# Polarimetric Properties of Event Horizon Telescope Targets from ALMA

Ciriaco Goddi, Iván Martí-Vidal, Hugo Messias, Geoffrey C. Bower, Avery E.

Broderick, Jason Dexter, Daniel P. Marrone, Monika Moscibrodzka, Hiroshi

Nagai, Juan Carlos Algaba, et al.

► To cite this version:

Ciriaco Goddi, Iván Martí-Vidal, Hugo Messias, Geoffrey C. Bower, Avery E. Broderick, et al. Polari-
metric Properties of Event Horizon Telescope Targets from ALMA. The Astrophysical journal letters,
2021, 910, 10.3847/2041-8213/abee6a. insu-03713795

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Distributed under a Creative Commons Attribution 4.0 International License
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Polarimetric Properties of Event Horizon Telescope Targets from ALMA

Ciriaco Goddi¹,² ID, Iván Martí-Vidal³,⁴ ID, Hugo Messias⁵ ID, Geoffrey C. Bower⁶ ID, Avery E. Broderick⁷,⁸,⁹ ID, Jason Dexter¹⁰ ID, Daniel P. Marrone¹¹ ID, Monika Moscibrodzka¹ ID, Hiroshi Nagai¹²,¹³ ID, Juan Carlos Algaba¹⁴ ID, Keiichi Asada¹⁵, Geoffrey B. Crew¹⁶ ID, José L. Gómez¹⁷ ID, C. M. Violette Impellizzeri²,⁵ ID, Michael Janssen¹⁸ ID, Matthias Kadler¹⁹ ID, Thomas P. Krichbaum¹⁸ ID, Rocco Lico¹⁷,¹⁸ ID, Lynn D. Matthews¹⁶ ID, Antonios Nathanail²⁰,²¹ ID, Angelo Ricarte²²,²³ ID, Eduardo Ros¹⁸ ID, Ziri Younsi²⁰,²⁴ ID, Kazunori Akiyama¹²,¹⁶,²²,²⁵ ID, Antxon Alberdi¹⁷ ID, Walter Alef¹⁸, Richard Anantua²²,²³,²⁶ ID, Rebecca Azulay³,⁴,¹⁸ ID, Anne-Kathrin Baczko¹⁸ ID, David Ball¹¹, Mislav Baloković²⁷,²⁸ ID, John Barrett¹⁶ ID, Bradford A. Benson²⁹,³⁰ ID, Dan Bintley³¹, Lindy Blackburn²²,²³ ID, Raymond Blundell²³ ID, Wilfred Boland³², Katherine L. Bouman²²,²³,³³ ID, Hope Boyce³⁴,³⁵ ID, Michael Bremer³⁶, Christiaan D. Brinkerink¹ ID, Roger Brissenden²²,²³ ID, Silke Britzen¹⁸ ID, Dominique Broguiere³⁶, Thomas Bronzwaer¹, Do-Young Byun³⁷,³⁸ ID, John E. Carlstrom³⁰,³⁹,⁴⁰,⁴¹, Andrew Chael⁴²,¹³³ ID, Chi-kwan Chan¹¹,⁴³ ID, Shami Chatterjee⁴⁴ ID, Koushik Chatterjee⁴⁵ ID, Ming-Tang Chen⁶, Yongjun Chen (陈永军)⁴⁶,⁴⁷ ID, Paul M. Chesler²² ID, Ilje Cho³⁷,³⁸ ID, Pierre Christian⁴⁸ ID, John E. Conway⁴⁹ ID, James M. Cordes⁴⁴ ID, Thomas M. Crawford³⁰,³⁹ ID, Alejandro Cruz-Osorio²⁰ ID, Yuzhu Cui¹³,⁵⁰ ID, Jordy Davelaar¹,²⁶,⁵¹ ID, Mariafelicia De Laurentis²⁰,⁵²,⁵³ ID, Roger Deane⁵⁴,⁵⁵,⁵⁶ ID, Jessica Dempsey³¹ ID, Gregory Desvignes⁵⁷ ID, Sheperd S. Doeleman²²,²³ ID, Ralph P. Eatough¹⁸,⁵⁸ ID, Heino Falcke¹ ID, Joseph Farah²²,²³,⁵⁹ ID, Vincent L. Fish¹⁶ ID, Ed Fomalont²⁵ ID, H. Alyson Ford⁶⁰ ID, Raquel Fraga-Encinas¹ ID, William T. Freeman⁶¹,⁶² ID, Per Friberg³¹ ID, Christian M. Fromm²⁰,²²,²³ ID, Antonio Fuentes¹⁷ ID, Peter Galison²²,⁶³,⁶⁴ ID, Charles F. Gammie⁶⁵,⁶⁶ ID, Roberto García³⁶ ID, Olivier Gentaz³⁶, Boris Georgiev⁸,⁹ ID, Roman Gold⁷,⁶⁷ ID, Arturo I. Gómez-Ruiz⁶⁸,⁶⁹ ID, Minfeng Gu (顾敏峰)⁴⁶,⁷⁰ ID, Mark Gurwell²³ ID, Kazuhiro Hada¹³,⁵⁰ ID, Daryl Haggard³⁴,³⁵ ID, Michael H. Hecht¹⁶, Ronald Hesper⁷¹ ID, Luis C. Ho (何子山)⁷²,⁷³ ID, Paul Ho¹⁵ ID, Mareki Honma¹³,⁵⁰,⁷⁴ ID, Chih-Wei L. Huang¹⁵ ID, Lei Huang (黄磊)⁴⁶,⁷⁰ ID, David H. Hughes⁶⁸, Makoto Inoue¹⁵ ID, Sara Issaoun¹ ID, David J. James²²,²³ ID, Buell T. Jannuzi¹¹ ID, Britton Jeter⁸,⁹ ID, Wu Jiang (江悟)⁴⁶ ID, Alejandra Jimenez-Rosales¹, Michael D. Johnson²²,²³ ID, Svetlana Jorstad⁷⁵,⁷⁶ ID, Taehyun Jung³⁷,³⁸ ID, Mansour Karami⁷,⁸ ID, Ramesh Karuppusamy¹⁸ ID, Tomohisa Kawashima⁷⁷ ID, Garrett K. Keating²³ ID, Mark Kettenis⁷⁸ ID, Dong-Jin Kim¹⁸ ID, Jae-Young Kim¹⁸,³⁷ ID, Jongsoo Kim³⁷ ID, Junhan Kim¹¹,³³ ID, Motoki Kino¹²,⁷⁹ ID, Jun Yi Koay¹⁵ ID, Yutaro Kofuji⁵⁰,⁷⁴ ID, Patrick M. Koch¹⁵ ID, Shoko Koyama¹⁵ ID, Michael Kramer¹⁸ ID, Carsten Kramer³⁶ ID, Cheng-Yu Kuo¹⁵,⁸⁰ ID, Tod R. Lauer⁸¹ ID, Sang-Sung Lee³⁷ ID, Aviad Levis³³ ID, Yan-Rong Li (李彦荣)⁸² ID, Zhiyuan Li (李志远)⁸³,⁸⁴ ID, Michael Lindqvist⁴⁹ ID, Greg Lindahl²³ ID, Jun Liu (刘俊)¹⁸ ID, Kuo Liu¹⁸ ID, Elisabetta Liuzzo⁸⁵ ID, Wen-Ping Lo¹⁵,⁸⁶ ID, Andrei P. Lobanov¹⁸, Laurent Loinard⁸⁷,⁸⁸ ID, Colin Lonsdale¹⁶ ID, Ru-Sen Lu (路如森)¹⁸,⁴⁶,⁴⁷ ID, Nicholas R. MacDonald¹⁸ ID, Jirong Mao (毛基荣)⁸⁹,⁹⁰,⁹¹ ID, Nicola Marchili¹⁸,⁸⁵ ID, Sera Markoff⁴⁵,⁹² ID, Alan P. Marscher⁷⁵ ID, Satoki Matsushita¹⁵ ID, Lia Medeiros¹¹,⁹³ ID, Karl M. Menten¹⁸ ID, Izumi Mizuno³¹ ID, Yosuke Mizuno²⁰,⁹⁴ ID, James M. Moran²²,²³ ID, Kotaro Moriyama¹⁶,⁵⁰ ID, Cornelia Müller¹,¹⁸ ID, Gibwa Musoke¹,⁴⁵ ID, Alejandro Mus Mejías³,⁴ ID, Neil M. Nagar⁹⁵ ID, Masanori Nakamura¹⁵,⁹⁶ ID, Ramesh Narayan²²,²³ ID, Gopal Narayanan⁹⁷, Iniyan Natarajan⁵⁴,⁵⁶,⁹⁸ ID, Joey Neilsen⁹⁹ ID, Roberto Neri³⁶ ID, Chunchong Ni⁸,⁹ ID, Aristeidis Noutsos¹⁸ ID, Michael A. Nowak¹⁰⁰ ID, Hiroki Okino⁵⁰,⁷⁴ ID, Héctor Olivares¹ ID, Gisela N. Ortiz-León¹⁸ ID, Tomoaki Oyama⁵⁰ ID, Feryal Özel¹¹, Daniel C. M. Palumbo²²,²³ ID, Jongho Park¹⁵ ID, Nimesh Patel²³, Ue-Li Pen⁷,¹⁰,¹⁰,¹⁰²⁰ ID, Dominic W. Pesce²²,²³ ID, Vincent Piétu³⁶, Richard Plambeck¹⁰⁴ ID, Aleksandar PopStefanija⁹⁷ ID, Oliver Porth²⁰,⁴⁵ ID, Felix M. Pötzl¹⁸ ID, Ben Prather⁶⁵ ID, Jorge A. Preciado-López⁷ ID, Dimitrios Psaltis¹¹ ID, Hung-Yi Pu⁷,¹⁵,¹⁰⁵ ID, Venkatessh Ramakrishnan⁹⁵ ID, Ramprasad Rao⁶ ID, Mark G. Rawlings³¹ ID, Alexander W. Raymond²²,²³ ID, Luciano Rezzolla¹⁰⁶,¹⁰⁷,¹⁰⁸ ID, Bart Ripperda²⁶,¹⁰⁹ ID, Greek Roelofs¹ ID, Alan Rogers¹⁶ ID, Mel Rose¹¹ ID, Arash Roshanineshat¹¹, Helge Rottmann¹⁸, Alan L. Roy¹⁸ ID, Chet Ruszczyk¹⁶ ID, Kazi L. J. Rygl⁸⁵ ID, Salvador Sánchez¹¹⁰, David Sánchez-Arguelles⁶⁸,⁶⁹ ID, Mahito Sasada⁵⁰,¹¹¹ ID, Tuomas Savolainen¹⁸,¹¹²,¹¹³ ID, F. Peter Schloerb⁹⁷ ID, Karl-Friedrich Schuster³⁶, Lijing Shao¹⁸,⁷³ ID, Zhiqiang Shen (沈志强)⁴⁶,⁴⁷ ID, Des Small⁷⁸ ID, Bong Won Sohn³⁷,³⁸,¹¹⁴ ID, Jason SooHoo¹⁶ ID, He Sun (孙赫)³³ ID, Fumie Tazaki⁵⁰ ID, Alexandra J. Tetarenko¹¹⁵ ID, Paul Tiede⁸,⁹ ID, Remo P. J. Tilanus¹,²,¹¹,¹¹⁶ ID, Michael Titus¹⁶ ID, Kenji Toma¹¹⁷,¹¹⁸ ID, Pablo Torne¹⁸,¹¹⁰ ID, Tyler Trent¹¹ ID, Efthalia Traianou¹⁸ ID, Sascha Trippe¹¹⁹ ID, Ilse van Bemmel⁷⁸ ID, Huib Jan van Langevelde⁷⁸,¹²⁰ ID, Daniel R. van Rossum¹ ID, Jan Wagner¹⁸ ID, Derek Ward-Thompson¹²¹ ID, John Wardle¹²² ID, Jonathan Weintroub²²,²³ ID, Norbert Wex¹⁸ ID, Robert Wharton¹⁸ ID, Maciek Wielgus²²,²³ ID, George N. Wong⁶⁵ ID, Qingwen Wu (吴庆文)¹²³ ID, Doosoo Yoon⁴⁵ ID, André Young¹ ID, Ken Young²³ ID, Feng Yuan (袁峰)⁴⁶,⁷⁰,¹²⁴ ID, Ye-Fei Yuan (袁业飞)¹²⁵ ID, J. Anton Zensus¹⁸ ID, Guang-Yao Zhao¹⁷ ID, Shan-Shan Zhao⁴⁶ ID, Gabriele Bruni¹²⁶ ID, A. Gopakumar¹²⁷, Antonio Hernández-Gómez¹⁸ ID, Ruben Herrero-Illana¹⁷,¹²⁸ ID, Adam Ingram¹²⁹ ID, S. Komossa¹⁸ ID, Y. Y. Kovalev¹⁸,¹³⁰,¹³¹ ID, Dirk Muders¹⁸ ID, Manel Perucho³,⁴ ID, Florian Rösch¹⁹, and Mauri Valtonen¹³² ID
¹ Department of Astrophysics, Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radboud University, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands; cgoddi@gmail.com
² Leiden Observatory—Allegro, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands
³ Departament d'Astronomia i Astrofísica, Universitat de València, C. Dr. Moliner 50, E-46100 Burjassot, València, Spain
⁴ Observatori Astronómic, Universitat de València, C. Catedrático José Beltrán 2, E-46980 Paterna, València, Spain
⁵ Joint ALMA Observatory, Alonso de Cordova 3107, Vitacura 763-0355, Santiago de Chile, Chile
⁶ Institute of Astronomy and Astrophysics, Academia Sinica, 645 N. A'ohoku Place, Hilo, HI 96720, USA
⁷ Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada

⁸ Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada

⁹ Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, ON N2L 3G1 Canada

¹⁰ JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309, USA

¹¹ Steward Observatory and Department of Astronomy, University of Arizona, 933 N. Cherry Ave., Tucson, AZ 85721, USA

¹² National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

¹³ Department of Astronomical Science, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

¹⁴ Department of Physics, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia

¹⁵ Institute of Astronomy and Astrophysics, Academia Sinica, 11F of Astronomy-Mathematics Building, AS/NTU No. 1, Sec. 4, Roosevelt Rd, Taipei 10617, Taiwan, R.O.C.

¹⁶ Massachusetts Institute of Technology Haystack Observatory, 99 Millstone Road, Westford, MA 01886, USA

¹⁷ Instituto de Astrofísica de Andalucía-CSIC, Glorieta de la Astronomía s/n, E-18008 Granada, Spain

¹⁸ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn, Germany

¹⁹ Institut für Theoretische Physik und Astrophysik Universität Würzburg, Emil Fischer, Str. 31 D-97074, Würzburg, Germany

²⁰ Institut für Theoretische Physik, Goethe-Universität Frankfurt, Max-von-Laue-Straße 1, D-60438 Frankfurt am Main, Germany

²¹ Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, GR 15783 Zografos, Greece

²² Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA

²³ Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA

²⁴ Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking, Surrey, RH5 6NT, UK

²⁵ National Radio Astronomy Observatory, 520 Edgemont Rd, Charlottesville, VA 22903, USA

²⁶ Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA

²⁷ Yale Center for Astronomy & Astrophysics, 52 Hillhouse Avenue, New Haven, CT 06511, USA

²⁸ Department of Physics, Yale University, P.O. Box 2018120, New Haven, CT 06520, USA

²⁹ Fermi National Accelerator Laboratory, MS209, P.O. Box 500, Batavia, IL, 60510, USA

³⁰ Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA

³¹ East Asian Observatory, 660 N. A’ohoku Place, Hilo, HI 96720, USA

³² Nederlandse Onderzoekschool voor Astronomie (NOVA), P.O. Box 9513, 2300 RA Leiden, The Netherlands

³³ California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, USA

³⁴ Department of Physics, McGill University, 3600 rue University, Montréal, QC H3A 2T8, Canada

³⁵ McGill Space Institute, McGill University, 3550 rue University, Montréal, QC H3A 2A7, Canada

³⁶ Institut de Radioastronomie Millimétrique, 300 rue de la Piscine, F-38406 Saint Martin d’Hères, France

³⁷ Korea Astronomy and Space Science Institute, Daedok-daero 776, Yuseong-gu, Daejeon 34055, Republic of Korea

³⁸ University of Science and Technology, Gajeong-ro 217, Yuseong-gu, Daejeon 34113, Republic of Korea

³⁹ Kavli Institute for Cosmological Physics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL, 60637, USA

⁴⁰ Department of Physics, University of Chicago, 5720 South Ellis Avenue, Chicago, IL 60637, USA

⁴¹ Enrico Fermi Institute, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA

⁴² Princeton Center for Theoretical Science, Jadwin Hall, Princeton University, Princeton, NJ 08544, USA

⁴³ Data Science Institute, University of Arizona, 1230 N. Cherry Ave., Tucson, AZ 85721, USA

⁴⁴ Cornell Center for Astrophysics and Planetary Science, Cornell University, Ithaca, NY 14853, USA

⁴⁵ Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The Netherlands

⁴⁶ Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, People’s Republic of China

⁴⁷ Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, Nanjing 210008, People’s Republic of China

⁴⁸ Physics Department, Fairfield University, 1073 North Benson Road, Fairfield, CT 06824, USA

⁴⁹ Department of Space, Earth and Environment, Chalmers University of Technology, Onsala Space Observatory, SE-43992 Onsala, Sweden

⁵⁰ Mizusawa VLBI Observatory, National Astronomical Observatory of Japan, 2-12 Hoshigaoka, Mizusawa, Oshu, Iwate 023-0861, Japan

⁵¹ Department of Astronomy and Columbia Astrophysics Laboratory, Columbia University, 550 W 120th Street, New York, NY 10027, USA

⁵² Dipartimento di Fisica “E. Pancini,” Università di Napoli “Federico II,” Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli, Italy

⁵³ INFN Sez. di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli, Italy

⁵⁴ Wits Centre for Astrophysics, University of the Witwatersrand, 1 Jan Smuts Avenue, Braamfontein, Johannesburg 2050, South Africa

⁵⁵ Department of Physics, University of Pretoria, Hatfield, Pretoria 0028, South Africa

⁵⁶ Centre for Radio Astronomy Techniques and Technologies, Department of Physics and Electronics, Rhodes University, Makhanda 6140, South Africa

⁵⁷ LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 place Jules Janssen, F-92195 Meudon, France

⁵⁸ National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing 100101, People’s Republic of China

⁵⁹ University of Massachusetts Boston, 100 William T. Morrissey Boulevard, Boston, MA 02125, USA

⁶⁰ Steward Observatory and Department of Astronomy, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA

⁶¹ Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 32-D476, 77 Massachusetts Ave., Cambridge, MA 02142, USA

⁶² Google Research, 355 Main St., Cambridge, MA 02142, USA

⁶³ Department of History of Science, Harvard University, Cambridge, MA 02138, USA

⁶⁴ Department of Physics, Harvard University, Cambridge, MA 02138, USA

⁶⁵ Department of Physics, University of Illinois, 1110 West Green Street, Urbana, IL 61801, USA

⁶⁶ Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 West Green Street, Urbana, IL 61801, USA

⁶⁷ CP3-Origins, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark

⁶⁸ Instituto Nacional de Astrofísica, Óptica y Electrónica. Apartado Postal 51 y 216, 72000. Puebla Pue., México

⁶⁹ Consejo Nacional de Ciencia y Tecnología, Av. Insurgentes Sur 1582, 03940, Ciudad de México, México

⁷⁰ Key Laboratory for Research in Galaxies and Cosmology, Chinese Academy of Sciences, Shanghai 200030, People’s Republic of China

⁷¹ NOVA Sub-mm Instrumentation Group, Kapteyn Astronomical Institute, University of Groningen, Landleven 12, 9747 AD Groningen, The Netherlands

⁷² Department of Astronomy, School of Physics, Peking University, Beijing 100871, People’s Republic of China

⁷³ Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, People’s Republic of China

⁷⁴ Department of Astronomy, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

⁷⁵ Institute for Astrophysical Research, Boston University, 725 Commonwealth Ave., Boston, MA 02215, USA

⁷⁶ Astronomical Institute, St. Petersburg University, Universitetskij pr., 28, Petrodvorets, 198504 St. Petersburg, Russia

⁷⁷ Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8582, Japan

⁷⁸ Joint Institute for VLBI ERIC (JIVE), Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands

⁷⁹ Kogakuin University of Technology & Engineering, Academic Support Center, 2665-1 Nakano, Hachioji, Tokyo 192-0015, Japan

⁸⁰ Physics Department, National Sun Yat-Sen University, No. 70, Lien-Hai Rd, Kaosiung City 80424, Taiwan, R.O.C

⁸¹ National Optical Astronomy Observatory, 950 North Cherry Ave., Tucson, AZ 85719, USA
⁸² Key Laboratory for Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan Road, Shijingshan District, Beijing, People's Republic of China

⁸³ School of Astronomy and Space Science, Nanjing University, Nanjing 210023, People's Republic of China

⁸⁴ Key Laboratory of Modern Astronomy and Astrophysics, Nanjing University, Nanjing 210023, People's Republic of China

⁸⁵ Italian ALMA Regional Centre, INAF-Istituto di Radioastronomia, Via P. Gobetti 101, I-40129 Bologna, Italy

⁸⁶ Department of Physics, National Taiwan University, No.1, Sect. 4, Roosevelt Rd., Taipei 10617, Taiwan, R.O.C

⁸⁷ Instituto de Radioastronomía y Astrofísica, Universidad Nacional Autónoma de México, Morelia 58089, México

⁸⁸ Instituto de Astronomía, Universidad Nacional Autónoma de México, CdMx 04510, México

⁸⁹ Yunnan Observatories, Chinese Academy of Sciences, 650011 Kunming, Yunnan Province, People's Republic of China

⁹⁰ Center for Astronomical Mega-Science, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, 100012, People's Republic of China

⁹¹ Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, 650011 Kunming, People's Republic of China

⁹² Gravitation Astroparticle Physics Amsterdam (GRAPPA) Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands

⁹³ School of Natural Sciences, Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, USA

⁹⁴ Tsung-Dao Lee Institute and School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, People's Republic of China

⁹⁵ Astronomy Department, Universidad de Concepción, Casilla 160-C, Concepción, Chile

⁹⁶ National Institute of Technology, Hachinohe College, 16-1 Uwanotai, Tamonoki, Hachinohe City, Aomori 039-1192, Japan

⁹⁷ Department of Astronomy, University of Massachusetts, 01003, Amherst, MA, USA

⁹⁸ South African Radio Astronomy Observatory, Observatory 7925, Cape Town, South Africa

⁹⁹ Villanova University, Mendel Science Center Rm. 263B, 800 E Lancaster Ave, Villanova PA 19085

¹⁰⁰ Physics Department, Washington University CB 1105, St Louis, MO 63130, USA

¹⁰¹ Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada

¹⁰² Dunlap Institute for Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada

¹⁰³ Canadian Institute for Advanced Research, 180 Dundas St West, Toronto, ON M5G 1Z8, Canada

¹⁰⁴ Radio Astronomy Laboratory, University of California, Berkeley, CA 94720, USA

¹⁰⁵ Department of Physics, National Taiwan Normal University, No. 88, Sec. 4, Tingzhou Rd., Taipei 116, Taiwan, R.O.C.

