (DCF; Davis & Greenstein, 1951;
Chandrasekhar & Fermi, 1953, associated with substructures on the shells)
described in Paper I.

Src |  $\alpha$ (∘J2000) |  $\delta$ (∘J2000) |  Radius ($\arcsec$) |  Tk (K) |  $n_{e}$ ($\times 10^{3}$ cm-3) |  M${}_{\rm{H\scaleto{$II$}{1.2ex}}}$ (M⊙) |  $L$ ($L_{\odot}$) |  $v_{ex}$ (km s-1) |  $B_{\rm{resist}}$ $\mu$G
---|---|---|---|---|---|---|---|---|---
A | 260.08 | $-35.91$ | 100 | 60 | 20 | 0.4 | $8\times 10^{4}$ | 15.7 | 534
C | 260.14 | $-35.85$ | 40 | 70-80 | 2 | 3 | $7\times 10^{4}$ | 14 | 267
D | 260.18 | $-35.82$ | 40 | 40-50 | 3 | 5 | $2\times 10^{5}$ | 14 | 308
E | 260.21 | $-35.77$ | 20 | 50-60 | 7 | 1 | $8\times 10^{4}$ | 15∙ | 397
F | 260.22 | $-35.78$ | 10 | 60 | 40 | 0.03 | $3\times 10^{4}$ | 15∙ | 744
V | 259.99 | $-35.96$ | 30 | 50-60 |  |  |  |  |
Table 4: Sources studied in Kraemer & Jackson (1999), Rodriguez et al. (1982),
and Balser et al. (2016) as shown in Figure 10. The kinetic temperature,
radius, volume and column density are listed for each source from Kraemer &
Jackson (1999) and the electron volume density, Hii mass, and stellar
luminosity are from Rodriguez et al. (1982). The expansion velocities from
Russeil et al. (2016, see their Table 1) are denoted by $v_{ex}$. The $v_{ex}$
values denoted by $\bullet$ are estimates based on the available $v_{ex}$ of
other bubbles. $B_{\rm{resist}}$ is the minimum magnetic field strength needed
to resist the bubble’s impact. These sources are associated with the WISE and
Simpson bubbles.

####  4.1.3 Energy balance of individual bubbles: Bubbles with radial
polarization signatures

W1, W5 (and S5), W6, W7 (and S7-a), and W8 all exhibit radial polarization.
Among these, W5 (and S5) and W7 (and S7-a) have Zeeman observations associated
with them. W5 and S5 correspond to source D, which is identified as an
extended, amorphous, and roughly spherical region. Source D contains H2O maser
observations (Moran & Rodriguez, 1980) and has a lower molecular hydrogen
density than any other source in NGC 6334 (Kraemer & Jackson, 1999). We found
that a magnetic field strength of 308 $\mu$G is required to resist the bubble,
which is approximately a factor of three greater than the magnetic fields
observed with Zeeman or DCF in the vicinity of this region. Therefore, we
suggest that the field lines in this region are pushed and influenced by the
gas pressure as evident by the radial polarization (tangential magnetic field)
morphology.

The center of W6 coincides with source C. Sarma et al. (2000) found no OH
absorption toward the continuum peak of this source to detect Zeeman
splitting. This source is non-spherical and likely contains an O7 star (Straw
et al., 1989; Kraemer & Jackson, 1999). When projected onto the plane of the
sky, W6 appears to contain a dense filament, as illustrated in the middle-
right panel of Figure 6. This filament can be located inside, at the front, or
at the back of the bubble in three dimensions. Magnetic fields run parallel to
this filament on the plane of the sky, while the edges of the bubble exhibit
radial polarization behavior.

Three explanations can be made for the magnetic morphology of the filament
associated with W6: 1) The dense filament may be located on the shell (in 3D;
foreground or background of the bubble) and thus the field lines may appear
running parallel to the filament due to their tangential morphology to the
shell. 2) The filament may be located within the bubble, showing the general
field morphology inside the Hii region. 3) The filament may be located inside
or on the bubble, with parallel field lines formed by the filament’s gas
inflow (instead of by the Hii region). In this case, the field lines may have
transitioned from perpendicular to parallel (with respect to the filament)
after gravity took over and material flowed along the filament (e.g., Liu et
al., 2018; Busquet, 2020; Pillai et al., 2020). Given that the overall
magnetic field morphology of NGC 6334 appears to be perpendicular to the
larger cloud, we suggest that the third scenario is most likely.

Additionally, given the presence of two dense regions (each containing
numerous cores) to the north and south of this bubble (see Figure 11), one
could argue that the observed radial polarization pattern (tangential magnetic
fields; see Figure 6) at the edge of this bubble is the result of material
inflow to these two systems. We refer to these two regions as core-hub systems
(see Figure 11), and suggest that these tangential fields are caused by the
interaction of the field lines with W6, not by the gravitational pull exerted
by the two core-hub systems. This suggestion is backed up by the following
arguments: First, we note that a magnetic field strength of 267 $\mu$G is
required to counteract the bubble’s effects, while the average field strength
of the filament is $\sim 144\,\mu$G (Paper I). Second, we estimate the
gravitational pull exerted on W6 by the two dense core-hubs and find that it
is one or two orders of magnitude lower than the gas or magnetic pressure of
the bubble.

Figure 11: Two dense star-forming regions within NGC 6334, each containing a
number of cores. W6 is bounded on both sides by the two core-hub systems.

To calculate the gravitational pressure exerted on the bubble by the hubs, we
use

$P_{\rm{grav}}=\frac{GM\rho}{r},$ (9)

where $G$, $M$, $\rho$, and $r$ denote the gravitational constant, the mass of
each of the hub systems (to the north or south), the volume density of the
bubble, and the distance between the bubble and each core-hub center,
respectively. We use the Virial core masses (upper estimates) from Russeil et
al. (2010) to approximate the mass of each core-hub region. The sums of all
cores in the northern and southern hubs are 5270 $M_{\odot}$ and 2124
$M_{\odot}$, respectively, resulting in a gravitational potential
significantly less than the gas or the magnetic pressure. Even if we assume a
mass of 104 $M_{\odot}$ for each hub, a distance of 2 pc from the center of
the bubble, and a value of $\sim 10^{3}-10^{4}\times m_{p}$ for $\rho$ (where
$m_{p}$ is the mass of a proton), we find that gravitational pressure is one
or two orders of magnitudes less than gas or magnetic pressure. Therefore, we
suggest that observed radial polarization in this region is caused by the
bubble.

The center of W7 (and the shell of S7) corresponds to the center of source A,
which has a magnetic field that varies across its diameter ($\sim 200\arcsec$;
Sarma et al., 2000). The second strongest maser (H2O masers; Moran &
Rodriguez, 1980) in NGC 6334 and a Herbig-Haro-like object are both associated
with this source, which has a bipolar structure, as illustrated in Figure 7
(due to the Hii region being constrained by a dense molecular gas structure).
The molecular toroid at the center of this source contains $\sim
2000\rm{M}_{\odot}$ (Sarma et al., 2000) and may serve as a nursery for the
formation of a protocluster of stars (Persi et al., 2009). Our results
indicate that the observed Zeeman and DCF measurements are smaller than the
$B_{\rm{resist}}$ value that would be needed to provide support in this region
by a factor of five (or an order of magnitude), thus the field lines are
clearly altered by the two lobes, resulting in the observed radial
polarization.

W8 corresponds to the southernmost continuum source (source V; McBreen et al.,
1979), which exhibits evidence for recent star formation activity (Kraemer &
Jackson, 1999) and is associated with H2O and OH masers (Moran & Rodriguez,
1980). This source contains a near-infrared bipolar nebula (Persi, 2019) and
has no associated Zeeman magnetic field detections.

To summarize, the observations and analyses presented in this section strongly
suggest that Hii regions are responsible for the radial polarization seen in
W5 (and S5), W6, W7 (and S7-a), and W8. These bubbles show evidence of radial
polarization at a radius or a range of radii accompanied by increased
polarization fraction, which is likely due to ordered magnetic fields.
Additionally, some studies (Hoang et al., 2019; Lee et al., 2020; Tram et al.,
2021) predict an increase in polarization fraction as the distance from the
center of the bubble increases, which can work together with ordered field
lines and result in the observed locally maximal polarization fractions.