¹⁰⁶ Institut für Theoretische Physik, Max-von-Laue-Strasse 1, D-60438 Frankfurt, Germany

¹⁰⁷ Frankfurt Institute for Advanced Studies, Ruth-Moufang-Strasse 1, D-60438 Frankfurt, Germany

¹⁰⁸ School of Mathematics, Trinity College, Dublin 2, Ireland

¹⁰⁹ Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA

¹¹⁰ Instituto de Radioastronomía Milimétrica, IRAM, Avenida Divina Pastora 7, Local 20, E-18012, Granada, Spain

¹¹¹ Hiroshima Astrophysical Science Center, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan

¹¹² Aalto University Department of Electronics and Nanoengineering, PL 15500, FI-00076 Aalto, Finland

¹¹³ Aalto University Metsähovi Radio Observatory, Metsähovintie 114, FI-02540 Kylmälä, Finland

¹¹⁴ Department of Astronomy, Yonsei University, Yonsei-ro 50, Seodaemun-gu, 03722 Seoul, Republic of Korea

¹¹⁵ East Asian Observatory, 660 N. A'ohoku Place, Hilo, HI 96720, USA

¹¹⁶ Netherlands Organisation for Scientific Research (NWO), Postbus 93138, 2509 AC Den Haag, The Netherlands

¹¹⁷ Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai 980-8578, Japan

¹¹⁸ Astronomical Institute, Tohoku University, Sendai 980-8578, Japan

¹¹⁹ Department of Physics and Astronomy, Seoul National University, Gwanak-gu, Seoul 08826, Republic of Korea

¹²⁰ Leiden Observatory, Leiden University, Postbus 2300, 9513 RA Leiden, The Netherlands

¹²¹ Jeremiah Horrocks Institute, University of Central Lancashire, Preston PR1 2HE, UK

¹²² Physics Department, Brandeis University, 415 South Street, Waltham, MA 02453, USA

¹²³ School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, People's Republic of China

¹²⁴ School of Astronomy and Space Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing 100049, People's Republic of China

¹²⁵ Astronomy Department, University of Science and Technology of China, Hefei 230026, People's Republic of China

¹²⁶ INAF—Istituto di Astrofisica e Planetologia Spaziali, via Fosso del Cavaliere 100, I-00133 Roma, Italy

¹²⁷ Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Mumbai 400005, India

¹²⁸ European Southern Observatory (ESO), Alonso de Córdova 3107, Casilla, 19001, Vitacura, Santiago de Chile, Chile

¹²⁹ Department of Physics, Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK

¹³⁰ Astro Space Center of Lebedev Physical Institute, Profsoyuznaya 84/32, 117997 Moscow, Russia

¹³¹ Moscow Institute of Physics and Technology, Institutsky per. 9, Dolgoprudny 141700, Russia

¹³² Finnish Centre for Astronomy with ESO (FINCA), Quantum, Vesiilinnantie 5, FI-20014 Turun yliopisto, Finland

*Received 2021 February 2; revised 2021 March 11; accepted 2021 March 12; published 2021 March 24*

## Abstract

We present the results from a full polarization study carried out with the Atacama Large Millimeter/submillimeter Array (ALMA) during the first Very Long Baseline Interferometry (VLBI) campaign, which was conducted in 2017 April in the λ3 mm and λ1.3 mm bands, in concert with the Global mm-VLBI Array (GMVA) and the Event Horizon Telescope (EHT), respectively. We determine the polarization and Faraday properties of all VLBI targets, including Sgr A*, M87, and a dozen radio-loud active galactic nuclei (AGNs), in the two bands at several epochs in a time window of 10 days. We detect high linear polarization fractions (2%–15%) and large rotation measures (RM > 10³.³–10⁵.⁵ rad m⁻²), confirming the trends of previous AGN studies at millimeter wavelengths. We find that blazars are more strongly polarized than other AGNs in the sample, while exhibiting (on average) order-of-magnitude lower RM values, consistent with the AGN viewing angle unification scheme. For Sgr A* we report a mean RM of (−4.2 ± 0.3) × 10⁵ rad m⁻² at 1.3 mm, consistent with measurements over the past decade and, for the first time, an RM of (−2.1 ± 0.1) × 10⁵ rad m⁻² at 3 mm, suggesting

<figure><img src="image_3.png" /></figure>

<footnote n="133">¹³³ NASA Hubble Fellowship Program, Einstein Fellow.</footnote>
that about half of the Faraday rotation at 1.3 mm may occur between the 3 mm photosphere and the 1.3 mm source. We also report the first unambiguous measurement of RM toward the M87 nucleus at millimeter wavelengths, which undergoes significant changes in magnitude and sign reversals on a one year timescale, spanning the range from -1.2 to 0.3 × 10⁵ rad m⁻² at 3 mm and -4.1 to 1.5 × 10⁵ rad m⁻² at 1.3 mm. Given this time variability, we argue that, unlike the case of Sgr A*, the RM in M87 does not provide an accurate estimate of the mass accretion rate onto the black hole. We put forward a two-component model, comprised of a variable compact region and a static extended region, that can simultaneously explain the polarimetric properties observed by both the EHT (on horizon scales) and ALMA (which observes the combined emission from both components). These measurements provide critical constraints for the calibration, analysis, and interpretation of simultaneously obtained VLBI data with the EHT and GMVA.

*Unified Astronomy Thesaurus concepts: Magnetic fields (994); Relativistic jets (1390); Active galactic nuclei (16); Radio jets (1347); Polarimetry (1278); Interferometry (808); Long baseline interferometry (932); Galactic center (565); Supermassive black holes (1663); Blazars (164); Radio galaxies (1343); Quasars (1319)*

# 1. Introduction

Active galactic nuclei (AGNs) are known to host super-massive black holes (SMBHs), which accrete gas through a disk and drive powerful relativistic jets that are observed on scales of parsecs to megaparsecs (Blandford et al. 2019). Magnetic fields are believed to play a major role in the formation of such relativistic jets, by either extracting energy from a spinning SMBH via the Blandford–Znajek mechanism (Blandford & Znajek 1977) or by tapping into the rotational energy of a magnetized accretion flow via the Blandford–Payne mechanism (Blandford & Payne 1982).

Polarization observations are a powerful tool to probe magnetic fields and to understand their role in black hole mass-accretion and launching and acceleration of relativistic AGN jets. In fact, the radio emission from AGNs and their associated jets is thought to be produced by synchrotron processes, and thus it displays high intrinsic linear polarization (LP; e.g., Pacholczyk 1970; Trippe et al. 2010; Agudo et al. 2018). LP fractions and polarization vector orientations can provide details on the magnetic field strength and topology. Besides LP, circular polarization (CP) may also be present as a consequence of Faraday conversion of the linearly polarized synchrotron emission (Beckert & Falcke 2002), and can also help constrain the magnetic field configuration (e.g., Muñoz et al. 2012).

As the linearly polarized radiation travels through magnetized plasma, it experiences Faraday rotation of the LP vectors. The externally magnetized plasma is also known as the “Faraday screen” and the amount of Faraday rotation is known as the “rotation measure” (RM). If the background source of polarized emission is entirely behind (and not intermixed with) the Faraday screen, the RM can be written as an integral of the product of the electron number density ($n_e$) and the magnetic field component along the line of sight ($B_‖$) via

$$RM = 8.1 \times 10^5 \int n_e [\text{cm}^{-3}] \mathbf{B}[\text{G}] \cdot d\mathbf{l} [\text{pc}] \text{ rad m}^{-2}. \quad (1)$$

Thus, by measuring the RM one can also constrain the electron density, $n_e$, and the magnetic field, $B_‖$, in the plasma surrounding SMBHs. Under the assumption that the polarized emission is produced close to the SMBH and then Faraday-rotated in the surrounding accretion flow, the RM has been used in some cases to infer the accretion rate onto SMBHs (e.g., Marrone et al. 2006, 2007; Kuo et al. 2014; Plambeck et al. 2014; Bower et al. 2018). Alternatively, the polarized emission may be Faraday-rotated along the jet boundary layers (e.g., Zavala & Taylor 2004; Martí-Vidal et al. 2015). Therefore, Faraday-rotation measurements

can provide crucial constraints on magnetized accretion models and jet formation models.

RM studies are typically conducted at centimeter wavelengths using the Very Large Array (VLA) or the Very Long Baseline Array (VLBA; e.g., Zavala & Taylor 2004). However, centimeter wavelengths are strongly affected by synchrotron self-absorption close to the central engines and can therefore only probe magnetized plasma in the optically thin regions at relatively larger distances (parsec scales) from the SMBH (Gabuzda et al. 2017; Kravchenko et al. 2017). On the other hand, emission at millimeter wavelengths is optically thin from the innermost regions of the jet base (and accretion disk), enabling us to study the plasma and magnetic fields much closer to the SMBH. In addition, LP can be more easily detected at millimeter wavelengths because the millimeter emission region is smaller (e.g., Lobanov 1998), and so depolarization induced by RM variations across the source (e.g., owing to a tangled magnetic field) is less significant. Finally, since Faraday rotation is smaller at shorter wavelengths (with a typical $\lambda^2$ dependence), millimeter-wavelength measurements more clearly reflect the intrinsic LP properties, and therefore the magnetic field of the system.

Unfortunately, polarimetric measurements at millimeter wavelengths have so far been limited by sensitivity and instrumental systematics. The first interferometric measurements of RM at (sub-)millimeter wavelengths were conducted toward Sgr A* with the Berkeley–Illinois–Maryland Association (BIMA) array (Bower et al. 2003, 2005) and the Submillimeter Array (SMA Marrone et al. 2006, 2007), which yielded an RM ~ -5 × 10⁵ rad m⁻². SMA measurements toward M87 provided an upper limit |RM| < 7.5 × 10⁵ rad m⁻² (Kuo et al. 2014). Other AGNs with RM detections with millimeter interferometers include 3C 84 with RM = 8 × 10⁵ rad m⁻² (Plambeck et al. 2014; see also Nagai et al. 2017 for a similarly high RM measured with the VLBA at 43 GHz), PKS 1830-211 (at a redshift $z = 2.5$) with RM ~ 10⁷ rad m⁻² (Martí-Vidal et al. 2015), and 3C 273 with RM = 5 × 10⁵ rad m⁻² (Hovatta et al. 2019). Additional examples of AGN RM studies with millimeter single-dish telescopes can be found in Trippe et al. (2012) and Agudo et al. (2018).

In order to progress in this field, polarization interferometric studies at millimeter wavelengths should be extended to a larger sample of AGNs and it will be important to investigate both time- and frequency-dependent effects, by carrying out observations at multiple frequency bands and epochs. Ultimately, observational studies should be conducted at the highest possible angular resolutions in order to resolve the innermost regions of the accretion flow and/or the base of relativistic jets.
The advent of the Atacama Large Millimeter/submillimeter Array (ALMA) as a phased array (hereafter phased-ALMA; Matthews et al. 2018; Goddi et al. 2019b) as a new element to Very Long Baseline Interferometry (VLBI) at millimeter wavelengths (hereafter mm-VLBI) has been a game changer in terms of sensitivity and polarimetric studies. In this work, we present a complete polarimetric analysis of ALMA observations carried out during the first VLBI campaign.

## 1.1. mm-VLBI with ALMA

The first science observations with phased-ALMA were conducted in 2017 April (Goddi et al. 2019b), in concert with two different VLBI networks: the Global mm-VLBI Array (GMVA) operating at 3 mm wavelength (e.g., Marti-Vidal et al. 2012) and the Event Horizon Telescope (EHT) operating at 1.3 mm wavelength (Event Horizon Telescope Collaboration et al. 2019a). These observations had two “key science” targets, the SMBH candidate at the Galactic center, Sgr A*, and the nucleus of the giant elliptical galaxy M87 in the Virgo cluster, M87*, both enabling studies at horizon-scale resolution (Doeleman et al. 2008, 2012; Goddi et al. 2017; Event Horizon Telescope Collaboration et al. 2019b). In addition to those targets, VLBI observations with phased-ALMA also targeted a sample of a dozen radio-loud AGNs, including the closest and most luminous quasar 3C 273, the bright γ-ray-emitting blazar 3C 279, the closest radio-loud galaxy Centaurus A (Cen A), and the best supermassive binary black hole candidate OJ 287.

In 2019, the first EHT observations with phased-ALMA yielded groundbreaking results, most notably the first ever event-horizon-scale image of the $M87^*$ SMBH (Event Horizon Telescope Collaboration et al. 2019a, 2019b, 2019c, 2019d, 2019e, 2019f). Beyond this breakthrough, EHT observations have now imaged polarized emission in the ring surrounding $M87^*$, resolving for the first time the magnetic field structures within a few Schwarzschild radii ($R_{Sch}$) of an SMBH (Event Horizon Telescope Collaboration et al. 2021a). In addition, these new polarization images enable us to place tight constraints on physical models of the magnetized accretion flow around the $M87^*$ SMBH and, in general, on relativistic jet launching theories (Event Horizon Telescope Collaboration et al. 2021b).

Both the VLBI imaging and the theoretical modeling use constraints from ALMA observations (Event Horizon Telescope Collaboration et al. 2021a, 2021b). In fact, besides providing a huge boost in sensitivity and uv-coverage (Event Horizon Telescope Collaboration et al. 2019c; Goddi et al. 2019a), the inclusion of ALMA in a VLBI array provides another important advantage: standard interferometric visibilities among the ALMA antennas are computed by the ALMA correlator and simultaneously stored in the ALMA archive together with the VLBI recording of the phased signal (Matthews et al. 2018; Goddi et al. 2019b). Furthermore, VLBI observations are always performed in full-polarization mode in order to supply the inputs to the polarization conversion process (from linear to circular) at the VLBI correlators, carried out using the POLCONVERT software (Martí-Vidal et al. 2016) after the “Level 2 Quality Assurance” (QA2) process (Goddi et al. 2019b). Therefore, VLBI observations with ALMA yield a full-polarization interferometric data set, which provides both source-integrated information for refinement and validation of VLBI data calibration (Event Horizon Telescope Collaboration et al. 2021a) as well as observational constraints to theoretical models (Event Horizon Telescope Collaboration et al. 2021b). Besides these applications, this data set carries valuable

scientific value on its own and can be used to derive millimeter emission, polarization, and Faraday properties of a selected sample of AGNs on arcsecond scales.

## 1.2. This Letter

In this Letter, we present a full polarization study carried out with ALMA in the $\lambda_3$ mm and $\lambda_1$ mm bands toward Sgr A*. M87, and a dozen radio-loud AGNs, with particular emphasis on their polarization and Faraday properties. The current Letter is structured as follows.

Section 2 summarizes the 2017 VLBI observations (Section 2.1), the procedures followed for the data calibration (Section 2.2), the details of the full-polarization image deconvolution (Section 2.3), and additional observations on M87 (Section 2.4).

Section 3 describes the procedures of data analysis. After presenting some representative total-intensity images of Sgr A* and M87 (Section 3.1), two independent algorithms to estimate the Stokes parameters of the compact cores are described (Section 3.2). The Stokes parameters for each source and spectral window are then converted into fractional LP and electric vector position angle (EVPA; Section 3.3.1), and used to estimate Faraday rotation (Section 3.3.2) and (de)polarization effects (Section 3.3.3). Finally, the CP analysis is summarized in Section 3.3.4.

Section 4 reports the polarimetric and Faraday properties of all the GMVA and EHT target sources, with dedicated subsections on AGNs, M87, and Sgr A*.

In Section 5, the polarization properties presented in the previous sections are used to explore potential physical origins of the polarized emission and location of Faraday screens in the context of SMBH accretion and jet formation models. Section 5.1.1 presents a comparison between the $\lambda_3$ mm and $\lambda_1$ mm bands, including a discussion on the effects of synchrotron opacity and Faraday rotation; Section 5.1.2 presents a comparison between the case of blazars and other AGNs; Section 5.1.3 discusses depolarization in radio galaxies and its possible connection to instrumental effects. Section 5.2 is devoted to the special case of M87, including a discussion about the origin of the Faraday screen (internal versus external; Section 5.2.1) as well as a simple two-component Faraday model (Section 5.2.2). Finally, Section 5.3 is dedicated to the special case of Sgr A*.

Conclusions are drawn in Section 6.

This Letter is supplemented with a number of appendices including: the list of ALMA projects observed during the VLBI campaign in 2017 April (Appendix A), a full suite of polarimetric images (Appendix B) for all the observed targets, comparisons between multiple flux-extraction methods (Appendix C) and between the polarimetry results obtained during the VLBI campaign and the monitoring program with the Atacama Compact Array (Appendix D), tables with polarimetric quantities per ALMA spectral-window (Appendix E), Faraday RM plots (Appendix F), quality assessment of the circular polarization estimates (Appendix G), and millimeter spectral indices of all the observed targets (Appendix H). Finally, a two-component polarization model for M87, which combines constraints from ALMA and EHT observations, is presented in Appendix I.

# 2. Observations, Data Processing, and Imaging

## 2.1. 2017 VLBI Observations with ALMA

The observations with phased-ALMA were conducted as part of Cycle 4 during the 2017 VLBI campaign in ALMA
Band 3 (April 1–3) and Band 6 (April 5–11). The ALMA data were acquired simultaneously with the VLBI observations (in this sense they are a “byproduct” of the VLBI operations). The ALMA array was in the compact configurations C40-1 (with 0.15 km longest baseline) and, after April 6, C40-3 (with 0.46 km longest baseline). Only antennas within a radius of 180 m (from the array center) were used for phasing on all days. About 37 antennas were normally phased together, which is equivalent to a telescope of 73 m diameter.<fnref n="134" /> In both Band 3 and 6, the spectral setup includes four spectral windows (SPWs) of 1875 MHz, two in the lower and two in the upper sideband, correlated with 240 channels per SPW (corresponding to a spectral resolution of 7.8125 MHz<fnref n="135" />). In Band 3 the four SPWs are centered at 86.268, 88.268, 98.328, and 100.268 GHz<fnref n="136" /> while in Band 6 they are centered at 213.100, 215.100, 227.100, and 229.100 GHz.

Three projects were observed in Band 3 with the GMVA (science targets: OJ 287, Sgr A*, 3C 273) and six projects were observed in Band 6 with the EHT (science targets: OJ 287, M87, 3C 279, Sgr A*, NGC 1052, Cen A). The projects were arranged and calibrated in “tracks” (where one track consists of the observations taken during the same day/session). In Appendix A we provide a list of the observed projects and targets on each day, with the underlying identifications of (calibration and science target) sources within each project (see Tables A1 and A2 in Appendix A). More details of the observation structure and calibration sources can be found in Goddi et al. (2019b).

## 2.2. Data Calibration and Processing

During phased-array operations, the data path from the antennas to the ALMA correlator is different with respect to standard interferometric operations (Matthews et al. 2018; Goddi et al. 2019b). This makes the calibration of VLBI observations within the Common Astronomy Software Applications (CASA) package intrinsically different and some essential modification in the procedures is required with respect to ALMA standard observations. The special steps added to the standard ALMA polarization calibration procedures (e.g., Nagai et al. 2016) are described in detail in Goddi et al. (2019b). The latter focus mostly on the LP calibration and the polarization conversion at the VLBI correlators (Martí-Vidal et al. 2016). In this Letter we extend the data analysis also to CP.

Only sources observed in VLBI mode were calibrated in polarization (see Section 5 in Goddi et al. 2019b). Therefore the sources exclusively observed for ordinary ALMA calibration during the VLBI schedule gaps (i.e., Flux and Gain calibrators) are excluded from this analysis (compare the source list in Tables A1 and A2 in Appendix A with Tables 4 and 6 in Goddi et al. 2019b). Two additional sources observed on April 7, 3C 84 and J0006–0623, are also excluded from the following analysis. These sources are in fact flagged in a final flagging step (run on the fully calibrated uv-data before imaging and data analysis), which removes visibility data

points having amplitudes outside a certain range (set by three times the rms from the median of the data) and a source elevation below 25°. Finally, the two weakest targets observed at 1.3 mm, NCG 1052 and J0132–1654, were found to fall below the flux threshold (correlated flux density of >0.5 Jy on intra-ALMA baselines) required to enable on-source phasing of the array as commissioned (Matthews et al. 2018). Despite these two sources being detected with high signal-to-noise ratio (S/N) in total intensity (S/N > 1000) and polarized flux (S/N > 50 for J0132–1654), we recommend extra care in interpreting these source measurements owing to lower data quality.

## 2.3. Full-Stokes Imaging

All targets observed in Band 3 and Band 6 are imaged using the CASA task `tclean` in all Stokes parameters: *I*, *Q*, *U*, *V*. A Briggs weighting scheme (Briggs 1995) is adopted with a robust parameter of 0.5, and a cleaning gain of 0.1. A first quick cleaning (100 iterations over all four Stokes parameters) is done in the inner 10" and 4" in bands 3 and 6, respectively. Providing there is still significant emission (>$7\sigma$) in the residual maps (e.g., in M87 and Sgr A*), an automatic script changes the cleaning mask accordingly, and a second, deeper cleaning is done down to $2\sigma$ (these two clean steps are run with parameter `interactive=False`). A final interactive clean step (with `interactive=True`) is run to adjust the mask to include real emission which was missed by the automatic masking and to clean deeper sources with complex structure and high-signal residuals (this step was essential for proper cleaning of Sgr A*). No self-calibration was attempted during the imaging stage (the default calibration scheme for ALMA–VLBI data already relies on self-calibration; see Goddi et al. 2019b for details).

We produced maps of size 256 × 256 pixels, with a pixel size of 0.5" and 0.2" in Band 3 and Band 6, respectively, resulting in maps with a field of view (FOV) of 128" × 128" and 51" × 51", respectively, thereby comfortably covering the primary beams of ALMA Band 3 (60") and Band 6 (27") antennas. We produced maps for individual SPWs and by combining SPWs in each sideband (SPW = 0,1 and SPW = 2,3), setting the `tclean` parameters `deconvolver='hogbom'` and `nterms=1`, as well as by combining all four SPWs, using `deconvolver='mtmfs'` and `nterms=2`. The latter achieved better sensitivity and yielded higher-quality images,<fnref n="137" /> so we used the combined SPW images for the imaging analysis presented in this Letter (except for the per-SPW analysis).

Representative total-intensity images in Band 3 and Band 6 are shown in Figure 1 (Stokes *I*) and 2 (Stokes *I* + polarized intensity), whereas the full suite of images including each source observed in Band 3 and Band 6 on each day of the 2017 VLBI campaign is reported in Appendix B (Figures B1–B6).

The array configurations employed during phased-array observations yielded synthesized beams in the range [4"7–6"1] × [2"4–3"4] in Band 3 and [1"2–3"0] × [0"7–1"5] in Band 6 (depending on the day and the target). Images on different days achieved different sensitivities and angular resolutions, depending on the time on-source and baseline lengths of the phased-array.