####  4.1.4 Energy balance of individual bubbles: Bubbles without radial
polarization

W2 (and S2-a), W3 (and S3) are located in a denser region of NGC 6334 and are
spatially associated with sources E (S2-a) and F (S3). The magnetic field in
the neighborhood of sources E and F exhibits an hourglass morphology (Zhang et
al., 2014; Cortés et al., 2021). Two possible explanations for the magnetic
field morphology associated with these bubbles are as follows: 1) Because dust
polarization observations are more sensitive to denser regions, we may be
observing plane-of-sky magnetic fields associated with the foreground or
background of these Hii regions, possibly accumulated on the shells; or 2) due
to the higher densities in these regions, the ionized gas and outflow may lack
the energy required to be dynamically important and alter the magnetic field
morphology. Additionally, these two bubbles are younger and less evolved than
other regions analyzed in this study. Therefore, they might not have had
enough time to advance far enough into their cloud environment and reorder the
field lines there.

To explore these possibilities, we estimate the background and/or foreground
(i.e., non-Hii) contribution to the $I$, $Q$, and $U$ parameters in this
neighborhood. To this end, we pick the interior region of S2-a that has a more
coherent magnetic field morphology compared to the rest of the region (within
$r\simeq 24\arcsec$) and average its Stokes $I$, $Q$, and $U$ values. We then
subtract these values from the corresponding observed values (in each pixel)
and repeat the radial polarization analysis. The results are shown in Figure
12, where W2 exhibits no sign of radial polarization again and W3 (between
$30\arcsec$ to $75\arcsec$; and S3 outside the bubble) and S2-a (at 27″) show
evidence of radial polarization.

The new (subtracted) radial polarization patterns associated with these
bubbles may indicate that these bubbles have altered the field lines (first
explanation). However, the observed magnetic field strengths are not small
enough to confirm this. S2-a coincides with source E and its observed Zeeman
measurements ($340\pm 78$ with OH; Sarma et al., 2000) have a similar value as
$B_{\rm{resist}}$ (397 $\mu$G). W3 and S3 correspond to source F, an ultra-
compact Hii region with magnetic field strength of $\sim-2000$ to $-5000$
$\mu$G (OH Zeeman; Hunter et al., 2018). This observed field value is greater
(by a factor of two or more) than the region’s $B_{\rm{resist}}$ value of 744
$\mu$G. These field values indicate that the bubbles had no observable impact
on the field lines due to the high density of the region (second explanation).
Higher resolution observations of these bubbles may shed light on the roles
that these bubbles may have played in shaping the field lines in this region.

Figure 12: Radial polarization analysis with non-Hii effects subtracted for
W2, S2-a, W3, S3. The vertical dashed line shows each bubble’s radius
identified by the WISE and Simpson catalogs. The black markers indicate the
number of pixels contained in each annulus. The blue points represent
$\cos{\theta_{r}}$. In these plots, evidence of radial polarization is present
at $27\arcsec$ for S2-a, between $\sim 33\arcsec$ to $45\arcsec$ for W3, and
beyond $25\arcsec$ for S3.

###  4.2 Machine vision algorithms to identify regions impacting field lines

Using published catalogs, we identified bubbles with radial polarization in
Section 3. In this section, we explore the feasibility of future studies using
machine vision to identify regions with circular magnetic field morphologies
(such as NGC 6334 Hii regions, where the field lines are oriented tangential
to the bubble boundaries). To this end, we use the circular Hough transform
technique (CHT).

CHT has been applied to a number of fields, most notably industrial
applications such as eye detection (e.g., Wan Mohd Khairosfaizal & Nor’aini,
2009) and traffic control (e.g., Widyantoro & Saputra, 2015). Edge detection
algorithms are required when applying the CHT technique. To achieve the best
results, we employ Canny edge detection777We use the already-existing edge-
detection class in the Skit-image Python library (van der Walt et al., 2014).
(Canny, 1986), a numerical technique developed to optimize edge derivation.
The Canny edge detection technique requires (as input) the smoothing width of
the image as well as two threshold values for a double thresholding system
(hysteresis thresholding), with the higher threshold typically set to be twice
as high as the lower one.

Our approach includes the following two main steps, to locate regions that
have pushed the magnetic field lines perpendicular to bubbles:

  1. 1.

We apply the CHT on two distinct maps: one is the presence of polarization
data with SNR($I$)$>10$ and SNR($PI$)$>3$ (hereafter referred to as PolPres
map), and the other is the polarization fraction (PF map; with the same
selection criteria). The PolPres map has pixel values of 0 or 1 to indicate
the presence or absence of data meeting the aforementioned selection criteria.
The pixel values of the PF map are not binary and influence the edge
detection. Different threshold values for both PolPres and PF maps, as well as
the automatic Otso threshold determination888skimage.filters.threshold_otsu,
all yield results similar to the default threshold values of the Canny edge
detection library.

  2. 2.

Using the circular Hough transform, we identify all possible circular patterns
with radii ranging from $8\arcsec$ to $\sim 130\arcsec$, separately in each
map. We then select those features that are identified in both maps at a
similar location and radius (with a $\sim 40\arcsec$ difference allowance for
their center location and a one-pixel difference allowance for their radius).
Because some patterns are identified multiple times, we then average the radii
and locations of bubble centers that are close together (within $20\arcsec$).
We refer to the final selected circular features as CHT bubbles and denote
them with the letter C followed by a number corresponding to the WISE bubbles.

Figure 13: Identified bubbles using Circular Hough Transform. We identify
bubbles that have altered the magnetic field lines. Some bubbles are
identified multiple times, which are then averaged to one. The dashed black
rectangle indicates the location of the two merging sub-filaments discussed in
Paper I.

In Section 3, we found that W1, W5, W6, W7, and W8 exhibit radial
polarization999W2, S2-a, W3, and S3 do not exhibit radial polarization in the
observations., among which W1, W5, and W7 are the only ones with polarization
data covering more than $\sim 20\%$ of the bubble’s shell. Therefore, we
propose that this technique should identify W1, W5, and W7. As proposed, we
find that the technique identifies W1, W5, and W7 (denoted as C1, C5, and C7,
illustrated in Figure 13). As a result, we believe the technique is promising
and should be examined further with additional observations. Furthermore, the
edges of W6 and S7-a (corresponding to C6 and C7-a) and an additional circular
feature, C0, are identified in this technique. C6 coincides with the southern
edge of W6 (a sub-region with clear radial polarization pattern), and C7-a
overlaps with north-eastern side of S7-a.

The magnetic fields associated with C0 exhibit a radial polarization
morphology between $\sim 45\arcsec$ and $53\arcsec$ (see Figure 14). Because
this region overlaps with W4, we suggest that C0 may be a distinct Hii region
that was previously undetected due to line-of-sight confusion with W4. These
findings indicate that while the CHT technique is used in a basic and simple
form here, it has significant potential for detecting bubbles that have
altered the magnetic field lines. These regions may be detected in full sky
observations using more complex CHT techniques (e.g., Yadav et al., 2014)
and/or machine learning.

Figure 14: Radial polarization analysis of C0. The mean polarization fraction,
the total number of pixels in each shell (which satisfy the selection criteria
of SNR($I$)$>10$ and SNR($PI$)$>3$), and $\cos(\theta_{r})$ are all shown by
the red, black, and blue markers.

###  4.3 Cloud and magnetic field co-evolution

The large-scale $B_{\textsc{POS}}$ lines are predominantly perpendicular to
the main ridge of NGC 6334 (Li et al., 2015), which are altered on
substructure scales by Hii regions within the cloud. We suggest that these
$B_{\textsc{POS}}$ lines were initially even more coherent and perpendicular
to the filament, but were then altered by feedback mechanisms, such as Hii
regions, or gas flows (see the filament within W6), as illustrated in a
schematic view by Figure 15.