<footnote n="134">134 A few more antennas participated in the observations without being phased, the so-called “comparison” antennas, which are mostly used to provide feedback on the efficiency of the phasing process (see Matthews et al. 2018; Goddi et al. 2019b for details).</footnote>

<footnote n="135">135 The recommended continuum setup for standard ALMA observations in full polarization mode is somewhat different and consists of 64 channels, 31.25 MHz wide, per SPW.</footnote>

<footnote n="136">136 The “uneven” frequency separation with SPW = 2 is due to constraints on the first and second Local Oscillators in ALMA’s tuning system.</footnote>

<footnote n="137">137 The `deconvolver='mtmfs'` performed best when combining all four SPW, yielding on average 30%–40% better sensitivity than `deconvolver='hogbom'` combining two SPWs at a time, as expected for rms $\alpha I/\sqrt{\Delta\nu}$. However, `deconvolver='hogbom'` performed poorly when combining all four SPWs, especially for steep spectral index sources, yielding up to 50% worse rms than `deconvolver='mtmfs'`</footnote>
<figure><img src="image_4.png" /></figure>

**Figure 1.** Representative total intensity images. Left panel: image of Sgr A* at 3 mm on April 3 (gray-scale and blue contour) and at 1.3 mm (yellow contours) on 2017 April 6. The image showcases the well-known “mini-spiral” structure surrounding the central compact core, including the eastern and northern arms, the western arc, and the bar at the center. The contour levels at 1.3 mm are $5\sigma \times 2''$ where $\sigma = 0.44$ mJy beam$^{-1}$ and $n = 0, 1, 2, 3...$ up to the peak flux density; the contour level at 3 mm corresponds to $20\sigma$ ($\sigma = 0.8$ mJy beam$^{-1}$). The peak flux density is $2.5 \pm 0.1$ ($2.6 \pm 0.3$) Jy beam$^{-1}$ and the integrated flux density across the entire source is $9.9 \pm 0.5$ ($4.9 \pm 0.5$) Jy at a representative frequency of 93 (221) GHz. The field of view (FOV) is given by the primary beam in Band 3 (~60'') and 1 pc corresponds to $24''$. The beamsizes are $5''_0 \times 2''_7$ (P.A. = -81°1) in Band 3 and $2''_2 \times 1''_3$ (P.A. = -77°5) in Band 6, shown as blue and yellow ovals, respectively, in the lower left corner. Right panel: image of M87 at 1.3 mm on 2017 April 11. The image showcases the structure of the kiloparsec-scale relativistic jet comprised of a bright core at the nucleus and the knots along the jet labeled as D, F, A, B, C; HST-1 is not resolved from the nucleus in these images. The rms noise level is $0.16$ mJy beam$^{-1}$, and the contour levels are a factor of 10 and 40 of the rms. The peak flux density is $1.34$ Jy beam$^{-1}$ and the integrated flux density is $1.57$ Jy at a representative frequency of 221 GHz. The FOV is given by the primary beam in Band 6 (~27'' at 1.3 mm). 1 kpc corresponds to $12''$. This observation was conducted with the most extended array during the VLBI campaign, yielding the highest angular resolution (beam size = $1''_2 \times 0''_8$, P.A. = 79°3, shown in the lower left corner). In both panels the four observing spectral windows (see Section 2.1) were used together for imaging. The intensity brightness is plotted using a logarithmic weighting function (starting from the $5\sigma$ level), in order to highlight the full extent of both the mini-spiral (in Sgr A*) and the jet (in M87).

<figure><img src="image_5.png" /></figure>

**Figure 2.** Polarization images of Sgr A* (left panel) and M87 (right panel) at 1.3 mm on 2017 April 6. The raster image and blue contour show the total intensity emission, the orange contours show the linearly polarized emission, and the black vectors showcase the orientation of the electric vector position angles (EVPAs) (their length is linearly proportional to the polarized flux). The total intensity brightness is plotted using a logarithmic weighting function (starting from the $1\sigma$ level), the blue contour corresponds to $5\sigma$ (where $\sigma$ is the Stokes *I* map rms), while the orange contour levels are $5\sigma \times 2''$ (where $\sigma$ is the linear polarization (LP) map rms and $n = 0,1,2,3...$ up to the peak in the image). The LP fraction at the peak of the compact core is reported in the upper left corner in each panel. The EVPAs are plotted every 8 pixels ($1''_6$ or about 1 per beam) for Sgr A* and every 4 pixels ($0''_8$ or about 2 per beam) for M87 (in order to sample the jet more uniformly). According to the measured RM, the EVPAs toward the compact core should be rotated by -23° (east of north) in Sgr A* and by -16° in M87. The beamsizes (shown as an oval in the lower left corner) are $2''_2 \times 1''_3$ (P.A. -77°) and $2''_2 \times 1''_5$ (P.A. -69°) in the left and right panels, respectively. Note that there are several tiny EVPAs plotted across the mini-spiral, apparently locating regions with polarized flux above the image rms noise cutoff ($5\sigma$). The LP and EVPA errors are however dominated by the systematic leakage (0.03% of *I* onto *QU*), which is not added to the images. Once these systematic errors are added, the LP flux in those points falls below the $3\sigma$ measurement threshold. Therefore we do not claim detection of polarized emission outside of the central core in Sgr A*. Besides, only the polarization within the inner 1/3 of the primary beam is guaranteed by ALMA. The full set of 1.3 mm observations of Sgr A* and M87 are reported in Figures B1 and B2, respectively.

particular, the relatively large range of beamsizes in Band 6 is due to the fact that, during the EHT campaign, progressively more antennas were moved out from the “central cluster” (with a

diameter < 150 m). As a consequence, on the last day of the campaign (April 11) the observations were carried out with a more extended array, yielding a beam size in the range
[1′′2–1′′5] × [0′′7–0′′9] (i.e., an angular resolution roughly two times better than that of other tracks). Tables B1 and B2 in Appendix B report the synthesized beam size and the rms achieved in the images of each Stokes parameter for each source observed in Band 3 and Band 6 on each day.

## 2.4. Additional ALMA Polarization Datasets on M87

In addition to the 2017 April data, we also analyzed ALMA data acquired during the 2018 VLBI campaign as well as ALMA archival polarimetric experiments targeting M87.

The 2018 VLBI campaign was conducted as part of Cycle 5 in Band 3 (April 12–17) and Band 6 (April 18–29). The observational setup was the same as in Cycle 4, as outlined in Section 2.1 (a full description of the 2018 VLBI campaign will be reported elsewhere). Three observations of M87 at $\lambda$1.3 mm were conducted on April 21, 22, and 25 under the project 2017.1.00841.V. For the data processing and calibration, we followed the same procedure used for the 2017 observations, as outlined in Section 2.2.

The archival experiments include three observations at $\lambda$3 mm carried out on 2015 September and November (project codes: 2013.1.01022.S and 2015.1.01170.S, respectively) and 2016 October (project code: 2016.1.00415.S), and one observation at $\lambda$1.3 mm from 2018 September (project code: 2017.1.00608.S). For projects 2013.1.01022.S and 2015.1.01170.S, we used directly the imaging products released with the standard QA2 process and publicly available for download from the ALMA archive. For projects 2016.1.00415.S and 2017.1.00608.S, we downloaded the raw visibility data and the QA2 calibration products from the ALMA archive, and we revised the polarization calibration after additional data flagging, following the procedures outlined in Nagai et al. (2016).

The data imaging was performed following the same procedures outlined in Section 2.3. After imaging, we found that in 2017.1.00608.S, Stokes *I*, *Q*, and *U* are not co-located: *U* is shifted ~0.07 to the east, while *Q* is shifted ~0.13 west and ~0.07 north, with respect to *I*. This shift (whose origin is unknown) prevents us from assessing reliably the polarimetric properties of M87. Therefore, we will not use 2017.1.00608.S in the analysis presented in this Letter. The analysis and results of the other data sets will be presented in Section 4.2.

# 3. Data Analysis

## 3.1. Representative Total Intensity Images

The sources targeted by the GMVA and EHT are generally unresolved at arcsecond scales and their images are mostly consistent with point sources (see the images displayed in Appendix B). The EHT key science targets, Sgr A* and M87, are clear exceptions, and show complex/extended structures across tens of arcseconds. We show representative images of Sgr A* (3 mm, April 3; 1.3 mm, April 6) and M87 (1.3 mm, April 11) in Figure 1. The images displayed cover an area corresponding to the primary beam of the ALMA antennas (27" in Band 6 and 60" in Band 3; the correction for the attenuation of the primary beam is not applied to these maps).

The Sgr A* images clearly depict the well-known “mini-spiral” structure that traces ionized gas streams surrounding the central compact source; the mini-spiral has been studied in a wide range of wavelengths (e.g., Zhao et al. 2009; Irons et al. 2012; Roche et al. 2018). The “eastern arm,” the “northern arm,” and the “bar” are clearly seen in both Band 3 and Band 6,

while the “western arc” is clearly traced only in the Band 3 image (it falls mostly outside of the antenna primary beam for Band 6). Similar images were obtained in the 100, 250, and 340 GHz bands in ALMA Cycle 0 by Tsuboi et al. (2016, see their Figure 1). Since Sgr A* shows considerable variability in its core at millimeter wavelengths (e.g., Bower et al. 2018), the displayed maps and quoted flux values throughout this Letter should be considered as time-averaged images/values at the given epoch.

The M87 jet has been observed across the entire electromagnetic spectrum (e.g., Prieto et al. 2016), and imaged in detail at radio wavelengths from $\lambda$1 meter (with LOFAR: de Gasperin et al. 2012) through $\lambda$[15–0.7] cm (with the VLA and the VLBA: e.g., Hada et al. 2013; Walker et al. 2018) up to $\lambda$3 mm (with the GMVA: e.g., Kim et al. 2018). VLA images at lower radio frequencies (e.g., Biretta et al. 1995) showcase a bright component at the nucleus and a kiloparsec-scale relativistic jet, extending across approximately 25" (~2 kpc) from the central core. Images of the kiloparsec-scale relativistic jet were also produced with ALMA Cycle-0 observations at $\lambda$3 mm (Doi et al. 2013) and with the SMA at $\lambda$1 mm (Tan et al. 2008; Kuo et al. 2014), but could only recover the bright central core and the strongest knots along the jet.

Our $\lambda$1.3 mm ALMA image showcases a similar structure, but the higher dynamic range (when compared with these earlier studies) allows us to recover the continuous structure of the straight and narrow kiloparsec-scale jet across approximately 25" from the nucleus, including knots D, F, A, B, C, at increasing distance from the central core (HST-1 is not resolved from the nucleus in these images). The jet structure at larger radii ($\gtrsim$2 kpc) as well as the jet-inflated radio lobes, imaged in great detail with observations at lower frequencies, are not recovered in our images (see for example the NRAO 20 cm VLA image).

## 3.2. Extracting Stokes Parameters in the Compact Cores

We extract flux values for Stokes *I*, *Q*, *U*, and *V* in the compact cores of each target observed in Band 3 and Band 6. We employ three different methods which use both the visibility data and the full-Stokes images. In the uv-plane analysis, we use the external CASA library UVMULTIFIT (Martí-Vidal et al. 2014). To reduce its processing time, we first average all (240) frequency channels to obtain one-channel four-SPW visibility uv-files. We assume that the emission is dominated by a central point source at the phase center and we fit a delta function to the visibilities to obtain Stokes *I*, *Q*, *U*, and *V* parameters in each individual SPW. Uncertainties are assessed with Monte Carlo (MC) simulations, as the standard deviation of 1000 MC simulations for each Stokes parameter. For the image-based values, we take the sum of the central nine pixels of the CLEAN model component map (an area of 3 × 3 pixels, where the pixel size is 0.2" in Band 6 and 0.5" in Band 3). Summing only the central pixels in the model maps allows one to isolate the core emission from the surroundings in sources with extended structure. A third independent method provides the integrated flux by fitting a Gaussian model to the compact source at the phase-center in each image with the CASA task IMFIT. In the remaining of this Letter, we will indicate these three methods as UVMF, 3 × 3, and INTF.

From a statistical perspective, any fitting method in the visibility domain should be statistically more reliable than a $\chi^2$-based fitting analysis in the image plane (whose pixels have
<table><caption>**Table 1**
Frequency-averaged Polarization Properties of GMVA Targets (at a Representative Frequency of 93 GHz)</caption><thead><tr><th>Source</th><th>Day (2017)</th><th>I (Jy)</th><th>Spectral Index α</th><th>LP (%)</th><th>EVPA<sup>a</sup> (deg)</th><th>χ<sub>0</sub> (deg)</th><th>RM (10<sup>5</sup> rad m<sup>-2</sup>)</th><th>Depol. (10<sup>-4</sup> GHz<sup>-1</sup>)</th></tr></thead><tbody><tr><td>OJ 287</td><td>Apr 2</td><td>5.97 ± 0.30</td><td>-0.619 ± 0.029</td><td>8.811 ± 0.030</td><td>-70.02 ± 0.10</td><td>-71.85 ± 0.37</td><td>0.0305 ± 0.0062</td><td>2.244 ± 0.071</td></tr><tr><td>J0510+1800</td><td>Apr 2</td><td>3.11 ± 0.16</td><td>-0.6360 ± 0.0059</td><td>4.173 ± 0.030</td><td>81.86 ± 0.21</td><td>65.49 ± 0.81</td><td>0.273 ± 0.013</td><td>2.639 ± 0.078</td></tr><tr><td>4C 01.28</td><td>Apr 2</td><td>4.86 ± 0.24</td><td>-0.480 ± 0.033</td><td>4.421 ± 0.030</td><td>-32.27 ± 0.19</td><td>-31.73 ± 0.74</td><td>-0.009 ± 0.012</td><td>2.117 ± 0.054</td></tr><tr><td>Sgr A*</td><td>Apr 3</td><td>2.52 ± 0.13</td><td>-0.08 ± 0.13</td><td>0.735 ± 0.030</td><td>8.1 ± 1.4</td><td>135.4 ± 5.3</td><td>-2.13 ± 0.10</td><td>4.72 ± 0.13</td></tr><tr><td>J1924-2914</td><td>Apr 3</td><td>5.11 ± 0.26</td><td>-0.462 ± 0.026</td><td>4.841 ± 0.030</td><td>-46.38 ± 0.18</td><td>-46.68 ± 0.70</td><td>0.005 ± 0.012</td><td>2.34 ± 0.22</td></tr><tr><td>NRAO 530</td><td>Apr 3</td><td>2.74 ± 0.14</td><td>-0.588 ± 0.010</td><td>0.921 ± 0.030</td><td>38.8 ± 1.0</td><td>51.5 ± 3.7</td><td>-0.213 ± 0.061</td><td>0.4372 ± 0.0034</td></tr><tr><td>4C 09.57</td><td>Apr 3</td><td>2.85 ± 0.14</td><td>-0.3056 ± 0.0057</td><td>4.069 ± 0.030</td><td>-28.47 ± 0.21</td><td>-31.15 ± 0.83</td><td>0.045 ± 0.014</td><td>0.43 ± 0.11</td></tr><tr><td>3C 279</td><td>Apr 4</td><td>12.93 ± 0.65</td><td>-0.3703 ± 0.0087</td><td>12.159 ± 0.030</td><td>43.906 ± 0.070</td><td>44.98 ± 0.27</td><td>-0.0179 ± 0.0045</td><td>0.456 ± 0.041</td></tr><tr><td>3C 273</td><td>Apr 4</td><td>9.86 ± 0.49</td><td>-0.2887 ± 0.0049</td><td>3.984 ± 0.030</td><td>-45.45 ± 0.22</td><td>-41.87 ± 0.85</td><td>-0.060 ± 0.014</td><td>-2.06 ± 0.38</td></tr></tbody></table>

**Note.**

correlated noise), and should therefore be preferred to image-based methods. However, we have two reasons for considering both approaches in this study: (i) some of our targets exhibit prominent emission structure at arcsecond scales (see Figure 1 and the maps in Appendix B), (ii) the observations are carried out with various array configurations, resulting in a different degree of filtering of the source extended emission. Both elements can potentially bias the flux values of the compact cores extracted in the visibility domain versus the image domain.

In Appendix C we present a comparative analysis of three flux-extraction methods to assess the magnitude of such systematic biases (reported in Table C1 in Appendix C). The statistical analysis shows that the Stokes *I* values estimated with UVMF are consistent with those estimated from the images, with a median absolute deviation (MAD) ≲ 0.07% and individual offsets <1% (for both point sources and extended sources) in the case of the 3 × 3 method (the agreement is slightly worse for the INTF method). These deviations are negligible when compared to the absolute uncertainty of ALMA’s flux calibration (10% in Band 6). This consistency generally holds also for Stokes *Q* and *U* (with MAD < 1%) and other derived parameters within their uncertainties (see Table C1 in Appendix C). We therefore conclude that, for the purpose of the polarimetric analysis conducted in this Letter, the uv-fitting method UVMF provides sufficiently precise flux values for the Stokes parameters (but see Appendix C for details on M87 and Sgr A*).

Goddi et al. (2019b) report the Stokes *I* flux values per source estimated in the uv-plane from amplitude gains using the CASA task *fluxscale*. We assess that the Stokes *I* estimated from the visibilities with UVMF are consistent with those estimated with *fluxscale* generally within 1%. In addition, Goddi et al. (2019b) compared the *fluxscale* flux values (after opacity correction) with the predicted values from the regular flux monitoring program with the ALMA Compact Array (ACA), showing that these values are generally within 10% (see their Appendix B and their Figure 16). In Appendix D we perform a similar comparative analysis for the sources commonly observed in the ALMA-VLBI campaign and the AMAPOLA polarimetric Grid Survey, concluding that our polarimetric measurements are generally consistent with historic trends of grid sources (see Appendix D for more details and comparison plots).

### 3.3. Polarimetric Data Analysis

In this section we use the measured values of the Stokes parameters to determine the polarization properties for all targets, including the fractional LP (Section 3.3.1), the EVPA and its variation as a function of frequency or Faraday rotation (Section 3.3.2), the degree of depolarization (Section 3.3.3), and the fractional CP (Section 3.3.4). These polarization quantities, averaged across the four SPWs, are reported in Tables 1 and 2 for each target observed with the GMVA and the EHT, respectively (while Table 3 summarizes all the ALMA polarimetric observations toward M87 analyzed in this Letter). For selected EHT targets, the polarization properties (per SPW and per day) are displayed in Figure 3.

#### 3.3.1. Linear Polarization and EVPA

The values estimated for Stokes *Q* and *U* can be combined to directly provide the fractional LP in the form $\sqrt{Q^2 + U^2}/I$, as well as the EVPA, $\chi$, via the equation $2\chi = \arctan(U/Q)$. Tables E1 and E2 in Appendix E report Stokes parameters, LP, and EVPA, for each SPW. The LP has been *debias*ed in order to correct for the LP bias in the low-S/N regime (this correction is especially relevant for low-polarization sources; see Appendix E for the debiased LP derivation).

The estimated LP fractions range from ≲0.1% to 0.2% for the most weakly polarized targets (Cen A and NGC 1052) to 15% for the most strongly polarized target (3C 279), consistent with previous measurements (see Appendix D). The uncertainties in LP include the fitting (thermal) error of Stokes *Q* and *U* and the (systematic) Stokes *I* leakage onto Stokes *Q* and *U* (0.03% of Stokes *I*) added in quadrature. This analysis yields LP uncertainties < 0.1%, similar to those quoted in previous studies (Nagai et al. 2016; Bower et al. 2018).

Figure 2 showcases representative polarization images of Sgr A* (left panel) and M87 (right panel) as observed at 1.3 mm on April 6. The individual images display the measured EVPAs overlaid on the polarized flux contour images and the total intensity images. Note that the EVPAs are not Faraday-corrected and that the measured<fnref n="138" /> magnetic field orientations should be rotated by 90°. In Sgr A*, polarized emission is present only toward the compact core, while none is observed

<footnote><sup>a</sup> The EVPAs are the frequency-averaged $\bar{\chi}$ (as defined in Equation (2)).</footnote>

<footnote n="138">¹³⁸ The actual magnetic field in the source may be different from the measured one, which can be affected by Lorentz transformation and light aberration.</footnote>
<table><caption>**Table 2**
Frequency-averaged Polarization Properties of EHT Targets (at a Representative Frequency of 221 GHz)</caption><thead><tr><th>Source</th><th>Day<br>(2017)</th><th>I<br>(Jy)</th><th>Spectral Index<br>α</th><th>LP<br>(%)</th><th>EVPA<sup>a</sup><br>(deg)</th><th>χ<sub>0</sub><br>(deg)</th><th>RM<br>(10<sup>5</sup> rad m<sup>-2</sup>)</th><th>Depol.<br>(10<sup>-4</sup> GHz<sup>-1</sup>)</th></tr></thead><tbody><tr><td>3C 279</td><td>Apr 5</td><td>8.99 ± 0.90</td><td>-0.642 ± 0.019</td><td>13.210 ± 0.030</td><td>45.180 ± 0.060</td><td>45.20 ± 0.51</td><td>-0.002 ± 0.048</td><td>0.242 ± 0.051</td></tr><tr><td>3C 279</td><td>Apr 6</td><td>9.36 ± 0.94</td><td>-0.619 ± 0.033</td><td>13.010 ± 0.030</td><td>43.340 ± 0.070</td><td>43.41 ± 0.52</td><td>-0.007 ± 0.049</td><td>0.303 ± 0.018</td></tr><tr><td>3C 279</td><td>Apr 10</td><td>8.56 ± 0.86</td><td>-0.6090 ± 0.0030</td><td>14.690 ± 0.030</td><td>40.140 ± 0.060</td><td>40.10 ± 0.46</td><td>0.004 ± 0.043</td><td>0.473 ± 0.033</td></tr><tr><td>3C 279</td><td>Apr 11</td><td>8.16 ± 0.82</td><td>-0.683 ± 0.019</td><td>14.910 ± 0.030</td><td>40.160 ± 0.060</td><td>40.15 ± 0.46</td><td>0.001 ± 0.043</td><td>1.027 ± 0.015</td></tr><tr><td>M87</td><td>Apr 5</td><td>1.28 ± 0.13</td><td>-1.212 ± 0.038</td><td>2.420 ± 0.030</td><td>-7.79 ± 0.36</td><td>-14.6 ± 2.8</td><td>0.64 ± 0.27</td><td>1.318 ± 0.031</td></tr><tr><td>M87</td><td>Apr 6</td><td>1.31 ± 0.13</td><td>-1.112 ± 0.011</td><td>2.160 ± 0.030</td><td>-7.60 ± 0.40</td><td>-23.6 ± 3.1</td><td>1.51 ± 0.30</td><td>0.888 ± 0.046</td></tr><tr><td>M87</td><td>Apr 10</td><td>1.33 ± 0.13</td><td>-1.171 ± 0.023</td><td>2.740 ± 0.030</td><td>0.03 ± 0.31</td><td>2.5 ± 2.5</td><td>-0.24 ± 0.23</td><td>0.540 ± 0.048</td></tr><tr><td>M87</td><td>Apr 11</td><td>1.34 ± 0.13</td><td>-1.208 ± 0.019</td><td>2.710 ± 0.030</td><td>-0.64 ± 0.32</td><td>3.5 ± 2.5</td><td>-0.39 ± 0.24</td><td>1.553 ± 0.064</td></tr><tr><td>Sgr A*</td><td>Apr 6</td><td>2.63 ± 0.26</td><td>-0.0270 ± 0.0030</td><td>6.870 ± 0.030</td><td>-65.83 ± 0.13</td><td>-14.7 ± 1.0</td><td>-4.84 ± 0.10</td><td>3.75 ± 0.10</td></tr><tr><td>Sgr A*</td><td>Apr 7</td><td>2.41 ± 0.24</td><td>-0.057 ± 0.059</td><td>7.230 ± 0.030</td><td>-65.38 ± 0.12</td><td>-18.77 ± 0.93</td><td>-4.412 ± 0.088</td><td>3.33 ± 0.12</td></tr><tr><td>Sgr A*</td><td>Apr 11</td><td>2.38 ± 0.24</td><td>-0.1450 ± 0.0080</td><td>7.470 ± 0.030</td><td>-49.33 ± 0.12</td><td>-14.66 ± 0.92</td><td>-3.281 ± 0.087</td><td>2.52 ± 0.32</td></tr><tr><td>J1924-2914</td><td>Apr 6</td><td>3.25 ± 0.32</td><td>-0.780 ± 0.012</td><td>6.090 ± 0.030</td><td>-49.28 ± 0.14</td><td>-53.6 ± 1.1</td><td>0.41 ± 0.10</td><td>0.13 ± 0.20</td></tr><tr><td>J1924-2914</td><td>Apr 7</td><td>3.15 ± 0.31</td><td>-0.8510 ± 0.0070</td><td>5.970 ± 0.030</td><td>-49.22 ± 0.15</td><td>-52.1 ± 1.2</td><td>0.27 ± 0.11</td><td>0.1470 ± 0.0080</td></tr><tr><td>J1924-2914</td><td>Apr 11</td><td>3.22 ± 0.32</td><td>-0.677 ± 0.031</td><td>4.870 ± 0.030</td><td>-51.82 ± 0.18</td><td>-56.2 ± 1.4</td><td>0.42 ± 0.13</td><td>0.16 ± 0.21</td></tr><tr><td>OJ 287</td><td>Apr 5</td><td>4.34 ± 0.43</td><td>-0.91 ± 0.10</td><td>9.020 ± 0.030</td><td>-61.190 ± 0.090</td><td>-62.32 ± 0.73</td><td>0.108 ± 0.069</td><td>0.11 ± 0.63</td></tr><tr><td>OJ 287</td><td>Apr 10</td><td>4.22 ± 0.42</td><td>-0.781 ± 0.088</td><td>7.000 ± 0.030</td><td>-61.81 ± 0.12</td><td>-62.6 ± 1.0</td><td>0.077 ± 0.091</td><td>0.09 ± 0.61</td></tr><tr><td>OJ 287</td><td>Apr 11</td><td>4.26 ± 0.43</td><td>-0.715 ± 0.043</td><td>7.150 ± 0.030</td><td>-59.61 ± 0.12</td><td>-62.97 ± 0.92</td><td>0.317 ± 0.087</td><td>0.110 ± 0.049</td></tr><tr><td>4C 01.28</td><td>Apr 5</td><td>3.51 ± 0.35</td><td>-0.73 ± 0.16</td><td>5.900 ± 0.030</td><td>-23.18 ± 0.15</td><td>-22.5 ± 1.1</td><td>-0.06 ± 0.11</td><td>0.58 ± 0.20</td></tr><tr><td>4C 01.28</td><td>Apr 10</td><td>3.59 ± 0.36</td><td>-0.679 ± 0.079</td><td>5.080 ± 0.030</td><td>-16.82 ± 0.17</td><td>-16.3 ± 1.3</td><td>-0.05 ± 0.12</td><td>0.68 ± 0.26</td></tr><tr><td>4C 01.28</td><td>Apr 11</td><td>3.57 ± 0.36</td><td>-0.630 ± 0.024</td><td>5.000 ± 0.030</td><td>-14.74 ± 0.18</td><td>-18.2 ± 1.4</td><td>0.33 ± 0.13</td><td>0.416 ± 0.054</td></tr><tr><td>NRAO 530</td><td>Apr 6</td><td>1.61 ± 0.16</td><td>-0.96 ± 0.14</td><td>2.350 ± 0.030</td><td>51.59 ± 0.37</td><td>51.7 ± 2.9</td><td>-0.01 ± 0.28</td><td>0.940 ± 0.062</td></tr><tr><td>NRAO 530</td><td>Apr 7</td><td>1.57 ± 0.16</td><td>-0.812 ± 0.017</td><td>2.430 ± 0.030</td><td>50.67 ± 0.36</td><td>51.1 ± 2.8</td><td>-0.04 ± 0.27</td><td>0.82 ± 0.15</td></tr><tr><td>J0132-1654</td><td>Apr 6</td><td>0.420 ± 0.040</td><td>-0.625 ± 0.086</td><td>1.990 ± 0.050</td><td>15.54 ± 0.67</td><td>23.4 ± 5.3</td><td>-0.74 ± 0.50</td><td>0.04 ± 0.40</td></tr><tr><td>J0132-1654</td><td>Apr 7</td><td>0.410 ± 0.040</td><td>-0.75 ± 0.10</td><td>2.010 ± 0.050</td><td>17.85 ± 0.78</td><td>14.3 ± 6.2</td><td>0.34 ± 0.58</td><td>-0.18 ± 0.21</td></tr><tr><td>NGC 1052</td><td>Apr 6</td><td>0.430 ± 0.040</td><td>-0.83 ± 0.11</td><td>0.120 ± 0.030</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>NGC 1052</td><td>Apr 7</td><td>0.380 ± 0.040</td><td>-1.33 ± 0.16</td><td>0.160 ± 0.040</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>Cen A</td><td>Apr 10</td><td>5.66 ± 0.57</td><td>-0.197 ± 0.038</td><td>0.070 ± 0.030</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>3C 273</td><td>Apr 6</td><td>7.56 ± 0.76</td><td>-0.705 ± 0.024</td><td>2.390 ± 0.030</td><td>-55.50 ± 0.36</td><td>-82.2 ± 2.8</td><td>2.52 ± 0.27</td><td>-2.54 ± 0.11</td></tr><tr><td>J0006-0623</td><td>Apr 6</td><td>1.99 ± 0.20</td><td>-0.789 ± 0.059</td><td>12.530 ± 0.030</td><td>16.480 ± 0.070</td><td>15.83 ± 0.57</td><td>0.061 ± 0.054</td><td>0.78 ± 0.27</td></tr></tbody></table>

**Note.**

<sup>a</sup> The EVPAs are the frequency-averaged $\bar{\chi}$ (as defined in Equation (2)).

from the mini-spiral. In M87, the EVPA distribution appears quite smooth along the jet, with no evident large fluctuations of the EVPAs in nearby regions, except between Knots A and B. For a negligible RM along the jet, one can infer that the magnetic field orientation is first parallel to the jet axis, then in Knot A it changes direction (tending to be perpendicular to the jet), and then turns back to be parallel in Knot B, and finally becomes perpendicular to the jet axis further downstream (Knot C). This behavior can be explained if Knot A is a standing or recollimation shock: if multiple standing shocks with different magnetic field configurations form along the jet and the latter is threaded with a helical magnetic field, its helicity (or magnetic pitch) would be different before and after the shock owing to a different radial dependence of the poloidal and toroidal components of the magnetic field (e.g., Mizuno et al. 2015). The EVPA distribution is also in good agreement with the polarization characteristics derived from observations at centimeter wavelengths with the VLA (e.g., Algaba et al. 2016). We nevertheless explicitly note that only the polarization within the inner third of the primary beam is guaranteed by the ALMA observatory. Since we focus on the polarization

properties in the core, the analysis presented in this Letter is not affected by this systematics.

### 3.3.2. Rotation Measure

Measuring the EVPA for each SPW (i.e., at four different frequencies) enables us to estimate the RM in the 3 mm band (spanning a 16 GHz frequency range of 85–101 GHz) and in the 1.3 mm band (spanning a 18 GHz frequency range of 212–230 GHz), respectively. In the simplest assumption that the Faraday rotation is caused by a single external Faraday screen (i.e., it occurs outside of the plasma responsible for the polarized emission), a linear dependence is expected between the EVPA and the wavelength squared. In particular, we fit the RM and the mean-wavelength ($\bar{\lambda}$) EVPA ($\bar{\chi}$) following the relation

$$ \chi = \bar{\chi} + \text{RM}(\lambda^2 - \bar{\lambda}^2), \quad (2) $$

where $\chi$ is the observed EVPA at wavelength $\lambda$ and $\bar{\chi}$ is the EVPA at wavelength $\bar{\lambda}$. The EVPA extrapolated to zero
<table><caption>**Table 3**
M87 Faraday RMs with ALMA</caption><thead><tr><th>Date</th><th>I<br>(Jy)</th><th>LP<br>(%)</th><th>EVPA<br>(deg)</th><th>χ<sub>0</sub><br>(deg)</th><th>RM<br>(10<sup>5</sup> rad m<sup>-2</sup>)</th><th>Beamsize</th><th>Project Code</th></tr></thead><tbody><tr><td colspan="8" style="text-align:center;">3 mm</td></tr><tr><td>2015 Sep 19</td><td>2.17 ± 0.11</td><td>1.37 ± 0.03</td><td>30.68 ± 0.74</td><td>41.7 ± 3.1</td><td>-0.201 ± 0.054</td><td>0"/53</td><td>2013.1.01022.S<sup>a</sup></td></tr><tr><td>2015 Nov 11</td><td>1.93 ± 0.10</td><td>1.30 ± 0.03</td><td>21.47 ± 0.69</td><td>3.9 ± 2.7</td><td>0.318 ± 0.049</td><td>0"/15</td><td>2015.1.01170.S<sup>a</sup></td></tr><tr><td>2016 Oct 4</td><td>1.85 ± 0.10</td><td>2.39 ± 0.03</td><td>33.35 ± 0.36</td><td>107.4 ± 1.4</td><td>-1.227 ± 0.023</td><td>0"/43</td><td>2016.1.00415.S</td></tr><tr><td colspan="8" style="text-align:center;">1.3 mm</td></tr><tr><td>2017 Apr 5</td><td>1.28 ± 0.13</td><td>2.42 ± 0.03</td><td>-7.78 ± 0.37</td><td>-14.6 ± 2.9</td><td>0.64 ± 0.27</td><td>1"/5</td><td>2016.1.01154.V</td></tr><tr><td>2017 Apr 6</td><td>1.31 ± 0.13</td><td>2.16 ± 0.03</td><td>-7.61 ± 0.39</td><td>-23.6 ± 3.1</td><td>1.51 ± 0.29</td><td>1"/8</td><td>2016.1.01154.V</td></tr><tr><td>2017 Apr 10</td><td>1.33 ± 0.13</td><td>2.74 ± 0.03</td><td>0.11 ± 0.32</td><td>3.5 ± 2.5</td><td>-0.32 ± 0.24</td><td>1"/5</td><td>2016.1.01154.V</td></tr><tr><td>2017 Apr 11</td><td>1.31 ± 0.13</td><td>2.71 ± 0.03</td><td>-0.63 ± 0.31</td><td>3.7 ± 2.4</td><td>-0.41 ± 0.23</td><td>1"/0</td><td>2016.1.01154.V</td></tr><tr><td>2018 Apr 21</td><td>1.11 ± 0.11</td><td>2.29 ± 0.03</td><td>27.18 ± 0.38</td><td>70.6 ± 3.0</td><td>-4.11 ± 0.28</td><td>0"/9</td><td>2017.1.00841.V</td></tr><tr><td>2018 Apr 22</td><td>1.18 ± 0.12</td><td>1.71 ± 0.03</td><td>26.42 ± 0.52</td><td>68.9 ± 4.0</td><td>-4.02 ± 0.39</td><td>0"/9</td><td>2017.1.00841.V</td></tr><tr><td>2018 Apr 25</td><td>1.14 ± 0.11</td><td>2.21 ± 0.03</td><td>36.12 ± 0.39</td><td>68.4 ± 3.0</td><td>-3.05 ± 0.29</td><td>0"/9</td><td>2017.1.00841.V</td></tr><tr><td>2018 Sep 25</td><td>1.16 ± 0.12</td><td>0.78 ± 0.04</td><td>...</td><td>...</td><td>...</td><td>0"/35</td><td>2017.1.00608.S<sup>b</sup></td></tr></tbody></table>

**Notes.**

wavelength (assuming that the $\lambda^2$ relation holds) is

$$ \chi_0 = \bar{\chi} - \text{RM}\bar{\lambda}^2. \quad (3) $$

The RM fitting is done using a weighted least-squares method of $\chi$ against $\lambda^2$. The $\bar{\chi}$, $\chi_0$, and the fitted RM values are reported in the sixth, seventh, and eighth columns of Tables 1 and 2, respectively.

The EVPA uncertainties quoted in Tables 1–3, and E1 and E2 in Appendix E, are typically dominated by the systematic leakage of 0.03% of Stokes *I* into Stokes *Q* and *U*. At 1.3 mm, this results in estimated errors between 0.06 for the most strongly polarized source (3C 279) and 0.8 for the weakest source (J0132–1654), with most sources in the range 0°1–0°4. These EVPA uncertainties imply RM propagated errors between $0.4 \times 10^4$ rad m$^{-2}$ and $6 \times 10^4$ rad m$^{-2}$, with most sources in the range $(1-3) \times 10^4$ rad m$^{-2}$. Similarly, at 3 mm we find EVPA uncertainties of 0.07–1.4, with a typical value of 0.2, and RM uncertainties in the range $(0.06-1.0) \times 10^4$ rad m$^{-2}$, with a typical value of $\sim 0.13 \times 10^4$ rad m$^{-2}$.

In Appendix F, we present plots of the measured EVPAs at the four ALMA SPWs and their RM fitted models as a function of $\lambda^2$ (displayed in Figures F1–F4) and we discuss the magnitude of thermal and systematic errors in the RM analysis.

### 3.3.3. Bandwidth Depolarization

In the presence of high RM, the large EVPA rotation within the observing frequency bandwidth will decrease the measured fractional polarization owing to Faraday frequency or “bandwidth” depolarization, which depends on the observing frequency band. The RM values inferred in this study (e.g., Table 2) introduce an EVPA rotation of less than one degree within each 2 GHz spectral window, indicating that the bandwidth depolarization in these data should be very low (<0.005%). However, if there is an internal component of Faraday rotation (i.e., the emitting plasma is itself causing the RM), there will be much higher frequency-dependent (de) polarization effects (the “differential” Faraday rotation), which will be related to the structure of the Faraday depth across the source (e.g., Cioffi & Jones 1980; Sokoloff et al. 1998).

We have modeled the frequency dependence of LP using a simple linear model:

$$ m = \bar{m} + m'(\nu - \bar{\nu}), \quad (4) $$

where *m* is the observed LP at frequency $\nu$, $\bar{m}$ is the LP at the mean frequency $\bar{\nu}$, and $m'$ is the change of LP per unit frequency (in GHz$^{-1}$). Given the relatively narrow fractional bandwidth ($\lesssim 2$ GHz), the linear approximation given in Equation (4) should suffice to model the frequency depolarization (multifrequency broadband single-dish studies fit more complex models; see for example Pasetto et al. 2016, 2018). We have fitted the values of $m'$ from a least-squares fit of Equation (4) to all sources and epochs, using LP estimates for each spectral window from Tables E1 and E2 in Appendix E. We show the fitting results for selected sources in Figure 3 (lower panels). There are clear detections of $m'$ for 3C 279, Sgr A*, and M87; these detections also differ between epochs. Such complex time-dependent frequency effects in the polarization intensity may be indicative of an internal contribution to the Faraday effects observed at millimeter wavelengths.

### 3.3.4. Circular Polarization

Measuring Stokes *V* provides, in principle, a direct estimate of the fractional CP as *V*/*I*. In practice, the polarization calibration for ALMA data in CASA is done by solving the polarization equations in the linear approximation, where parallel-hands and cross-hands visibilities are expressed as a linear function of *I*, *Q*, *U*, while it is assumed $V = 0$ (e.g., Nagai et al. 2016; Goddi et al. 2019b). A non-negligible Stokes *V* in the polarization calibrator will introduce a spurious instrumental Stokes *V* into the visibilities of all the other sources. Moreover, such a Stokes *V* introduces a bias in the estimate of the cross-polarization phase, $\beta$, at the reference antenna (see Appendix G), which translates into a leakage-like effect in the polconverted VLBI visibilities (see Equation (13) in Goddi et al. 2019b). The magnitude of such a bias may depend on the fractional CP of the polarization calibrator, the parallactic-angle

<footnote>a Stokes *I*, *Q*, and *U* were extracted from the images using the CASA task *IMFIT*. *UVMULTIFIT* was used for all the other experiments.</footnote>

<footnote>b The lower LP estimated for this project is likely caused by a systematic offset between Stokes *Q*, *U*, and *I* (see Section 2.4). 2017.1.00608.S was not used in the analysis.</footnote>
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Polarization properties of selected EHT targets observed during the 2017 VLBI campaign as a function of observing day. For each source (labeled at the top of each column), the top panel shows Stokes *I* (in Jy), the second panel shows the LP degree (in %), the third panel shows the EVPA (in degrees), the fourth panel shows the rotation measure (in units of $10^4$ rad m⁻²), and the bottom panel shows the depolarization (in units of $10^{-4}$ GHz⁻¹). The different symbols and colors in the upper three panels indicate four different observing bands centered at 213 GHz (black), 215 GHz (blue), 227 GHz (green), and 229 GHz (red), corresponding to SPW = 0,1,2,3. 3C 279 was used as polarization calibrator in all days, except on April 7 when J1924–2914 was used.</figcaption></figure>

coverage of the calibrator, and the specifics of the calibration algorithm. In Appendix G we attempt to estimate such a spurious contribution to Stokes V by computing the cross-hands visibilities of the polarization calibrator as a function of

parallactic angle (see Figures G1 and G2). This information can then be used to assess Stokes V and CP for all sources in all days (reported in Tables G1 and G2 in Appendix G for GMVA and EHT sources, respectively).
We stress two main points here. First, the reconstructed Stokes V values of the polarization calibrators are non-negligible and are therefore expected to introduce a residual instrumental X-Y phase difference in all other sources, after QA2 calibration. This can be seen in the dependence of the reconstructed Stokes V with feed angle in almost all the observed sources (displayed in Figure G2). The estimated X-Y residual phase offsets are of the order of 0.5°, but they can be as high as 2° (e.g., on April 5). These values would translate to a (purely imaginary) leakage term of the order of a few % in the polarization converted VLBI visibilities.

The second point is that there is a significant variation in the estimated values of reconstructed stokes V across the observing week. In particular, on April 5, 3C 279 shows a much higher value, indicating either an intrinsic change in the source, or systematic errors induced by either the instrument or the calibration. In either case, this anomalously large Stokes V in the polarization calibrator introduces a large X-Y phase difference in all other sources. This can be seen in the strong dependence of reconstructed Stokes V on feed angle for sources OJ 287 and 4C 01.28 (displayed in Figure G2, upper left panel) and in their relatively high Stokes V when compared to the following days (see Table G2 in Appendix G). Besides the anomalous value on April 5, it is interesting to note that the data depart from the sinusoidal model described by Equation (G2), for observations far from transit, especially on April 11. These deviations may be related to other instrumental effects which, however, we are not able to precisely quantify. For these reasons, we cannot precisely estimate the magnitude of the true CP fractions for the observed sources (see Appendix G for details). Nevertheless, our analysis still enables us to obtain order-of-magnitude values of CP. In particular, excluding the anomalous April 5, we report $CP=[-1.0, -1.5]$ % in Sgr A*, $CP \sim 0.3\%$ in M87, and possibly a lower CP level ($\sim 0.1\% - 0.2\%$) in a few other AGNs (3C 273, OJ 287, 4C 01.28, J0132-1654, J0006-0623; see Table G2 in Appendix G). In the 3 mm band, we do not detect appreciable CP above 0.1%, except for 4C 09.57 (-0.34%), J0510+1800 (-0.14%) and 3C 273 (0.14%). We note, however, that the official accuracy of CP guaranteed by the ALMA observatory is < 0.6% (1σ) or 1.8% (3σ), and therefore all of these CP measurements should be regarded as tentative detections.

# 4. Results

## 4.1. AGNs

We observed a dozen AGNs, 8 at 3 mm and 10 at 1.3 mm (with six observed in both bands), in addition to M87. Following the most prevalent classification scheme found in the literature (e.g., Lister & Homan 2005; Véron-Cetty & Véron 2010), our sample includes three radio galaxies (M87, NGC 1052, Cen A), three BL Lac objects (OJ 287, J0006-0623, 4C 09.57), and seven additional quasi-stellar objects (QSOs) (3C 273, 3C 279, NRAO 530, 4C 01.28, J1924-2914, J0132-1654, and J0510+1800). Following the standard definition of a blazar (i.e., an AGN with a relativistic jet nearly directed toward the line of sight), we can further combine the last two categories into seven blazars (3C 279, OJ 287, J1924-2914, 4C 01.28, 4C 09.57, J0006-0623, J0510+1800) and three additional QSOs (3C 273, NRAO 530, J0132-1654). The observed radio galaxies have a core that is considered as a low-luminosity AGN (LLAGN) (e.g., Ho 2008).

Their polarimetric quantities at 3 mm and 1.3 mm are reported in Tables 1 and 2, respectively, and displayed in Figure 3. Overall, we find LP fractions in the range 0.1%–15% (with S/N ~ 3–500σ) and RM in the range 10<sup>3.3</sup>–10<sup>5.5</sup> rad m<sup>-2</sup> (with S/N ~ 3–50σ), in line with previous studies at millimeter wavelengths with single-dish telescopes (e.g., Trippe et al. 2010; Agudo et al. 2018) and interferometers (e.g., Plambeck et al. 2014; Martí-Vidal et al. 2015; Hovatta et al. 2019). We also constrain CP to <0.3% in all the observed AGNs, consistent with previous single-dish (e.g., Thum et al. 2018) and VLBI (e.g., Homan & Lister 2006) studies, suggesting that at millimeter wavelengths AGNs are not strongly circularly polarized and/or that Faraday conversion of the linearly polarized synchrotron emission is not an efficient process (but see Vitrishchak et al. 2008).

In Appendix B, we also report maps of all the AGN targets observed at 1.3 mm (Figures B3–B5), and at 3 mm (Figure B6), showcasing their arcsecond-structure at millimeter wavelengths.

In the rest of this section, we briefly comment on the properties of selected AGNs.

3C 279. 3C 279 is a bright and highly magnetized gamma-ray-emitting blazar, whose jet is inclined at a very small viewing angle (~3°). At its distance ($z=0.5362$), 1" subtends 6.5 kpc. 3C 279 was observed on four days at 1.3 mm and one day at 3 mm. It is remarkably highly polarized both at 1.3 mm and 3 mm. At 1.3 mm, LP varies from 13.2% on April 5 to 14.9% in April 11, while the EVPA goes from 45° down to 40°. At 3 mm, LP is slightly lower (~12.9%) and the EVPA is 44°.

While at 1.3 mm we can only place a 1σ upper limit of <5000 rad m<sup>-2</sup>, at 3 mm we measure an RM = 1790 ± 460 rad m<sup>-2</sup> (with a ~4σ significance). Lee et al. (2015) used the Korean VLBI Network to measure the LP at 13, 7, and 3.5 mm, finding RM values in the range -650 to -2700 rad m<sup>-2</sup>, which appear to scale as a function of wavelength as λ<sup>-2.2</sup>. These VLBI measurements are not inconsistent with our 3 mm measurement and our upper limits at 1.3 mm, but more accurate measurements at higher frequencies are needed to confirm an increase of the RM with frequency.