Additionally, the physical properties of Hii regions may reveal the initial
orientation of the magnetic field prior to the Hii expansion. For instance,
studies (e.g., Chen et al., 2022) indicate that Hii regions may be elongated
along the initial orientation of the field lines as expansion perpendicular to
the field lines is met with resistance. Bonne et al. (2022) suggest that the
initial magnetic field orientation may have also enforced the orientation of
bipolar cavities in the Vela C cloud. We note that the elliptical elongations
of the NGC 6334 bubbles are reported in the MIR observations of Simpson et al.
(2012), but they are very small, except for S2-a as illustrated in Figure 16
where the elongation of the bubble is not completely aligned with the large-
scale magnetic fields (Chen et al., 2022).

The overall perpendicular $B_{\textsc{POS}}$ lines to the main ridge
(particularly at earlier evolutionary stages of the cloud) and the presence of
large bubbles in this region, such as W5 may indicate that NGC 6334 formed via
a cloud-cloud collision (Inoue & Fukui, 2013; Fukui et al., 2018, 2021;
Hayashi et al., 2021) or a shock-cloud interaction (Inutsuka et al., 2015;
Inoue et al., 2018; Abe et al., 2021). These cloud-formation models often
result in an arc-shaped (bow-shaped) magnetic field morphology (Heiles, 1987;
Tahani et al., 2019, 2022a, 2022b) that may appear perpendicular to the cloud
when projected onto the plane of the sky. The shock-cloud interaction model is
also supported in other regions by line-of-sight (Tahani et al., 2018, 2020)
and three-dimensional (Tahani et al., 2019, 2022a, 2022b; Tahani, 2022)
magnetic field and velocity (Arzoumanian et al., 2018; Bonne et al., 2020)
observations.

Figure 15: A schematic illustration of perpendicular $B_{\textsc{POS}}$ field
lines on a dense molecular cloud with Hii region influences. We propose that
the plane-of-sky magnetic field lines in NGC 6334 are generally perpendicular
to the main ridge and that the non-perpendicular lines are due to impacts by
Hii regions or the gas flow (filament within W6). The cloud (or main ridge),
magnetic field lines, and Hii regions are depicted with a cylinder, black
lines, and circular cavities, respectively.

##  5 Summary and conclusion

We investigated the magnetic field morphology of Hii regions associated with
NGC 6334, using the JCMT BISTRO 850 $\mu$m dust polarization observations. We
located these bubbles using the WISE (Anderson et al., 2014) and Simpson et
al. (2012) catalogs and studied the presence of radial polarization patterns
in each bubble by transforming the reference frame of the observations with
respect to the bubble. This enabled us to identify bubbles that had altered
their surrounding magnetic field morphology. Additionally, we compared the gas
and magnetic pressures within each bubble using previously determined Zeeman
magnetic field strengths in order to bolster our conclusion regarding the
magnetic field morphologies associated with these bubbles.

We found evidence of radial polarization associated with W1, W5 (or S5), W6,
W7 (or S7-a), and W8. The radial polarization is prominent in W5 (or S5) and
W6, weak in W1 and S7-a, and absent in W2. S2-a and W3 (and S3) may indicate
radial polarization after subtracting the non-Hii contributions. We propose
that the magnetic field morphology of the NGC 6334 cloud was originally
coherent and perpendicular to the cloud, but was altered during cloud
evolution as a result of internal feedback mechanisms or gas flow.

We found that the presence or indication of radial polarization (tangential
field lines) associated with Hii regions is accompanied by a higher
polarization fraction. Quantifying the relationship between polarization
fraction and bubble physical properties requires a statistical analysis of a
large number of bubbles and should be investigated in subsequent studies.

We found a bipolar polarization structure associated with W7, characterized by
a clear radial polarization pattern for its northern lobe. To our knowledge,
this is the first time that polarization data have been used to identify
bubbles (or lobes within Hii regions). To take this a step further, we applied
a computer vision approach based on the circular Hough transform on the dust
polarization observations to identify and recognize bubbles that had altered
their surrounding magnetic morphology. A more advanced computer vision or
machine learning algorithm can enhance this technique, allowing it to be
applied to additional regions or the entire sky.