The total intensity images at 1.3 mm reveal, besides the bright core, a jet-like feature extending approximately 5" toward southwest (Figure B3); such a feature is not discernible in the lower-resolution 3 mm image (Figure B6). The jet-like feature is oriented at approximately 40°, i.e., is roughly aligned with the EVPA in the core. Ultra-high-resolution images with the EHT reveal a jet component approximately along the same PA but on angular scales 10<sup>5</sup> times smaller (Kim et al. 2020).

3C 273. 3C 273 was the first discovered quasar (Schmidt 1963), and is one of the closest ($z=0.158$, 1" = 2.8 kpc) and brightest radio-loud quasars. 3C 273 was observed both at 1.3 mm and 3 mm (two days apart). Total intensity and LP are higher in the lower-frequency band: F=9.9 Jy and LP = 4.0% (at 3 mm) versus F=7.6 Jy and LP = 2.4% (1.3 mm). We estimate an RM = (2.52 ± 0.27) × 10<sup>5</sup> rad m<sup>-2</sup> at 1.3 mm, confirming the high RM revealed in previous ALMA observations (conducted in 2016 December with 0.8" angular resolution) by Hovatta et al. (2019) who report LP = 1.8% and a (twice as large) RM = (5.0 ± 0.3) × 10<sup>5</sup> rad m<sup>-2</sup>. We also report for the first time an RM measurement at 3 mm, RM = (-0.60 ± 0.14) × 10<sup>4</sup> rad m<sup>-2</sup>, about 40 times lower and with opposite sign with respect to the higher-frequency band. The χ<sub>0</sub> changes from -82 ± 3° at 1.3 mm to -41.9 ± 0.8 at 3 mm. These large differences may be
explained by opacity effects (Section 5.1.1; see also Hovatta et al. 2019). The EVPAs measured at 3 and 1.3 mm are in excellent agreement with predictions from the AMAPOLA survey (which however over-predicts LP~3.5% at 1.3 mm; see Figure D2).

The total intensity images both at 1.3 and 3 mm display, besides the bright core, a bright, one-sided jet extending approximately 20" (54 kpc) to the southwest. In the higher-resolution 1.3 mm image (Figure B5), the bright component of the jet is narrow and nearly straight, starts at a separation of ~10" from the core, and has a length of ~10". We also detect (at the 3σ level) two weak components of the inner jet (within ~10" from the core) joining the bright nucleus to the outer jet. The jet structure is qualitatively similar to previous λ cm images made with the VLA at several frequencies between 1.3 and 43 GHz (e.g., Perley & Meisenheimer 2017), where the outer jet appears highly linearly polarized.<fnref n="139" /> We do not detect LP in the jet feature.

OJ 287. The bright blazar OJ 287 (z = 0.306, 1" = 4.7 kpc) is among the best candidates for hosting a compact supermassive binary black hole (e.g., Valtonen et al. 2008). OJ 287 was observed on three days at 1.3 mm and one day at 3 mm.<fnref n="140" /> OJ 287 is one of the most highly polarized targets both at 1.3 mm (LP~7%–9%) and 3 mm (LP = 8.8%). LP drops from 9% on April 5 down to 7% on April 10, while the EVPA is stable around [-59°6, -61°8] at 1.3 mm and -70° at 3 mm. The LP variation and stable EVPA are consistent with the historical trends derived from the AMAPOLA survey (see Figure D1). Its flux density is also stable. At 1.3 mm, the EVPA either does not follow a λ²-law (April 5 and 11) or the formal fit is consistent with RM = 0 (April 10). Although we do not have an RM detection at 1.3 mm, we measure an RM = 3050 ± 620 rad m⁻² at 3 mm. A 30 yr monitoring of the radio jet in OJ 287 has revealed that its (sky-projected) PA varies both at centimeter and millimeter wavelengths and follows the modulations of the EVPA at optical wavelengths (Valtonen & Wiik 2012). The observed EVPA/jet-PA trend can be explained using a jet-precessing model from the binary black hole which successfully predicts an optical EVPA = -66°.5 in 2017 (Dey et al. 2021), consistent with actual measurements from optical polarimetric observations during 2016/17 (Valtonen et al. 2017) and close to the EVPA measured at 3 and 1.3 mm with ALMA.

NRAO 530. J1733-1304 (alias NRAO 530) is a highly variable QSO (at z = 0.902; 1" = 8 kpc) which exhibits strong gamma-ray flares. It was observed on two consecutive days at 1.3 mm and one day at 3 mm. It is linearly polarized at a ~2.4% level at 1.3 mm but only 0.9% at 3 mm. The EVPA goes from ~51° at 1.3 mm to 39° at 3 mm, while χ₀ is stable around 51°–52°. At 3 mm, we estimate RM = -0.21 ± 0.06 × 10⁵ rad m⁻² at a 3.6σ significance, which is comparable to the inter-band RM between 1 and 3 mm (-0.33 × 10⁵ rad m⁻²). These RM values are in agreement with those reported by Bower et al. (2018) at 1.3 mm.

The arcsecond-scale structure at 1.3 mm is dominated by a compact core with a second weaker component at a separation of approximately 10" from the core toward west (Figure B5). At 3 mm, there is another feature in opposite direction (to the east), which could be a counter-jet component (Figure B6).

This geometry is apparently inconsistent with the north–south elongation of the jet revealed on scales < 100 pc by recent VLBI multi-frequency (22, 43, and 86 GHz) imaging (e.g., Lu et al. 2011), although the Boston University Blazar monitoring program<fnref n="141" /> conducted with the VLBA at 7 mm has revealed significant changes in the jet position angle over the years, and possibly jet bending.

J1924–2914. J1924–2914 is a radio-loud blazar at z = 0.352 (1" = 5.1 kpc), which shows strong variability from radio to X-ray. It was observed on three days at 1.3 mm and one day at 3 mm. J1924–2914 appears strongly polarized with LP varying from 6.1% (on April 6) to 4.9% (on April 11) at 1.3 mm, and LP = 4.8% (on April 4) at 3 mm. The EVPA is stable around [-49°.2, -51°.8] at 1.3 mm and -46°.4 at 3 mm. We report RM ~[(0.3–0.4) ± 0.1) × 10⁵ rad m⁻² at 1.3 mm and a 3σ upper limit of 3600 rad m⁻² at 3 mm (approximately an order of magnitude lower). Bower et al. (2018) report a higher RM value of (-0.71 ± 0.06) × 10⁵ rad m⁻² at 1.3 mm from ALMA observations carried out in 2016 August, when the source LP was considerably lower (~2%). The AMAPOLA monitoring revealed a considerable variation in the source EVPA during 2016 March–December,<fnref n="142" /> likely due to a period of low LP. We therefore ascribe the difference with the Bower et al. (2018) measurement to source variability.

J1924–2914 is completely unresolved on arcsecond scales both at 1.3 mm and 3 mm (see Figures B4 and B6), a result consistent with images at centimeter wavelengths made with the VLA (e.g., Perley 1982).

4C 01.28. J1058+0133 (alias 4C 01.28) is a blazar at z = 0.888 (1" = 8 kpc). It was observed on three days at 1.3 mm and one day at 3 mm. The source is strongly polarized with a mean LP of 5.5% at 1.3 mm and 4.4% at 3 mm. At 1.3 mm, the LP varies by <15% while the EVPA changes from ~ -23° (April 5) to ~ -15° (April 11); the EVPA at 3 mm, measured on Apr 2, is -32°, apparently consistent with the trend at 1.3 mm. Both the measured EVPA and LP values at 1.3 mm and 3 mm follow very closely the time evolution predicted in the AMAPOLA survey (see Figure D1), where the LP and EVPA follow a trend parallel to the Stokes *I* evolution. On April 11, we tentatively detect RM ~(0.33 ± 0.13) × 10⁵ rad m⁻² at the ~3σ level; we however caution that on April 5 and 10 the EVPAs do not follow the λ² trend (Figure F1), and we do not have an RM detection at 3 mm (with a 3σ upper limit of 3600 rad m⁻²).

Cen A. Centaurus A (Cen A) is the closest radio-loud AGN (at a distance of 3.8 Mpc, 1" = 18 pc). Although it is a bright millimeter source (with F = 5.7 Jy), it is unpolarized at 1.3 mm (with a 3σ LP upper limit of 0.09%). We find a spectral index of -0.2 in the central core, consistent with a flat spectrum, as also measured between 350 and 698 GHz with (non-simultaneous) ALMA observations (Espada et al. 2017).

The total intensity images reveal a diffuse emission component around the central bright core, extending across 12" and mostly elongated north–south, and two additional compact components toward northeast separated by roughly 14" and 18" from the central core and aligned at P.A.~50° (see Figure B5, bottom-right panel). The first component could be associated with the inner circumnuclear disk, mapped in CO with the SMA (Espada et al. 2009) and ALMA (Espada et al. 2017), and may

<footnote n="139">¹³⁹ Perley & Meisenheimer (2017) report an LP as high as 55% in their at 15 GHz map along the jet boundaries (although in the central regions LP is much lower).</footnote>

<footnote n="140">¹⁴⁰ These ALMA observations of OJ 287 in 2017 April were preceded by a major X-ray–optical outburst in late 2016 to early 2017 (Komossa et al. 2020).</footnote>

<footnote n="141">¹⁴¹ https://www.bu.edu/blazars/VLBA_GLAST/1730.html</footnote>

<footnote n="142">¹⁴² www.alma.cl/~skameno/AMAPOLA/J1924-2914.flux.html</footnote>
indicate the presence of a dusty torus. The two additional
components correspond to two knots of the northern lobe of the
relativistic jet, labeled as A1 (inner) and A2 (outer) in a VLA
study by Clarke et al. (1992); no portion of the southern jet is
seen, consistent with previous observations (McCoy et al. 2017).

NGC 1052. NGC 1052 is a nearby (19.7 Mpc; 1" = 95 pc) radio galaxy which showcases an exceptionally bright twin-jet system with a large viewing angle close to 90 degrees (e.g., Baczko et al. 2016). With $F \sim 0.4$ Jy and $LP < 0.15\%$, it is the weakest millimeter source (along with J0132–1654) and the second least polarized AGN in our sample. The apparent discrepancy in flux density and spectral index between April 6 and 7 is most likely a consequence of the low flux density (below the threshold required by the commissioned on-source phasing mode; see Section 2.2) and the much poorer data quality on April 7, rather than time-variability of the source.

Remaining AGNs. J0006–0623 is the most highly polarized blazar (after 3C 279) observed at 1.3 mm, with $LP = 12.5\%$. J0132–1654 is the weakest QSO observed at 1.3 mm ($F \sim 0.4$ Jy) and has $LP \sim 2\%$. The blazar J0510+1800 has an $LP \sim 4\%$ at 3 mm and shows indication of a large RM ($\sim 0.27 \times 10^5$ rad m$^{-2}$), although the EVPA distribution does not follow a $\lambda^2$ dependence (see Figure F3, upper-right panel).

## 4.2. M87

We report the first unambiguous measurement of RM toward the M87 nucleus at millimeter wavelengths (Table 2; Appendix F, Figure F1, middle panels). We measure $(1.51 \pm 0.30) \times 10^5$ rad m$^{-2}$ (with a $5\sigma$ significance) on April 6 and tentatively $(0.64 \pm 0.27) \times 10^5$ rad m$^{-2}$ (with a $2.4\sigma$ significance) on April 5. On the last two days we can only report best-fit values of ($-0.24 \pm 0.23) \times 10^5$ rad m$^{-2}$ (with a $3\sigma$ confidence level range [-0.93, 0.45]) on April 10 and ($-0.39 \pm 0.24) \times 10^5$ rad m$^{-2}$ (with a $3\sigma$ confidence level range [-1.11, 0.33]) on April 11. Although we cannot determine precisely the RM value on all days, we can conclude that the RM appears to vary substantially across days and there is marginal evidence of sign reversal.

Before this study, the only RM measurement was done with the SMA at 230 GHz by Kuo et al. (2014), who reported a best-fit RM = ($-2.1 \pm 1.8) \times 10^5$ rad m$^{-2}$ ($1\sigma$ uncertainty) and could therefore only provide an upper limit. In order to better constrain the RM amplitude and its time variability, in addition to the 2017 VLBI observations (which are the focus of this Letter), we have also analyzed the ALMA data acquired during the 2018 April VLBI campaign as well as additional ALMA archival polarimetric experiments (these are introduced in Section 2.4). For two projects (2016.1.00415.S and 2017.1.00608.S) we produced fully calibrated uv-files and then used the UVMF flux extraction method with UVMULTIFIT to determine the M87 Stokes parameters. For the remaining two projects (2013.1.01022.S and 2015.1.01170.S), we used the full-Stokes images released with QA2. Since these images do not include clean component models, we used the INTF method to extract the Stokes parameters in the compact core directly in the images.<sup>143</sup>

Table 3 reports the full list of ALMA observations, project codes, and derived polarimetric parameters. In total, we have collected data from three and eight different

observations at 3 mm and 1.3 mm, respectively, spanning three years (from 2015 September to 2018 September). The main findings revealed by the analysis of the full data set are as follows.

1. The total flux density is quite stable on a weekly timescale, varying by $\lesssim 5\%$ in both 2017 and 2018 April, and exhibiting total excursion of about 15–20% across one year both at 1.3 mm (decreasing from 2017 April to 2018 April) and 3 mm (increasing from 2015 September to 2016 October).

2. We detect $LP \sim 1.7\%–2.7\%$ (2.3% mean; April 2017–2018) at 1.3 mm and $LP \sim 1.3\%–2.4\%$ (1.7% mean; 2015 September–2016 October) at 3 mm.

3. The EVPA distributions across the four ALMA SPWs clearly display a $\lambda^2$ dependence, on specific dates, within both the 1.3 mm and 3 mm bands (e.g., see Figures F1 and F4).

4. The magnitude of the RM varies both at 3 mm (range $|RM| = [0.2–1.2] \times 10^5$ rad m$^{-2}$) and 1.3 mm (range $|RM| = [1.5–4.1] \times 10^5$ rad m$^{-2}$, including $< 3\sigma$ non-detections).

5. The RM can either be positive or negative in both bands (with a preference for a negative sign), indicating that sign flips are present both at 3 and 1.3 mm.

6. In 2017 April, the RM magnitude appears to vary significantly (from non-detection up to $1.5 \times 10^5$ rad m$^{-2}$) in just 4–5 days.

7. In 2017 April, $\chi_0$ varies substantially across a week, being [-14.6 $\pm$ 2.8, -23.6 $\pm$ 3.1, 2.5 $\pm$ 2.5, 3.5 $\pm$ 2.5] in April 5, 6, 10, and 11, respectively. Therefore, although the EVPA at 1.3 mm changes only by $\sim$+8° during the observing week, the $\chi_0$ varies by -9° in the first two days, and +27° between the second day and the last two days. In 2018 April $\chi_0$ appears instead to be consistently around 68°:4–70°:6.<sup>144</sup> The $\chi_0$ derived from the three 3 mm experiments (2015 September, 2015 November and 2016 October) spans a range from $\sim$4° to 107° (see Figure 4 for a summary plot of RM+$\chi_0$ in all the available M87 observations).

8. The EVPAs measured at 1.3 mm in the 2017 campaign ($\sim$[-8, 0]°) are significantly different to those measured in the 2018 campaign ($\sim$[26, 36]°), which are instead consistent with those measured in 2015–2016 at 3 mm ($\sim$[21, 33]°).

9. We find hints of CP at 1.3 mm at the [-0.3 $\pm$ 0.6, -0.4 $\pm$ 0.6)% level, but these should be regarded as tentative measurements (see also Appendix G for caveats on the CP estimates).

We will interpret these findings in Section 5.2.

## 4.3. Sgr A*

In this section, we analyze the polarimetric properties of Sgr A* and its variability on a weekly timescale based on the ALMA observations at 1.3 mm and 3 mm.

LP. We measured LP between 6.9% and 7.5% across one week at 1.3 mm (Table 2). These values are broadly consistent with historic measurements using BIMA on several epochs in

<footnote n="143"><sup>143</sup> Based on the analysis of the 2017 data sets, we have assessed that INTF yields consistent polarimetric parameters with respect to UVMF and $3 \times 3$ (see Section 3.2 and Appendix C).</footnote>

<footnote n="144"><sup>144</sup> The change of about +10° in the EVPA at 1.3 mm between 2018 April 21 and 25 can be completely explained with a decrease in RM $\sim -1 \times 10^5$ rad m$^{-2}$.</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 4.** M87 EVPA as a function of $\lambda^2$ observed in multiple epochs at 3 mm (from 2015 September to 2016 November) and 1.3 mm (from 2017 to 2018 April). Each gray line is a linear fit to the EVPAs measured at the four ALMA Band 3 and Band 6 spectral windows, yielding the RM in each epoch, and the extrapolated intercept at the Y-axis is $\chi_0$. Note the large offset in $\chi_0$ between the 3 mm and 1.3 mm bands.</figcaption></figure>

the time span 2002–2004 at 227 GHz (7.8%–9.4%; Bower et al. 2003, 2005), SMA on several days in 2005 June–July (4.5%–6.9% at 225 GHz; Marrone et al. 2007), and more recently with ALMA in 2016 March–August at 225 GHz (3.7%–6.3%, 5.9% mean; Bower et al. 2018, who also report intra-day variability). Besides observations at 1.3 mm, LP variability has been reported also at 3.5 mm with BIMA (on a timescale of days; Macquart et al. 2006) and at 0.85 mm with the SMA (on a timescale from hours to days; Marrone et al. 2006). Altogether, these measurements imply significant time-variability of LP across timescales of hours/days to months/years.

While at 1.3 mm LP ~7%, at 3 mm we detect LP $\lesssim$1% (Table 1). It is interesting to note that the LP fraction increases from ~0.5% at ~86 GHz (our SPW = 0,1) up to ~1% at ~100 GHz (our SPW = 2,3; see Table E1 in Appendix E). This trend is consistent with earlier measurements at 22 GHz and 43 GHz with the VLA, and at 86 GHz and 112–115 GHz with BIMA, yielding upper limits of LP~0.2, 0.4%, 1% (Bower et al. 1999b), and 1.8% (Bower et al. 2001), respectively (but see Macquart et al. 2006, who report LP ~2% at 85 GHz with BIMA observations in 2004 March).

RM. We report a mean RM of $-4.2 \times 10^5$ rad m$^{-2}$ at 1.3 mm with a significance of ~50σ (Table 2; Appendix F, Figure F1, upper second to fourth panels), consistent with measurements over the past 15 yr since the first measurements with BIMA+JCMT (Bower et al. 2003), BIMA+JCMT+SMA (Macquart et al. 2006), and the SMA alone (Marrone et al. 2007).<fnref n="145" /> Across the observing week, we see a change in RM from $-4.84 \pm 0.1 \times 10^5$ rad m$^{-2}$ (on April 6) to $-3.28 \pm 0.09 \times 10^5$ rad m$^{-2}$ (on April 11), corresponding to a change of ~$-1.5 \times 10^5$ rad m$^{-2}$ (~30%), detected with a significance of ~20σ. This RM change can completely explain the EVPA variation from $-65^\circ.8 \pm 0^\circ.1$ to $-49^\circ.3 \pm 0^\circ.1$ (or a ~16° change across five

days), given the consistency in $\chi_0$ between 6 and 11 April (~-14°.7±1°.0; see Table 2). Marrone et al. (2007) find a comparable dispersion based on six measurements in the time period 2005 June–July ($\Delta$|RM| = $1.3 \times 10^5$ rad m$^{-2}$ excluding their most discrepant point, or $\Delta$|RM| = $3.8 \times 10^5$ rad m$^{-2}$ including all six measurements spanning almost two months). Bower et al. (2018) find an even larger $\Delta$|RM| = $-4.9 \times 10^5$ rad m$^{-2}$ across 5 months; they also report intra-day variability in a similar range on timescales of several hours.

Variations in RM appear to be coupled with LP fraction: the lower the polarization flux density, the higher the absolute value of the RM. In particular, we find $\Delta$LP ~ +5% ($\Delta$RM ~ -9%) and $\Delta$LP ~ +9% ($\Delta$RM ~ -32%) in April 7 and 11, respectively, with respect to April 6. This can be understood if a larger RM scrambles more effectively the polarization vector fields resulting in lower net polarization. Although with only three data points we cannot draw a statistically significant conclusion, we note that the same trend was also seen by Bower et al. (2018) on shorter (intra-day) timescales.

We report for the first time a measurement of RM at 3 mm, with a magnitude of ($-2.1 \pm 0.1) \times 10^5$ rad m$^{-2}$ (Table 1; Appendix F, Figure F1, upper-left panel). The RM magnitude at 3 mm (measured on April 3) is a factor of 2.3 (2.1) smaller than the RM value measured at 1.3 mm on April 6 (April 7). Furthermore, we note a large offset in $\chi_0$ between the 3 mm (+135° or -45° for a full 180° wrap) and the 1.3 mm bands (~[-14.7, -18.8]°), which is unlikely a consequence of time variability (given the $\chi_0$ consistency on Apr 6–11). The comparison of RM and $\chi_0$ in the two frequency bands (showcased in Figure 5) indicates the presence of both Faraday and intrinsic changes of the source. We will provide an interpretation of the differences observed between the two frequency bands in Section 5.3.

CP. We report a tentative detection of CP at 1.3 mm in the range (-1.0 ± 0.6)% to (-1.5 ± 0.6)%. This is consistent with the first detection with the SMA from observations carried out in 2005–2007 (Muñoz et al. 2012) and with a more recent ALMA study based on 2016 observations (Bower et al. 2018). This result suggests that the handedness of the millimeter wavelength CP is stable over timescales larger than 12 yr. Interestingly, historical VLA data (from 1981 to 1999) between 1.4 and 15 GHz show that the emission is circularly polarized at the 0.3% level and is consistently left-handed (Bower et al. 1999a, 2002), possibly extending the stability of the CP sign to 40 yr. Such a remarkable consistency of the sign of CP over (potentially four) decades suggests a stable magnetic field configuration (in the emission and conversion region).

Similarly to the RM, we also note a weak anti-correlation between LP and CP (although more observations are needed to confirm it).

We do not detect CP at 3 mm (< 0.06%, 3σ upper limit). Muñoz et al. (2012) and Bower et al. (2018) find that, once one combines the centimeter and millimeter measurements, the CP fraction as a function of frequency should be characterized by a power law with $\nu^{0.35}$. Using the measurements at 1.3 mm, this shallow power law would imply a CP fraction at the level of ~0.7%–1.1% at 3 mm, which would have been readily observable. The non-detection of CP at 3 mm suggests that the CP spectrum may not be monotonic.

Although the origin of the CP is not well understood, since a relativistic synchrotron plasma is expected to produce little CP, Muñoz et al. (2012) suggest that the observed CP is likely

<footnote n="145">¹⁴⁵ Both Bower et al. (2003) and Macquart et al. (2006) used non-simultaneous EVPA measurements in the frequency range 150–400 GHz and 83–400 GHz, respectively. Marrone et al. (2007) determined for the first time the RM comparing EVPAs measured simultaneously at each (1.3 and 0.85 mm) band.</footnote>
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Sgr A* EVPA as a function of $\lambda^2$ observed in 2017 at 3 mm (April 3) and 1.3 mm (April 6, 7, 11). Each gray line is a linear fit to the EVPAs measured at the four ALMA Band 3 and Band 6 spectral windows, yielding the RM in each epoch, and the extrapolated intercept at the Y-axis is $\chi_0$. Note the large offset in $\chi_0$ between the 3 mm and 1.3 mm bands, despite the consistency of $\chi_0$ at 1.3 mm across 6 days.</figcaption></figure>

generated close to the event horizon by the Faraday conversion which transforms LP into CP via thermal electrons that are mixed with the relativistic electrons responsible for the linearly polarized synchrotron emission (Beckert & Falcke 2002). In this scenario, while the high degree of order in the magnetic field necessary to produce LP ~7% at 1.3 mm naturally leads to a high CP in a synchrotron source, the absence of CP at 3 mm is consistent with the low LP measured. See Muñoz et al. (2012) for a detailed discussion of potential origins for the CP emission.

A final caveat is that, based on the analysis presented in Section 3.3.4 and Appendix G, the physical interpretations above should be considered as tentative.

**Flux-density variability.** We do not report significant variability in total intensity and polarized intensity, which is about 10% in six days (comparable to the absolute flux-scale uncertainty in ALMA Band 6). Marrone et al. (2006) and Bower et al. (2018) report more significant variability in all polarization parameters based on *intra-day* light curves in all four Stokes parameters. This type of analysis is beyond the scope of this Letter, and will be investigated elsewhere.

## 5. Discussion

In this section, we review general polarization properties of AGNs comparing the two (1.3 and 3 mm) frequency bands, different AGN classes, and depolarization mechanisms (Section 5.1); then we interpret the Faraday properties derived for M87 in the context of existing accretion and jet models as well as a new two-component polarization model (Section 5.2); finally we discuss additional constraints on the Sgr A* polarization model from a comparison of 1.3 mm and 3 mm observations (Section 5.3).

### 5.1. Polarization Degree and Faraday Rotation in AGNs

#### 5.1.1. 1.3 mm versus 3 mm

**Synchrotron emission opacity.** The total intensity spectral indexes for the AGN sources in the sample vary in the range

$\alpha = [-0.7, -0.3]$ at 3 mm and $\alpha = [-1.3, -0.6]$ at 1.3 mm, Cen A being the only exception, with $\alpha = -0.2$ (see Tables 1 and 2 and Appendix H). This contrasts with the flat spectra ($\alpha = 0$) typically found at longer centimeter wavelengths in AGN cores (e.g., Hovatta et al. 2014), corresponding to optically thick emission. In addition, we observe a spectral steepening (with $\Delta\alpha = [-0.2, -0.4]$) between 3 mm and 1.3 mm; although one should keep in mind the caveat of time variability, since the observations in the two frequency bands were close in time (within 10 days) but not simultaneous. Such spectral steepening can naturally be explained by decreased opacity of the synchrotron emission at higher frequencies in a standard jet model (e.g., Blandford & Königl 1979; Lobanov 1998).

**LP degree.** We detect LP in the range 0.9%–13% at 3 mm and 2%–15% at 1.3 mm (excluding the unpolarized sources NGC 1052 and Cen A). At 1.3 mm, the median fractional polarization is 5.1%, just slightly higher than the median LP at 3 mm, 4.2%, yielding a ratio of 1.2. If we consider only the sources observed in both bands, then the ratio goes slightly up to 1.3 (or 1.6 including also Sgr A*). Despite the low statistics, these trends are marginally consistent with results from previous single-dish surveys with the IRAM 30 m telescope (Agudo et al. 2014, 2018) and the Plateau de Bure Interferometer or PdBI (Trippe et al. 2010). In particular, Agudo et al. (2014) find an LP ratio of 1.6 between 1 mm and 3 mm based on simultaneous, single-epoch observations of a sample of 22 radio-loud ($F > 1$ Jy) AGNs, while Agudo et al. (2018) find an LP ratio of 2.6 based on long-term monitoring, non-simultaneous observations of 29 AGNs. Trippe et al. (2010) find similar numbers from a sample of 73 AGNs observed as part of the IRAM/PdBI calibration measurements during standard interferometer science operations.146 The comparison of these statistics at both wavelengths suggests a general higher degree of polarization at 1 mm as compared to 3 mm. This finding can be related either to a smaller size of the emitting region and/or to a higher ordering of the magnetic-field configuration (e.g., see the discussion in Hughes 1991). In fact, according to the standard jet model, the size of the core region decreases as a power-law of the observing frequency, which could help explain the higher LP observed at 1 mm. Alternatively, the more ordered magnetic-field configuration could be related to a large-scale (helical) magnetic-field structure along the jets.

**Faraday RM.** Among the six sources observed both at 3 mm and 1.3 mm, we have RM detections at the two bands only in 3C 273, where the estimated value at 3 mm is significantly lower than at 1.3 mm. For the remaining sources with RM detections at 3 mm (NRAO 530, OJ 287, and 3C 279) and at 1.3 mm (J1924–2914 and 4C 01.28), their $3\sigma$ upper limits, respectively at 1.3 and 3 mm, still allow a larger RM at the higher-frequency band.

A different “in-band” RM in the 3 and 1.3 mm bands can be explained either by (i) the presence of an internal Faraday screen or multiple external screens in the beam, or (ii) a different opacity of the synchrotron emission between the two bands. Case (i) will cause a non-$\lambda^2$ behavior of the EVPA and a non-trivial relation between the “in-band” RM determined at only two narrow radio bands. Evidence for non-$\lambda^2$ behavior of the EVPA can be possibly seen in OJ 287, 4C 01.28, and

<footnote n="146">146 The polarimetric data analysis is based on Earth rotation polarimetry and is antenna-based, i.e., executed for each antenna separately. Therefore, no interferometric polarization images are available from this study.</footnote>
J0006–0623 at 1.3 mm (Figure F2) and J0510+1800 at 3 mm (Figure F3). In order to estimate *B* or *n*<sub>e</sub> from the RM (see Equation (1)), one would need to sample densely the EVPA over a broader frequency range and perform a more sophisticated analysis, using techniques like the Faraday RM synthesis or Faraday tomography (e.g., Brentjens & de Bruyn 2005). This type of analysis is beyond the scope of this Letter and can be investigated in a future study (we refer to Section 5.2.1 for evidence of internal Faraday rotation and Section 5.2.2 for an example of a multiple-component Faraday model for the case of M87). Since the spectral index analysis shows that the AGNs in the sample become more optically thin at 1 mm, the observed differences in the “in-band” RM at 3 mm and 1.3 mm can be likely explained by synchrotron opacity effects alone (with the caveat of time variability since the observations are near-in-time but not simultaneous).

It is also interesting to note that we also see a sign reversal between the RM measured at 3 mm and 1.3 mm for 3C 273. RM sign reversals require reversals in $B_\|$ either over time (the observations in the two bands are not simultaneous) or across the emitting region (the orientation of the magnetic field is different in the 3 mm and 1 mm regions). With the data in hand we cannot distinguish between time variability or spatial incoherence of the magnetic field (we refer to Section 5.2 for a discussion on possible origins of RM sign reversals in AGNs).

### 5.1.2. Blazars versus Other AGNs

We find that blazars are more strongly polarized than other AGNs in our sample, with a median LP ~7.1% versus 2.4% at 1.3 mm, respectively. Furthermore, blazars have approximately an order-of-magnitude lower RM values (on average) than other AGNs, with a median value of ~0.07 × 10⁵ rad m⁻² at 1.3 mm (with the highest values of ~0.4 × 10⁵ rad m⁻² exhibited by J1924–2914), whereas for other AGNs we find a median value of ~0.4 × 10⁵ at 1.3 mm<fnref n="147" /> (with the highest values > 10⁵ rad m⁻² exhibited by M87 and 3C 273).

Bower et al. (2017) used the Combined Array for Millimeter Astronomy (CARMA) and the SMA to observe at 1.3 mm two LLAGNs, M81 and M84, finding upper limits to LP of 1%–2%. Similarly, Plambeck et al. (2014) used CARMA to observe the LLAGN 3C 84 at 1.3 and 0.9 mm, measuring an LP in the 1%–2% range, and a very high RM of ~($9 \pm 2$) × 10⁵. These low values of LP (and high values of RM) are comparable to what we find in M87, which is also classified as an LLAGN (e.g., Di Matteo et al. 2003).

When put together, these results suggest that blazars have different polarization properties at millimeter wavelengths from all other AGNs, including LLAGNs, radio galaxies, or regular QSOs.<fnref n="148" /> These millimeter polarization differences can be understood in the context of the viewing angle unification scheme of AGNs. A smaller viewing angle implies a stronger Doppler-boosting of the synchrotron emitting plasma in the jet, which in turn implies a higher polarization fraction for blazars. Furthermore, their face-on geometry allows the observer to reach the innermost radii of the nucleus/jet and reduces the impact of the “scrambling” of linearly polarized radiation by averaging different polarization components within the source

(e.g., Faraday and beam depolarization—see the next section), also resulting in higher LP (and lower RM).

### 5.1.3. Depolarization in Radio Galaxies

In the previous section we point out that radio galaxies and LLAGNs exhibit lower polarization degree than blazars. In particular, the radio galaxies Cen A and NGC 1052 do not show appreciable polarized intensity (LP<0.2%) at 1.3 mm. We suggest several depolarization mechanisms that may be at play in these radio galaxies (and potentially other LLAGNs).

a. Faraday depolarization due to a thick torus or a dense accretion flow.

b. Bandwidth depolarization due to a strong magnetic field.

c. Beam depolarization due to a disordered magnetic field.

d. Thermal (non-synchrotron) emission.

In the following, we elaborate on these mechanisms.

a. Faraday depolarization due to a thick torus or a dense accretion flow. Radio galaxies are often surrounded by an obscuring torus. The cold gas in the torus can be photoionized by UV photons from the inner accretion disk and the mixture of thermal and non-thermal material could be responsible for the strong depolarization of the inner regions via Faraday rotation—and one speaks of Faraday depolarization. In the case of NGC 1052, Fromm et al. (2018, 2019) created synthetic radio maps of the jets using special-relativistic hydrodynamic simulations and suggested that an obscuring torus can explain some of the observed properties of these jets. In fact, the presence of a massive (~$10^7 M_\odot$) and dense (> $10^7$ cm⁻³) molecular torus has been recently demonstrated with ALMA observations (Kameno et al. 2020). A clumpy torus is also known to surround the nucleus of Cen A (e.g., Espada et al. 2017), as also suggested by our 1.3 mm map (see Figure B5, bottom-right panel). Therefore the presence of a thick torus of cold gas could naturally explain the low polarization degree in both radio galaxies. A similar mechanism can be at play in LLAGNs whose radio emission is thought to be powered by synchrotron radiation from a geometrically thick, hot accretion flow (e.g., Narayan & Yi 1994; Blandford & Begelman 1999; Quataert & Gruzinov 2000).

b. Bandwidth depolarization due to a strong magnetic field. A large homogeneous magnetic field implies an intrinsically large homogeneous RM (see Equation (1)), resulting in the source appearing unpolarized in broadband observations—and one speaks of bandwidth depolarization. In NGC 1052, GMVA imaging at 86 GHz helped constrain the magnetic field at Schwarzschild radius ($R_{Sch}$) scales in the range 360–70,000 G (Baczko et al. 2016), providing evidence of an extremely high magnetic field near the SMBH. Coupled with its high inclination (e.g., Kadler et al. 2004), such a strong magnetic field would cause the source to appear unpolarized in ALMA broadband observations.

c. Beam depolarization due to a tangled magnetic field. If the magnetic field in the emitting regions or in a foreground Faraday screen is tangled or generally disordered on scales much smaller than the observing beam, magnetic field regions with similar polarization degrees but opposite signs will cancel out and the net observed polarization degree would be significantly decreased—and one speaks of beam depolarization. We do not have evidence of such a tangled magnetic field for any of the low LP sources in our sample, which will require

<footnote n="147">¹⁴⁷ In computing the median we exclude the unpolarized Cen A and NGC 1052 for which we cannot measure RM.</footnote>

<footnote n="148">¹⁴⁸ Similar conclusions were reached from VLBI imaging studies of large AGN samples at centimeter wavelengths (e.g., Hodge et al. 2018).</footnote>
high-resolution polarization imaging with the GMVA or
the EHT.

d. *Thermal (non-synchrotron) emission.* Multi-wavelength (MWL) studies in Cen A show that its spectral energy distribution (SED) is moderately inverted up to the infrared, possibly indicating a dust contribution at millimeter wavelengths (e.g., Espada et al. 2017). Using VLBI imaging at 229 GHz with the EHT, M. Janssen et al. (2021, submitted) measured a flux of ~2 Jy in the VLBI core, indicating that the EHT filters out ~65% of the emission seen by ALMA. While we cannot exclude contribution from thermal emission to the total flux measured by ALMA, the flux measured with the EHT must necessarily be associated with non-thermal emission. We therefore conclude that dust emission is an unlikely explanation for the lack of LP at 1.3 mm.

An improved data analysis including spectro-polarimetry could be helpful to measure the actual RM in both NGC 1052 and Cen A and thus assess which is the dominant depolarization mechanism among the ones discussed above (this is, however, beyond the scope of this Letter). As a final note, an interesting insight may come from a comparison between millimeter and IR wavelengths, where both NGC 1052 (Fernández-Ontiveros et al. 2019) and Cen A (Jones 2000; Lopez Rodriguez 2021) are highly polarized. These characteristic are similar to Cygnus A, where the low polarized core at millimeter wavelengths and the high polarized core at IR wavelengths may be the signature of an ordered magnetic field in the plane of the accretion disk supporting the accretion flow and/or jet formation (Lopez-Rodriguez et al. 2018).

## 5.2. Physical Origin of the Rotation Measure in M87

We can now use the polarimetric and Faraday properties of the millimeter emission from M87 reported in Section 4.2, to constrain properties of accretion models onto the M87 SMBH. Models aiming to explain the origin of the RM in M87 should match the following key observed features (see Section 4.2 for a full list of findings).

i. *Low LP and high RM.* M87 has a rather low LP (~2.3% mean at 1.3 mm) when compared to Sgr A* and other blazars in the sample (see Section 5.1.2), while the measured RM can be as high as a few times $10^5$ rad m$^{-2}$.

ii. *RM sign reversals.* Observations on different dates yield large differences in the measured RM values, which can be either positive or negative (in both the 3 mm and 1.3 mm bands). This requires sign flips in $B_\|$ over time and/or across the emitting region.

iii. *Rapid RM time variability.* In 2017 April, the RM magnitude appears to vary significantly (from non-detection up to $1.5 \times 10^5$ rad m$^{-2}$) in just 4–5 days. This suggests the presence of small-scale fluctuations in the emitting source and/or the Faraday screen.

iv. *$\lambda^2$ scaling.* Plots in Figures F1 and F4 clearly display a $\lambda^2$ dependence of the EVPA at 1.3 mm and 3 mm on specific days (although this is not always the case).

The MWL SED of the M87 core is best explained by emission from advection-dominated/radiatively inefficient accretion flow (ADAF/RIAF; Reynolds et al. 1996; Di Matteo et al. 2003) or from a jet (e.g., Dexter et al. 2012; Prieto et al. 2016; Mościbrodzka 2019), or emission from a combination of these two components (e.g., Broderick & Loeb 2009; Nemmen et al. 2014; Feng et al. 2016; Mościbrodzka et al. 2016, 2017;

Davelaar et al. 2019; Event Horizon Telescope Collaboration et al. 2019e). In the hybrid models, the low-frequency radio emission is produced by the jet while the optically thin millimeter/submillimeter (and X-ray) emission can either come from the jet base or the inner accretion flow.

The traditional approach adopted in previous studies was to assume that the large-scale ($r \sim 100 R_{\text{Sch}}$) accretion flow itself may act as a Faraday screen and that the core emission region lies entirely behind the same portion of the Faraday screen (e.g., the core emission size is small compared to the scale of any fluctuations in large-scale flow). In the framework of semi-analytic RIAF/ADAF models, the RM magnitude has then been used to estimate mass accretion rates onto black holes in Sgr A* (Marrone et al. 2006, 2007) and in 3C 84 (Plambeck et al. 2014). A similar approach has been used in M87, yielding estimates of the accretion rate in the range from $\dot{M} < 9 \times 10^{-4}$ (Kuo et al. 2014) to $\dot{M} \sim [0.2, 1] \times 10^{-3} M_{\odot} \text{yr}^{-1}$ (Feng et al. 2016), where the quoted values are either upper limits or depend on specific model assumptions (e.g., black hole spin or the exact location of the Faraday screen). From the largest RM that we measured, $4 \times 10^5$ rad m$^{-2}$ (on 2018 April), using Equation (9) in Marrone et al. (2006), we would infer a mass accretion rate of $\dot{M} = 7.7 \times 10^{-8} [\text{RM}]^{2/3} \sim 4 \times 10^{-4} M_{\odot} \text{yr}^{-1}$ assuming an inner boundary to the Faraday screen of $R_{\text{RM, in}} = 21 R_{\text{Sch}}$ (as suggested by Kuo et al. 2014).

While our estimates of mass accretion rates are consistent with previous similar estimates and upper limits from the ADAF/RIAF models, the observed properties listed above, especially the time variable RM and its sign reversals, provide new constraints. In particular, the timescale of the RM variability can be set by the rotating medium dynamical time ($\propto\sqrt{R^3/GM}$), thus constraining the radius at which the RM originates. The rapid variability observed in 2017 April implies that the RM should occur much closer to the SMBH (within a few $R_{\text{Sch}}$) than assumed in previous mass accretion models, which in turn suggests the possibility of a co-location of the emitting and rotating medium. In the alternative, the Faraday screen could be at further distance and the observed variability could be ascribed to rapid fluctuations in the emitting source. Therefore, both a turbulent accretion flow acting as a Faraday screen or a varying compact source with an external screen can explain the observed time variability. Finally, the accretion flow is not the only possible source of Faraday rotation. Since simulations show that relativistic jets can have a “spine-sheath” structure (e.g., McKinney 2006), the jet sheath can provide a magnetized screen surrounding the jet, and indeed it has been also suggested as a plausible source of Faraday rotation in AGNs (e.g., Zavala & Taylor 2004). Therefore, either (or both) the accretion flow and/or the jet can in principle be the sources of the millimeter emission and/or the Faraday rotation.

All the scenarios described above imply a more complicated physical origin of the Faraday rotation than is usually assumed in traditional semi-analytic models that use the RM to infer a mass accretion rate. We conclude that, unlike the case of Sgr A*, the RM in M87 may not provide an accurate estimate of the mass accretion rate onto the black hole.

In what follows, we review clues on the location of the Faraday screen using observational constrains from ALMA (Section 5.2.1) as well as information on horizon scales from the EHT (Section 5.2.2).
### 5.2.1. Location of the Faraday Screen: Internal versus External

We distinguish between two general cases: internal and external Faraday rotation.

I. Internal Faraday rotation: the accretion flow or jet can simultaneously be the source of synchrotron radiation and the Faraday screen.

a. *RM rapid time variability and sign reversals.* Recent time-dependent general relativistic magnetohydrodynamic (GRMHD) simulations of the M87 core (Ricarte et al. 2020) show that turbulence within the accretion flow is able to change $B_\|$ in both amplitude and orientation, resulting in significant RM fluctuations and sign reversals on the dynamical time at $R \simeq 2.5-5 R_{Sch}$, corresponding to short timescales of a few days for M87 (consistent with properties #ii and #iii).

b. *Beam Depolarization.* An internal Faraday screen could cause beam depolarization of the synchrotron emission. This has been theoretically predicted by GRMHD simulations of the M87 core emission, which yield low values of LP (typically in the range 1%–3%) and large Faraday RM ($\gtrsim 10^5$ rad m$^{-2}$) (Mościbrodzka et al. 2017; Event Horizon Telescope Collaboration et al. 2021b), broadly consistent with the observed feature #i. We however note that the beam depolarization could be also caused by external Faraday rotation in an inhomogeneous screen.

II. External Faraday rotation: the emission region lies entirely behind (and it is not inter-mixed with) the Faraday screen.

a. $\lambda^2$ scaling of the EVPA. A $\lambda^2$ dependence is typically adopted as observational evidence of the fundamental assumption on the location of the Faraday screen as external relative to the background source. Although it can be argued that EVPA variations in a narrow frequency range could be approximated to be linear (at 1.3/3 mm the fractional $\lambda^2$ bandwidth is only 16/32% of the central wavelength), good linear fits of EVPA versus $\lambda^2$ are also obtained from lower-frequency observations, including the ranges 2, 5, and 8 GHz (Park et al. 2019), 8, 15, 22, and 43 GHz (Algaba et al. 2016), and 24, 43, and 86 GHz (Kravchenko et al. 2020).

b. RM sign reversals and helical magnetic fields. Polari metric images with the VLBA at 43 GHz have revealed magnetic field vectors wrapped around the core (Walker et al. 2018), suggesting that toroidal fields might be dominant on scales of hundreds of $R_{Sch}$. Helical magnetic fields threading the jet may be produced by the differential rotation either in the BH ergosphere or in the innermost regions of the accretion disk (e.g., Broderick & Loeb 2009; Broderick & McKinney 2010; Tchekhovskoy et al. 2011). If toroidal fields are dominant in the sheath, one would expect transverse RM gradients across the jet, with opposite signs of the RM from one edge to the other, as shown in a handful cases where VLBI images resolve the jet width (e.g., Asada et al. 2002; Gómez et al. 2008; Gabuzda et al. 2014). Systematic changes in the signs of these gradients, leading to RM sign reversals in unresolved measurements, can be explained with a number of

models, including the magnetic “tower” model (Lynden-Bell 1996; Contopoulos & Kazanas 1998; Lico et al. 2017), or the “striped” jet model (Parfrey et al. 2015; Mahlmann et al. 2020; Nathanail et al. 2020). Nevertheless, it remains difficult to explain the rapid fluctuations observed in 2017 April with these models.

A long-term monitoring with beam-matched simultaneous observations at multiple frequency bands would be required to assess the frequency dependence of the RM and to conclusively discriminate between internal and external Faraday rotation. Clear evidence of $\lambda^2$ scaling in a wider frequency range would be evidence of the external scenario, while deviations from $\lambda^2$ would support the internal scenario. A time cadence from a few days to a few months would allow us to assess whether the RM sign flips are stochastic (favoring the internal scenario), or systematic (favoring the external scenario).

### 5.2.2. Two-component Polarization Model for M87

EHT estimates of the flux in the compact core, i.e., that arising on horizon scales, can at most account for 50% of that measured by ALMA, both in total intensity (Event Horizon Telescope Collaboration et al. 2019d) and polarized intensity (Event Horizon Telescope Collaboration et al. 2021a) emission. Natural origins for the additional emission are the larger-scale structures in the jet. The additional components may encompass many scales, be discrete features (e.g., HST-1), or be a combination thereof. In order to interpret these differences revealed by the EHT and ALMA, we adopt the simplest version of a multi-scale model permissible—a two-component model comprised of a variable compact region and static extended region (see Figure 6). We find that this is sufficient to harmonize the polarimetric properties observed by both the EHT and ALMA in 2017 April, including the interday variability in the ALMA RMs and the EVPA variation of the compact core as observed by the EHT.