## acknowledgments

This program is part of the JCMT BISTRO Large Program observed under project
code M17BL011. Team BISTRO-J is in part financially supported by 260
individuals. 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 in the United Kingdom,
Canada, and Ireland. Additional funds for the construction of SCUBA-2 and
POL-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.

We used LaTeX, Python and its associated libraries including astropy (Astropy
Collaboration et al., 2013), PyCharm, Jupyter notebook, SAO Image DS9, and the
Starlink (Currie et al., 2014) software. QuillBot101010https://quillbot.com/
was employed to edit the text.

M.Tahani is supported by the Banting Fellowship (Natural Sciences and
Engineering Research Council Canada) hosted at Stanford University and the
Kavli Institute for Particle Astrophysics and Cosmology (KIPAC) Fellowship.
D.J. is supported by the National Research Council of Canada and by a Natural
Sciences and Engineering Research Council Discovery Grant. T.O. acknowledges a
Grant-in-Aid for Scientific Research of JSPS (18K03691). Mo.Ta. is supported
by JSPS KAKENHI grant Nos.18H05442, 15H02063, and 22000005. J.K. is supported
by JSPS KAKENHI grant No.19K14775. W.K. is supported by the National Research
Foundation of Korea (NRF) grant funded by the Korea government (MSIT)
(NRF-2021R1F1A1061794). F.P. acknowledges support from the Spanish State
Research Agency (AEI) under grant number PID2019-105552RB-C43. C.E.
acknowledges the financial support from grant RJF/2020/000071 as a part of the
Ramanujan Fellowship awarded by the Science and Engineering Research Board
(SERB), Department of Science and Technology (DST), Government of India. L.F.
acknowledges support from the Ministry of Science and Technology of Taiwan,
under grants no. MoST107-2119-M-001-031- MY3, 111-2811-M-005-007 and
109-2112-M-005-003-MY3, and from Academia Sinica under grant no. AS-
IA-106-M03. F.K is supported by the Spanish program Unidad de Excelencia María
de Maeztu CEX2020-001058-M, financed by MCIN/AEI/10.13039/501100011033.

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##  Appendix A Error bars

To determine the error bars associated with $\cos(\theta_{r})$ we use the
following error propagation equation:

$\delta f=\sqrt{(\frac{\partial f}{\partial Q_{r}})^{2}(\delta
Q_{r})^{2}+(\frac{\partial f}{\partial U_{r}})^{2}(\delta U_{r})^{2}},$ (A1)

where $\delta Q_{r}$ and $\delta U_{r}$ represent the standard deviation of
the mean of $<Q_{r}>$ and $<U_{r}>$ of each annulus, respectively, and

$\displaystyle\centering f$ $\displaystyle=\cos{\theta_{r}},$ (A2)
$\displaystyle\theta_{r}$ $\displaystyle=0.5\times\arctan(<U_{r}>,<Q_{r}>),$
$\displaystyle\frac{\partial f}{\partial U_{r}}$
$\displaystyle=-0.5\times\sin{\theta_{r}}\times\frac{1}{<Q_{r}>\big{(}1+(\frac{<U_{r}>}{<Q_{r}>})^{2}\big{)}},$
$\displaystyle\frac{\partial f}{\partial Q_{r}}$
$\displaystyle=0.5\times\sin{\theta_{r}}\times\frac{1}{1+(\frac{<U_{r}>}{<Q_{r}>})^{2}},\times\frac{<U_{r}>}{<Q_{r}>^{2}}.$

##  Appendix B Elliptical bubble

The bubbles in the Simpson et al. (2012) catalog are initially classified as
ellipses. The Simpson catalog includes inner and outer radii for both X and Y
directions, as well as their eccentricity values, as illustrated in Figure 16.
We examined the radial polarization patterns of these regions and found that
they were very similar to the results presented in Figures 7 and 8, due to the
small eccentricity values of these bubbles.

Figure 16: The Simpson bubbles illustrated in their elliptical form. The
numbers show the Simpson bubbles specified in Figure 3. The inner and outer
radii corresponding to each bubble are illustrated with red ellipses.