Both the compact and extended components of the two-component model consist of total intensity, spectral index, linearly polarized flux, and polarization angle. We consider both internal and external Faraday screen models for the compact component. In both cases, the Faraday screen for the extended component is assumed to be external. A model likelihood is constructed using the integrated EHT Stokes *I*, *Q*, and *U* ranges presented in Table 7 in Appendix H2 of Event Horizon Telescope Collaboration et al. (2021a), and the ALMA core Stokes *I*, *Q*, and *U* values for the individual SPWs in Table E2 in Appendix E, assuming Gaussian errors. This likelihood is then sampled with the EMCEE python package (Foreman-Mackey et al. 2013) to obtain posterior probability distributions for the model components. For more details regarding the model, priors, and fit results, see Appendix I.

Across days, only the LP and EVPA of the compact component are permitted to vary. This is consistent with the extended component being associated with much larger physical structures and required by the polarimetric variability observed by the EHT (Event Horizon Telescope Collaboration et al. 2021a). There is no evidence that variability in any other component of the two-component model is required: despite static Faraday screens, permitting the polarization of the compact component to vary is capable of reproducing the rapid changes in the ALMA RMs. In this picture, the observed
<figure><img src="image_9.png" /><figcaption>**Figure 6.** Two-component model, comprised of a compact (blue) and extended (red) polarized emission regions with corresponding small-scale and large-scale Faraday screens. The small screen, which may be external (shown) or internal (not shown), acts only on the compact component, which is observed by the EHT. ALMA observes the combined emission from both components.</figcaption></figure>

RMs arise in part from the wavelength-dependent competition between the two components, and thus are not directly indicative of the properties of either Faraday screen.

Nevertheless, via this model we are able to separately constrain the RMs that are observed on ALMA and EHT scales; these are shown in Figure 7. Specifically, while the RM of the large-scale Faraday screen is comparable to the 2017 April values reported in Table 3, that associated with the compact component is not directly constrained by the ALMA measurements and can be factors of many larger: at 95% confidence, the compact RM is between $-5.4 \times 10^5 \text{ rad m}^{-2}$ and $-2.9 \times 10^5 \text{ rad m}^{-2}$. Interestingly, the estimated range is consistent with the RM inferred from low-inclination GRMHD models of the M87 core (Ricarte et al. 2020; Event Horizon Telescope Collaboration et al. 2021b) and comparable to the 2018 April values reported in Table 3. This consistency suggests the possibility that in 2018 April ALMA may be seeing the core RM (e.g., as a consequence of a different beating of the two components). This hypothesis can be directly tested with the 2018 EHT observations which, unlike the 2017 ones, covered the full frequency spacing of ALMA (212–230 GHZ; see Section 2.1), and are therefore expected to directly measure the resolved RM of the core. This will in turn allow us to quantify the interplay between compact and extended components, and potentially explain the time variability observed with ALMA.

### 5.3. Constraints on Sgr A* Model from Polarization and Faraday Properties at 3 and 1.3 mm

Measurements of Faraday rotation at radio/millimeter wavelengths, either toward Sgr A* itself (e.g., Marrone et al. 2007; Bower et al. 2018) or the nearby pulsar PSR J1745-2900 (e.g., Eatough et al. 2013; Kravchenko et al. 2016), have been used to probe the magnetized accretion flow in Sgr A* on scales from tens of $R_{\text{Sch}}$ out to the Bondi radius ($\sim 10^5 R_{\text{Sch}}$). Using the same semi-analytic RIAF/ADAF models introduced in Section 5.2 (Marrone et al. 2006), from the measured RM values at 1.3 mm we obtain an

<figure><img src="image_10.png" /><figcaption>**Figure 7.** Posteriors implied by the 2017 April 5, 6, 10, and 11 ALMA and EHT observations for the RMs measured on ALMA (extended) and EHT (compact) scales in the two component model when it is assumed that the compact Faraday screen is external (lower left, blue) and internal (upper right, red) to the emission region. Contours are shown for the 50%, 90%, and 99% quantiles. For comparison, the 2σ range of 2017 April 5, 6, 10, and 11 ALMA RMs reported in Table 3 are shown as the black crosses and gray bands.</figcaption></figure>

accretion rate of order $10^{-8} \text{ M}_\odot \text{yr}^{-1}$ (assuming $R_{\text{RM, in}} = 10 R_{\text{Sch}}$), with a maximum variation of approximately 20% across the observing week.

We have derived for the first time the polarization and Faraday properties of Sgr A* both at 3 mm and 1.3 mm in a time window of 10 days. Since the synchrotron photosphere in the accretion flow moves outward with decreasing frequency (because of increased opacity), the polarized emission at 3 mm and 1.3 mm is expected to arise from different locations with potentially different magnetic field structures. Any variation of the intrinsic EVPA or RM with frequency can therefore provide interesting insights on the polarized source and magnetic field structure. In Section 4.3 we infer that the intrinsic polarization vector is rotated between the 3 mm ($\chi_o \sim +135^\circ$ or $-45^\circ$ assuming a full $180^\circ$ wrap) and the 1.3 mm ($\chi_o \sim [-15^\circ, -19^\circ]$) bands and that the RM magnitude at 3 mm is about half of the RM value measured at 1.3 mm over a three-day separation. From earlier VLBI measurements, we know that the emission at millimeter wavelengths must come from very closely situated regions of the black hole, with an intrinsic (i.e., unscattered) size of $\sim 120 \mu\text{as}$ (or $12 R_{\text{Sch}}$) at 3.5 mm (Issaoun et al. 2019) and $\sim 50 \mu\text{as}$ (or $5 R_{\text{Sch}}$) at 1.3 mm (Lu et al. 2018). Therefore the radius of the 3.5 mm source is 2.4 times larger than that of the 1.3 mm source, i.e., very close to the ratio of the RM values measured with ALMA at the two wavelengths (see RM paragraph in Section 4.3). Taken at face value, this result suggests that about half of the Faraday rotation at 1.3 mm may occur between the 3 mm photosphere and the 1.3 mm source.

Although this result would be extremely constraining for the model of Sgr A*, we should point out two caveats: (i) possible presence of multiple components; (ii) potential RM time variability. We explain these caveats below.
*Multiple components.* In addition to the mini-spiral, which is however unpolarized (see Section 3.3.1) and thus should not contribute significantly to the polarized flux, the presence of a relativistic compact jet has been proposed based on theoretical modeling of the source SED, in particular to explain the radio emission in Sgr A* (e.g., Falcke & Markoff 2000). In addition, the only available VLBI polarimetry study at 1.3 mm has shown that the polarization structure of Sgr A* is complex (Johnson et al. 2015) and can be in principle different at the two wavelengths. Therefore, we cannot completely exclude the presence of an additional jet component to the accretion flow or a more complex morphology for the intrinsic polarization. Nevertheless, we argue that the stability of LP, RM, and CP (including their sign) observed in Sgr A* over more than a decade, unlike the case of M87, favors the presence of a single dominating polarized component.

*RM time variability.* At 1.3 mm, the RM changes by $+1.5 \times 10^5$ rad m$^{-2}$ (~30%) between April 6/7 and 11. Assuming the same rate of time variability at 3 mm and 1.3 mm, such variability is likely not responsible for a factor of two difference over three days. Likewise, the large offset in $\chi_0$ observed at 3 mm and 1.3 mm is unlikely a consequence of time variability, given the $\chi_0$ consistency on April 6–11. Larger variations in RM were, however, recorded by Marrone et al. (2007) and Bower et al. (2018) on timescales from hours to months (see for example Figure 12 in Bower et al. 2018). Since the observations in the two frequency bands were close in time but not simultaneous, we cannot definitely exclude time variability as the origin of the observed difference in RM magnitude at 3 mm and 1.3 mm.

Future simultaneous measurements over a wider wavelength range (including 3 mm and 1.3 mm) will allow us to separate time variability and source structure effects.

## 6. Conclusions

We have determined and analyzed the polarization and Faraday properties of Sgr A*, the nucleus of M87, and a dozen radio-loud AGNs, observed with ALMA during the 2017 VLBI campaign in the 3 mm and 1 mm bands in concert with the GMVA and the EHT, respectively.

Our main findings can be summarized as follows.

1. The AGN sources in our sample are highly polarized, with linear polarization degrees in the range 2–15% at 1.3 mm and 0.9%–13% at 3 mm. The radio galaxies NGC 1052 and Cen A are the only exceptions with LP<0.2%.

2. The AGN sources have negative spectral indexes varying in the range $\alpha = [-1.3, -0.2]$, in contrast with the flat spectra ($\alpha = 0$) typically found at longer cm wavelengths in AGN cores. We also observe a spectral steepening between the 3 mm and the 1.3 mm bands, which can naturally be explained by decreased opacity of the synchrotron emission at higher frequencies in a standard jet model (e.g., Lobanov 1998).

3. We find marginal evidence for a general higher degree of polarization and RM magnitude in the 1 mm band as compared to the 3 mm band (a trend which is consistent with single-dish surveys). The increase of polarized intensity at higher frequency may be the result of an increased magnetic-field order in the inner portions of jets and/or to the smaller size of the high-frequency-emitting

regions. The increase of RM with frequency can be explained by opacity effects: emission at higher frequencies is generated in, and propagates along, regions with higher magnetic fields and plasma densities (e.g., Hovatta et al. 2014). Given the small number statistics (eight AGNs observed at 3 mm, 11 at 1.3 mm, and six in both bands) and the caveat of time variability (in a time window of 10 days), simultaneous observations of a larger AGN sample at multiple frequency bands are needed to confirm these results.

4. The blazars (seven in our sample) have on average the highest level of polarization (LP ~7.1% at 1.3 mm) and an order of magnitude lower RM (~0.07 × $10^5$ rad m$^{-2}$ at 1.3 mm) when compared with other AGNs in our sample (with LP ~2.4% and RM ~0.4 × $10^5$ rad m$^{-2}$, respectively). These millimeter polarization differences can be understood in the context of the viewing angle unification scheme of AGNs: blazars' face-on geometry implies a stronger Doppler-boosting of the synchrotron-emitting plasma in the jet and reduces the effect of Faraday and beam depolarization in the accretion flow, resulting in higher LP (and lower RM). Future observations of a broader sample of sources are necessary for assessing the statistical significance of these trends.

5. We constrain the circular polarization fraction in the observed AGNs to <0.3%. For Sgr A* we report $CP = [-1.0, -1.5]\%$, consistent with previous SMA and ALMA studies. However, we explicitly note that the ALMA observatory does not guarantee a CP level <0.6% (1$\sigma$), therefore these measurements should be regarded as tentative detections.

6. We derive for the first time the polarization and Faraday properties of Sgr A* both at 3 mm and 1.3 mm in a time window of 10 days. The RM magnitude at 3 mm, $(-2.1 \pm 0.1) \times 10^5$ rad m$^{-2}$, is about half of the RM value measured at 1.3 mm over a three-day separation, suggesting that about half of the Faraday rotation at 1.3 mm may occur between the 3 mm photosphere and the 1.3 mm source (although we cannot exclude effects related to time variability).

7. We report the first unambiguous measurement of Faraday rotation toward the M87 nucleus at millimeter wavelengths. At variance with Sgr A*, the M87 RM exhibits significant changes in magnitude and sign reversals. At 1.3 mm, it spans from positive values $(+1.5 \times 10^5$ rad m$^{-2}$ at a $5\sigma$ level), to <3$\sigma$ non-detections in 2017 April, to negative values ($-3$ to $-4 \times 10^5$ rad m$^{-2}$ at a $10\sigma$ level) in 2018 April. At 3 mm the RM measured values span the range from $-1.2$ to $0.3 \times 10^5$ rad m$^{-2}$ from 2015 September to 2016 October. The large scatter and time variability revealed by the ALMA measurements suggest a more complicated physical origin of the Faraday rotation than is usually assumed in models using the RM to infer a mass accretion rate. We conclude that, unlike the case of Sgr A*, the RM in M87 may not provide an accurate estimate of the mass accretion rate onto the black hole.

8. The observed RM in M87 may result from Faraday rotation internal to the emission region, as commonly found in GRMHD models of turbulent accretion flows or expected in a structured jet, or from a time-varying helical magnetic field threading the jet boundary layer acting as an external Faraday screen. As an alternative, we put
forward a two-component model comprised of a variable compact region and static extended region. We find that this simple model is able to simultaneously explain the polarimetric properties observed in 2017 April by both the EHT (on horizon scales) and ALMA (which observes the combined emission from both components).

The ALMA measurements presented in this work provide critical constraints for the calibration and analysis of simultaneously obtained VLBI data. This is an essential resource for two instruments like the EHT and the GMVA which have the resolving power to reveal polarization structures and measure magnetic field strengths and particle densities on horizon scales (in the case of M87 and Sgr A*) and/or in the inner few parsecs for the AGNs.

ALMA is a partnership of the European Southern Observatory (ESO; Europe, representing its member states), NSF, and National Institutes of Natural Sciences of Japan, together with National Research Council (Canada), Ministry of Science and Technology (MOST; Taiwan), Academia Sinica Institute of Astronomy and Astrophysics (ASIAA; Taiwan), and Korea Astronomy and Space Science Institute (KASI; Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, Associated Universities, Inc. (AUI)/NRAO, and the National Astronomical Observatory of Japan (NAOJ). The NRAO is a facility of the NSF operated under cooperative agreement by AUI. This Letter makes use of the following ALMA data: ADS/JAO.ALMA#2016.1.00413.V ADS/JAO.ALMA#2016.1.01116.V ADS/JAO.ALMA#2016.1.01216.V ADS/JAO.ALMA#2016.1.01114.V ADS/JAO.ALMA#2016.1.01154.V ADS/JAO.ALMA#2016.1.01176.V ADS/JAO.ALMA#2016.1.01198.V ADS/JAO.ALMA#2016.1.01290.V ADS/JAO.ALMA#2016.1.01404.V ADS/JAO.ALMA#2017.1.00841.V ADS/JAO.ALMA#2013.1.01022.S ADS/JAO.ALMA#2015.1.01170.S ADS/JAO.ALMA#2016.1.00415.S ADS/JAO.ALMA#2017.1.00608.S The authors of the present Letter thank the following organizations and programs: the Academy of Finland (projects 274477, 284495, 312496, 315721); the Advanced European Network of E-infrastructures for Astronomy with the SKA (AENEAS) project, supported by the European Commission Framework Programme Horizon 2020 Research and Innovation action under grant agreement 731016; the Alexander von Humboldt Stiftung; an Alfred P. Sloan Research Fellowship; Allegro, the European ALMA Regional Centre node in the Netherlands, the NL astronomy research network NOVA and the astronomy institutes of the University of Amsterdam, Leiden University and Radboud University; the black hole Initiative at Harvard University, through a grant (60477) from the John Templeton Foundation; the China Scholarship Council; Agencia Nacional de Investigación y Desarrollo (ANID), Chile via NCN19_058 (TITANs) and Fondecyt 3190878; Consejo Nacional de Ciencia y Tecnología (CONACYT, Mexico, projects U0004-246083, U0004-259839, F0003-272050, M0037-279006, F0003-281692, 104497, 275201, 263356); the Delaney Family via the Delaney Family John A. Wheeler Chair at Perimeter Institute; Dirección General de Asuntos del Personal Académico–Universidad Nacional Autónoma de México (DGAPA–UNAM, projects IN112417 and IN112820); the European Research Council Synergy Grant “BlackHoleCam: Imaging the Event Horizon of Black Holes” (grant 610058); the Generalitat Valenciana postdoctoral grant APOSTD/2018/177 and GenT Program (project CIDEGENT/2018/021); MICINN Research

Project PID2019-108995GB-C22; the Gordon and Betty Moore Foundation (grants GBMF-3561, GBMF-5278); the Istituto Nazionale di Fisica Nucleare (INFN) sezione di Napoli, iniziative specifiche TEONGRAV; the International Max Planck Research School for Astronomy and Astrophysics at the Universities of Bonn and Cologne; the Jansky Fellowship program of the National Radio Astronomy Observatory (NRAO); Joint Princeton/Flatiron and Joint Columbia/Flatiron Postdoctoral Fellowships, research at the Flatiron Institute is supported by the Simons Foundation; the Japanese Government (Monbukagakusho: MEXT) Scholarship; the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for JSPS Research Fellowship (JP17J08829); the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (CAS, grants QYZDJ-SSW-SLH057, QYZDJSSW-SYS008, ZDBS-LY-SLH011); the Leverhulme Trust Early Career Research Fellowship; the Max-Planck-Gesellschaft (MPG); the Max Planck Partner Group of the MPG and the CAS; the MEXT/JSPS KAKENHI (grants 18KK0090, JP18K13594, JP18K03656, JP18H03721, 18K03709, 18H01245, 25120007); the Malaysian Fundamental Research Grant Scheme (FRGS) FRGS/1/2019/STG02/UM/02/6; the MIT International Science and Technology Initiatives (MISTI) Funds; the Ministry of Science and Technology (MOST) of Taiwan (105-2112-M-001-025-MY3, 106-2112-M-001-011, 106-2119-M-001-027, 107-2119-M-001-017, 107-2119-M-001-020, and 107-2119-M-110-005, MOST 108-2112-M-001-048 and MOST 109-2124-M-001-005); the National Aeronautics and Space Administration (NASA, Fermi Guest Investigator grant 80NSSC20K1567, NASA Astrophysics Theory Program grant 80NSSC20K0527, and Hubble Fellowship grant HST-HF2-51431.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555, ); the National Institute of Natural Sciences (NINS) of Japan; the National Key Research and Development Program of China (grant 2016YFA0400704, 2016YFA0400702); the National Science Foundation (NSF, grants AST-0096454, AST-0352953, AST-0521233, AST-0705062, AST-0905844, AST-0922984, AST-1126433, AST-1140030, DGE-1144085, AST-1207704, AST-1207730, AST-1207752, MRI-1228509, OPP-1248097, AST-1310896, AST-1337663, AST-1440254, AST-1555365, AST-1615796, AST-1715061, AST-1716327, AST-1716536, OISE-1743747, AST-1816420, AST-1903847, AST-1935980, AST-2034306); the Natural Science Foundation of China (grants 11573051, 11633006, 11650110427, 10625314, 11721303, 11725312, 11933007, 11991052, 11991053); a fellowship of China Postdoctoral Science Foundation (2020M671266); the Natural Sciences and Engineering Research Council of Canada (NSERC, including a Discovery Grant and the NSERC Alexander Graham Bell Canada Graduate Scholarships-Doctoral Program); the National Youth Thousand Talents Program of China; the National Research Foundation of Korea (the Global PhD Fellowship Grant: grants NRF-2015H1A2A1033752, 2015-R1D1A1A01056807, the Korea Research Fellowship Program: NRF-2015H1D3A1066561, Basic Research Support Grant 2019R1F1A1059721); the Netherlands Organization for Scientific Research (NWO) VICI award (grant 639.043.513) and Spinosa Prize SPI 78-409; the New Scientific Frontiers with Precision Radio Interferometry Fellowship awarded by the South African Radio Astronomy Observatory (SARAO), which is a facility of the National Research Foundation (NRF), an agency of the Department of Science and Technology (DST) of South Africa;
the Onsala Space Observatory (OSO) national infrastructure, for
the provisioning of its facilities/observational support (OSO
receives funding through the Swedish Research Council under
grant 2017-00648) the Perimeter Institute for Theoretical Physics
(research at Perimeter Institute is supported by the Government of
Canada through the Department of Innovation, Science and
Economic Development and by the Province of Ontario through
the Ministry of Research, Innovation and Science); the Spanish
Ministerio de Economía y Competitividad (grants PGC2018-
098915-B-C21, AYA2016-80889-P, PID2019-108995GB-C21);
the State Agency for Research of the Spanish MCIU through the
“Center of Excellence Severo Ochoa” award for the Instituto de
Astrofísica de Andalucía (SEV-2017-0709); the Toray Science
Foundation; the Consejería de Economía, Conocimiento, Empresas
y Universidad of the Junta de Andalucía (grant P18-FR-1769),
the Consejo Superior de Investigaciones Científicas (grant
2019AEP112); the US Department of Energy (USDOE) through
the Los Alamos National Laboratory (operated by Triad National
Security, LLC, for the National Nuclear Security Administration
of the USDOE (Contract 89233218CNA000001); the Italian
Ministero dell'Istruzione Università e Ricerca through the grant
Progetti Premiali 2012-iALMA (CUP C52113000140001); the
European Union's Horizon 2020 research and innovation program
under grant agreement No 730562 RadioNet; ALMA North
America Development Fund; the Academia Sinica; Chandra
TM6-17006X; the GenT Program (Generalitat Valenciana)
Project CIDEGENT/2018/021; NASA NuSTAR award
80NSSC20K0645; Chandra award DD7-18089X. This work
used the Extreme Science and Engineering Discovery Environment
(XSEDE), supported by NSF grant ACI-1548562, and
CyVerse, supported by NSF grants DBI-0735191, DBI-1265383,
and DBI-1743442. XSEDE Stampede2 resource at TACC was
allocated through TG-AST170024 and TG-AST080026N.
XSEDE JetStream resource at PTI and TACC was allocated
through AST170028. The simulations were performed in part on
the SuperMUC cluster at the LRZ in Garching, on the LOEWE
cluster in CSC in Frankfurt, and on the HazelHen cluster at the
HLRS in Stuttgart. This research was enabled in part by support
provided by Compute Ontario (http://computeontario.ca), Calcut
Quebec (http://www.calculquebec.ca) and Compute Canada
(http://www.computecanada.ca). We thank the staff at the
participating observatories in the GMVA and EHT, correlation
centers, and institutions for their enthusiastic support. The GMVA
is coordinated by the VLBI group at the Max-Planck-Institut für
Radioastronomie (MPIfR) and consists of telescopes operated by
MPIfR, IRAM, Onsala, Metsahovi, Yebes, the Korean VLBI
Network, the Green Bank Observatory and the VLBA. APEX is a
collaboration between the MPIfR (Germany), ESO, and the
Onsala Space Observatory (Sweden). The SMA is a joint project
between the SAO and ASIAA and is funded by the Smithsonian
Institution and the Academia Sinica. The JCMT is operated by the
East Asian Observatory on behalf of the NAOJ, ASIAA, and
KASI, as well as the Ministry of Finance of China, Chinese
Academy of Sciences, and the National Key R&D Program (No.
2017YFA0402700) of China. Additional funding support for the
JCMT is provided by the Science and Technologies Facility

Council (UK) and participating universities in the UK and
Canada. The LMT is a project operated by the Instituto Nacional
de Astrófisica, Óptica, y Electrónica (Mexico) and the University
of Massachusetts at Amherst (USA). The IRAM 30 m telescope
on Pico Veleta, Spain is operated by IRAM and supported by
CNRS (Centre National de la Recherche Scientifique, France),
MPG (Max-Planck-Gesellschaft, Germany) and IGN (Instituto
Geográfico Nacional, Spain). The SMT is operated by the Arizona
Radio Observatory, a part of the Steward Observatory of the
University of Arizona, with financial support of operations from
the State of Arizona and financial support for instrumentation
development from the NSF. The SPT is supported by the National
Science Foundation through grant PLR-1248097. Partial support
is also provided by the NSF Physics Frontier Center grant PHY-
1125897 to the Kavli Institute of Cosmological Physics at the
University of Chicago, the Kavli Foundation and the Gordon and
Betty Moore Foundation grant GBMF 947. The SPT hydrogen
maser was provided on loan from the GLT, courtesy of ASIAA.
The EHTC has received generous donations of FPGA chips from
Xilinx Inc., under the Xilinx University Program. The EHTC has
benefited from technology shared under open-source license by
the Collaboration for Astronomy Signal Processing and Electro-
nics Research (CASPER). The EHT project is grateful to
T4Science and Microsemi for their assistance with Hydrogen
Masers. This research has made use of NASA's Astrophysics
Data System. We gratefully acknowledge the support provided by
the extended staff of the ALMA, both from the inception of the
ALMA Phasing Project through the observational campaigns of
2017 and 2018. We would like to thank A. Deller and W. Brisken
for EHT-specific support with the use of DiFX. We thank Sergio
Martin for the help interpreting the Sgr A* spectrum in SPW = 2.
We acknowledge the significance that Maunakea, where the SMA
and JCMT EHT stations are located, has for the indigenous
Hawaiian people. M.P. acknowledges support by the Spanish
Ministry of Science through Grants PID2019-105510GB-C31,
and PID2019-107427GB-C33, and from the Generalitat Valenci-
ana through grant PROMETEU/2019/071.

Appendix A
Projects Observed during the 2017 VLBI Campaign

Tables A1 and A2 list the projects observed in the 3 mm and 1.3 mm bands, ordered by date of execution. Each row reports the observing date, the ALMA project code, the science target, the source used as polarization calibrator, other sources observed in the project, and the duration of each observation. In Table A2, each row-group refers to an individual VLBI run or “Track,” which includes observations of different projects carried out during the same night. The calibration of EHT projects was done per track (and not per project; see Goddi et al. 2019b). Two sources listed in Table A2, 3C 84 and J0006–0623, both observed on April 7, were excluded from the analysis presented in this Letter: 3C 84 was observed with an elevation below 25°, while J0006–0623 was observed for just ~2 minutes close to an elevation of 25°; the resulting calibrated data display critical phase and amplitude scatter and hence were flagged before data analysis (see Section 2.2).
<table><caption>**Table A1**
Projects and Sources Observed in the 3 mm Band</caption><thead><tr><th>Date</th><th>Project</th><th>Target</th><th>Pol. Cal.</th><th>Other Sources</th><th>UT Range</th></tr></thead><tbody><tr><td>2017 Apr 2</td><td>2016.1.01116.V</td><td>OJ 287</td><td>4C 01.28</td><td>J0510+1800</td><td>06:55:08–15:19:43</td></tr><tr><td>2017 Apr 3</td><td>2016.1.00413.V</td><td>Sgr A*</td><td>NRAO 530</td><td>J1924–2914, 4C 09.57</td><td>20:52:28–04:43:54</td></tr><tr><td>2017 Apr 4</td><td>2016.1.01216.V</td><td>3C 273</td><td>3C 279</td><td>...</td><td>00:24:57–05:32:46</td></tr></tbody></table>

<table><caption>**Table A2**
Projects and Sources Observed in the 1.3 mm Band</caption><thead><tr><th>Date</th><th>Project</th><th>Target</th><th>Pol. Cal.</th><th>Other Sources</th><th>UT Range</th></tr></thead><tbody><tr><td rowspan="4">2017 Apr 5</td><td>2016.1.01114.V</td><td>OJ 287</td><td>3C 279</td><td>4C 01.28, M87</td><td>04/22:12–05/09:13</td></tr><tr><td>2016.1.01154.V</td><td>M87</td><td>3C 279</td><td>4C 01.28, OJ 287</td><td>04/22:12–05/03:22</td></tr><tr><td>2016.1.01176.V</td><td>3C 279</td><td>3C 279</td><td>M87</td><td>05/03:24–05/07:18</td></tr><tr><td></td><td></td><td></td><td></td><td>05/07:19–05/09:13</td></tr><tr><td rowspan="4">2017 Apr 6</td><td>2016.1.01154.V</td><td>M87</td><td>3C 279</td><td>3C 279</td><td>06/00:18–06/16:19</td></tr><tr><td>2016.1.01404.V</td><td>Sgr A*</td><td>3C 279</td><td>NRAO 530, J1924–2914</td><td>06/00:18–06/08:02</td></tr><tr><td>2016.1.01290.V</td><td>NGC 1052</td><td>3C 279</td><td>J0132–1654, J0006–0623</td><td>06/08:03–06/14:40</td></tr><tr><td></td><td></td><td></td><td></td><td>06/14:51–06/16:19</td></tr><tr><td rowspan="3">2017 Apr 7</td><td>2016.1.01404.V</td><td>Sgr A*</td><td>J1924–2914</td><td>NRAO 530</td><td>07/03:45–07/20:47</td></tr><tr><td>2016.1.01290.V</td><td>NGC 1052</td><td>J1924–2914</td><td>J0132–1654, 3C 84<sup>a</sup></td><td>07/03:45–07/14:31</td></tr><tr><td></td><td></td><td></td><td>J0006–0623<sup>a</sup></td><td>07/19:23–07/20:47</td></tr><tr><td rowspan="4">2017 Apr 10</td><td>2016.1.01114.V</td><td>OJ 287</td><td>3C 279</td><td>4C 01.28, M87</td><td>09/23:02–10/10:02</td></tr><tr><td>2016.1.01176.V</td><td>3C 279</td><td>3C 279</td><td>Cen A, M87</td><td>09/23:02–10/03:49</td></tr><tr><td>2016.1.01198.V</td><td>Cen A</td><td>3C 279</td><td>–</td><td>10/03:51–10/06:21</td></tr><tr><td></td><td></td><td></td><td></td><td>10/06:23–10/10:02</td></tr><tr><td rowspan="5">2017 Apr 11</td><td>2016.1.01114.V</td><td>OJ 287</td><td>3C 279</td><td>4C 01.28</td><td>10/21:44–11/10:31</td></tr><tr><td>2016.1.01154.V</td><td>M87</td><td>3C 279</td><td>...</td><td>10/21:44–11/00:22</td></tr><tr><td>2016.1.01176.V</td><td>3C 279</td><td>3C 279</td><td>M87</td><td>11/00:23–11/05:03</td></tr><tr><td>2016.1.01404.V</td><td>Sgr A*</td><td>3C 279</td><td>J1924–2914</td><td>11/05:05–11/08:45</td></tr><tr><td></td><td></td><td></td><td></td><td>11/08:46–11/14:03</td></tr></tbody></table>

**Note.**

**Appendix B**
Polarimetric Images

Tables B1 and B2 report the main imaging parameters for each source observed on each day of the 2017 VLBI campaign in Band 3 and Band 6, respectively. These parameters include the on-source time, the rms achieved in each Stokes parameter, and the synthesized beam size. The on-source time is computed after full calibration and flagging of bad data (see Section 2.2). The rms does not simply scale as $\sqrt{T_{\text{on-source}}}$ but depends on several parameters such as source structure, number of observing antennas, array configuration, weather, and details of the VLBI scheduling blocks (e.g., low-elevation scans). The synthesized beam size changes by a factor of two at 1.3 mm due to the changing array configuration during the observing week (see Section 2.1). The resulting images are dynamic range limited and showcase different structures on different days (depending on the array beam size).

The full suite of polarization images for all the sources observed in the VLBI campaign are shown in Figures B1–B6. In particular, Figure B1 displays 1.3 mm images of Sgr A* in the three days of the EHT observations, Figures B2 and B3 display the 1.3 mm images of M87 and 3C 279 on the four days of the EHT observations. Figures B4 and B5 report 1.3 mm maps for all the other AGN sources observed with the EHT for three days and one/two days, respectively. Finally, Figure B6 shows 3 mm maps of the sources observed with the GMVA. In each plot, the black vectors showcase the orientation of the EVPAs, while their length is linearly proportional to the polarized flux. The EVPAs are plotted every 8 pixels (i.e., are spaced by 1"6 at 1.3 mm and 4" at 3 mm) for all sources, except for M87, where the EVPAs are plotted every 4 pixels (i.e., are spaced by 0"8), in order to sample more uniformly the jet. Note that the EVPAs are not Faraday-corrected and that the magnetic field vectors should be rotated by 90°.

<footnote><sup>a</sup> Flagged before data analysis (see text in Appendix A and Section 2.2).</footnote>
<table><caption>**Table B1**
Frequency-averaged Imaging Parameters of GMVA Sources (at a Representative Frequency of 93 GHz)</caption><thead><tr><th>Source</th><th>T<sub>on source</sub><br>(hr)</th><th>rms(I)<br>(mJy)</th><th>rms(Q)<br>(mJy)</th><th>rms(U)<br>(mJy)</th><th>rms(V)<br>(mJy)</th><th>Synthesized Beam<br>θ<sub>M</sub>(") × θ<sub>m</sub>(") (P.A.(°))</th></tr></thead><tbody><tr><td colspan="7" style="text-align: center;">Apr 2</td></tr><tr><td>OJ 287</td><td>2.584</td><td>0.31</td><td>0.34</td><td>0.46</td><td>0.17</td><td>4"′′7 × 2"′′7 (−86°2)</td></tr><tr><td>4C 01.28</td><td>0.269</td><td>0.17</td><td>0.30</td><td>0.36</td><td>0.14</td><td>4"′′9 × 2"′′4 (−86°8)</td></tr><tr><td>J0510+1800</td><td>0.363</td><td>0.31</td><td>0.29</td><td>0.52</td><td>0.12</td><td>5"′′8 × 2"′′5 (−70°1)</td></tr><tr><td colspan="7" style="text-align: center;">Apr 3</td></tr><tr><td>J1924–2914</td><td>0.270</td><td>0.16</td><td>0.65</td><td>0.13</td><td>0.13</td><td>5"′′5 × 2"′′5 (−75°2)</td></tr><tr><td>NRAO 530</td><td>0.479</td><td>0.02</td><td>0.02</td><td>0.02</td><td>0.03</td><td>4"′′8 × 2"′′4 (−83°5)</td></tr><tr><td>Sgr A*</td><td>2.643</td><td>0.80</td><td>0.09</td><td>0.08</td><td>0.04</td><td>5"′′0 × 2"′′7 (−81°1)</td></tr><tr><td>4C 09.57</td><td>0.133</td><td>0.09</td><td>0.08</td><td>0.14</td><td>0.07</td><td>6"′′1 × 2"′′7 (72°0)</td></tr><tr><td colspan="7" style="text-align: center;">Apr 4</td></tr><tr><td>3C 273</td><td>1.396</td><td>0.48</td><td>0.26</td><td>0.54</td><td>0.13</td><td>5"′′0 × 3"′′4 (−86°7)</td></tr><tr><td>3C 279</td><td>0.215</td><td>0.37</td><td>0.20</td><td>0.15</td><td>0.18</td><td>5"′′0 × 3"′′4 (−85°8)</td></tr></tbody></table>

<table><caption>**Table B2**
Frequency-averaged Imaging Parameters of EHT Sources (at a Representative Frequency of 221 GHz)</caption><thead><tr><th>Source</th><th>T<sub>on-source</sub><br>(hr)</th><th>rms(I)<br>(mJy)</th><th>rms(Q)<br>(mJy)</th><th>rms(U)<br>(mJy)</th><th>rms(V)<br>(mJy)</th><th>Synthesized Beam<br>θ<sub>M</sub>(") × θ<sub>m</sub>(") (P.A.(°))</th></tr></thead><tbody><tr><td colspan="7" style="text-align: center;">Apr 5</td></tr><tr><td>M87</td><td>1.645</td><td>0.18</td><td>0.05</td><td>0.05</td><td>0.02</td><td>2"′′0 × 1"′′0 (−85°5)</td></tr><tr><td>3C 279</td><td>1.068</td><td>0.24</td><td>0.09</td><td>0.07</td><td>0.16</td><td>2"′′2 × 0"′′9 (−80°9)</td></tr><tr><td>OJ 287</td><td>1.406</td><td>0.13</td><td>0.16</td><td>0.15</td><td>0.11</td><td>2"′′0 × 1"′′1 (88°7)</td></tr><tr><td>4C 01.28</td><td>0.230</td><td>0.12</td><td>0.11</td><td>0.08</td><td>0.12</td><td>2"′′0 × 0"′′9 (87°0)</td></tr><tr><td colspan="7" style="text-align: center;">Apr 6</td></tr><tr><td>J0006–0623</td><td>0.045</td><td>0.47</td><td>0.12</td><td>0.15</td><td>0.13</td><td>2"′′2 × 1"′′4 (−81°1)</td></tr><tr><td>J0132–1654</td><td>0.059</td><td>0.06</td><td>0.06</td><td>0.06</td><td>0.06</td><td>2"′′3 × 1"′′4 (87°8)</td></tr><tr><td>NGC 1052</td><td>0.373</td><td>0.05</td><td>0.03</td><td>0.03</td><td>0.03</td><td>2"′′7 × 1"′′3 (80°3)</td></tr><tr><td>Sgr A*</td><td>2.529</td><td>0.44</td><td>0.18</td><td>0.33</td><td>0.08</td><td>2"′′2 × 1"′′3 (−77°5)</td></tr><tr><td>J1924–2914</td><td>0.269</td><td>0.10</td><td>0.07</td><td>0.08</td><td>0.11</td><td>2"′′2 × 1"′′3 (−82°5)</td></tr><tr><td>NRAO 530</td><td>0.269</td><td>0.04</td><td>0.06</td><td>0.05</td><td>0.05</td><td>2"′′2 × 1"′′3 (−76°4)</td></tr><tr><td>M87</td><td>1.613</td><td>0.24</td><td>0.06</td><td>0.06</td><td>0.02</td><td>2"′′2 × 1"′′5 (−69°4)</td></tr><tr><td>3C 279</td><td>0.430</td><td>0.30</td><td>0.13</td><td>0.08</td><td>0.13</td><td>2"′′2 × 1"′′3 (−78°4)</td></tr><tr><td>3C 273</td><td>0.403</td><td>0.19</td><td>0.10</td><td>0.09</td><td>0.10</td><td>2"′′3 × 1"′′4 (−75°0)</td></tr><tr><td colspan="7" style="text-align: center;">Apr 7</td></tr><tr><td>NGC 1052</td><td>0.200</td><td>0.11</td><td>0.04</td><td>0.04</td><td>0.04</td><td>2"′′6 × 1"′′0 (−76°3)</td></tr><tr><td>J0132–1654</td><td>0.056</td><td>0.08</td><td>0.07</td><td>0.07</td><td>0.06</td><td>3"′′0 × 1"′′0 (−72°8)</td></tr><tr><td>NRAO 530</td><td>0.403</td><td>0.08</td><td>0.03</td><td>0.03</td><td>0.05</td><td>2"′′1 × 0"′′9 (−89°6)</td></tr><tr><td>J1924–2914</td><td>0.312</td><td>0.18</td><td>0.04</td><td>0.04</td><td>0.08</td><td>2"′′1 × 0"′′9 (89°7)</td></tr><tr><td>Sgr A*</td><td>4.109</td><td>0.25</td><td>0.14</td><td>0.13</td><td>0.04</td><td>2"′′1 × 0"′′9 (−88°6)</td></tr><tr><td colspan="7" style="text-align: center;">Apr 10</td></tr><tr><td>Cen A</td><td>1.401</td><td>0.11</td><td>0.07</td><td>0.07</td><td>0.12</td><td>2"′′3 × 0"′′9 (−79°0)</td></tr><tr><td>M87</td><td>0.454</td><td>0.25</td><td>0.06</td><td>0.07</td><td>0.04</td><td>2"′′0 × 1"′′0 (−88°9)</td></tr><tr><td>OJ 287</td><td>1.083</td><td>0.15</td><td>0.14</td><td>0.18</td><td>0.08</td><td>2"′′0 × 1"′′1 (−82°5)</td></tr><tr><td>3C 279</td><td>1.120</td><td>0.29</td><td>0.12</td><td>0.08</td><td>0.16</td><td>2"′′1 × 0"′′8 (−85°2)</td></tr><tr><td>4C 01.28</td><td>0.289</td><td>0.15</td><td>0.14</td><td>0.10</td><td>0.09</td><td>2"′′2 × 0"′′9 (80°0)</td></tr><tr><td colspan="7" style="text-align: center;">Apr 11</td></tr><tr><td>Sgr A*</td><td>1.934</td><td>0.35</td><td>0.24</td><td>0.20</td><td>0.06</td><td>1"′′2 × 0"′′7 (−85°1)</td></tr><tr><td>J1924–2914</td><td>0.244</td><td>0.29</td><td>0.10</td><td>0.10</td><td>0.14</td><td>1"′′2 × 0"′′7 (89°9)</td></tr><tr><td>3C 279</td><td>1.705</td><td>0.23</td><td>0.11</td><td>0.08</td><td>0.11</td><td>1"′′2 × 0"′′7 (−86°6)</td></tr><tr><td>M87</td><td>1.831</td><td>0.16</td><td>0.04</td><td>0.04</td><td>0.03</td><td>1"′′2 × 0"′′8 (79°3)</td></tr><tr><td>OJ 287</td><td>0.804</td><td>0.21</td><td>0.15</td><td>0.11</td><td>0.17</td><td>1"′′2 × 0"′′9 (59°6)</td></tr><tr><td>4C 01.28</td><td>0.110</td><td>0.26</td><td>0.17</td><td>0.14</td><td>0.23</td><td>1"′′5 × 0"′′8 (67°9)</td></tr></tbody></table>
<figure><img src="image_11.png" /><figcaption>**Figure B1.** Polarization images of Sgr A* at 1.3 mm (see Figure 2 for a description of the plotted quantities). The apparently lower quality of the image in the right panel is due to the fact that the observations on April 11 have about half the beam size, and are therefore less sensitive to the extended emission in the mini-spiral, when compared to the other two days (the beamsizes are shown as ovals in the lower left corner of each panel; see values reported in Table B2). Note that there are several tiny EVPAs plotted across the mini-spiral, apparently locating regions with polarized flux above the image rms noise cutoff (5σ). The LP and EVPA errors are, however, dominated by the systematic leakage (0.03% of *I* onto *QU*), which is not added to the images. Once these systematic errors are added, the LP flux in those points falls below the 3σ detection threshold. Therefore we do not claim detection of polarized emission outside of the central core in Sgr A*.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Figure B2.** Polarization images of M87 at 1.3 mm (see Figure 2 for a description of the plotted quantities). The apparently different jet structures (in total and polarized intensity) across days are due to different beamsizes (shown as ovals in the lower left corner of each panel; see values reported in Table B2).</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Figure B3.** Polarization images of 3C 279 at 1.3 mm (see Figure 2 for a description of the plotted quantities).</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Figure B4.** Polarization images of selected AGNs at 1.3 mm (see Figure 2 for a description of the plotted quantities).</figcaption></figure>
<figure><img src="image_15.png" /></figure>

**Figure B5.** Polarization images of selected AGNs at 1.3 mm (see Figure 2 for a description of the plotted quantities). Note that for NGC 1052 and Cen A no EVPA could be reliably derived owing to their low level of LP. We also note that although we detect polarized flux in Cen A above the image rms noise cutoff (5σ), once the systematic leakage (0.03% of *I* onto *QU*) is added to thermal noise, the LP flux would fall below the 3σ detection threshold. Therefore we do not claim detection of polarized emission in Cen A.
<figure><img src="image_16.png" /><figcaption>**Figure B6.** Polarization images of all targets observed at 3 mm (at a central frequency of 93 GHz). The beamsizes are shown as an oval in the lower left corner of each panel (see values reported in Table B1). See Figure 2 for a description of the plotted quantities.</figcaption></figure>

## Appendix C
### Comparative Analysis Across Multiple Flux-extraction Methods

Some of our targets (chiefly Sgr A* and M87, but also a few other AGNs; see Appendix B) reveal extended emission at arcsecond scales, which is differently resolved out by the different observing array configurations. Here we assess the impact of such extended emission in the flux values extracted in the visibility domain for the compact cores. For this purpose, we compare the parameters derived with UVMULTIFIT with those derived with two imaged-based methods: the sum of the nine central pixels in the CLEAN model image (3 × 3) and the integrated flux (INTF) from Gaussian fitting with the CASA task IMFIT<fnref n="149" /> (see Section 3.2). Table C1 reports the results from this comparative analysis between the image-based and the uv-based methods, showing the ratio of the four Stokes parameters, the LP, and the RM (3 × 3/UVMF and INTF/UVMF,

respectively), and the difference of the EVPA in degrees (3 × 3-UVMF and INTF-UVMF, respectively). Three sources (Cen A, NGC 1052, and J0132–1654) are excluded from this statistics due to their weak polarized signal.

Overall, the analysis clearly shows that Flux(3 × 3) < Flux (UVMF) < Flux(INTF) when considering the median of the results. On the one hand, one can interpret this as the 3 × 3 method being the least affected and INTF being the most affected by extended emission (with a weak dependence on the array-configuration resolution). On the other hand, the 3 × 3 method can also be more affected by phase and amplitude calibration errors (which will remove flux from the phase-center into the sidelobes), resulting in less recovered flux. Despite this systematic deviation, the median offsets are compatible with no significant difference within the MAD values. In Stokes *I*, both the offset and MAD are ≲ 0.4% across the methods, which is negligible when compared to the absolute uncertainty of ALMA’s flux calibration (10% in Band 6). In the case of Stokes *Q* and *U*, and resulting LP, the systematic offset and MAD between methods can be up to 1%. With the LP measured in our sample, these differences are

<footnote n="149">¹⁴⁹ IMFIT provides in output also the peak flux, but the integrated flux was preferred because its values were more consistent with the estimates from the other two methods.</footnote>
<table><caption>Table C1
Comparison of the Three Flux-extraction Methods for EHT Targets</caption><thead><tr><th>Method<sup>a</sup></th><th><i>I</i><sup>b</sup></th><th><i>Q</i><sup>b</sup></th><th><i>U</i><sup>b</sup></th><th><i>V</i><sup>b</sup></th><th>LP<sup>b</sup></th><th>EVPA<sup>c</sup> (°)</th><th>RM<sup>b</sup></th></tr></thead><tbody><tr><td>3 × 3</td><td>0.9995(0.0007)<sup>d</sup></td><td>0.989(0.008)</td><td>0.998(0.004)</td><td>1.00(0.04)</td><td>0.993(0.006)</td><td>0.0(0.1)</td><td>1.06(0.08)</td></tr><tr><td></td><td>0%<sup>d</sup></td><td>2%</td><td>1%</td><td>5%</td><td>10%</td><td>10%</td><td>0%</td></tr><tr><td>INTF</td><td>1.001(0.004)</td><td>1.00(0.01)</td><td>0.996(0.006)</td><td>1.00(0.04)</td><td>1.001(0.004)</td><td>0.04(0.09)</td><td>1.0(0.1)</td></tr><tr><td></td><td>0%</td><td>2%</td><td>17%</td><td>10%</td><td>5%</td><td>6%</td><td>0%</td></tr></tbody></table>

### Notes.

<sup>a</sup> This table compares UVMULTIFIT (UVMF) with: the sum of the nine central pixels (3 × 3) of the model image; and the integrated flux (INTF) from IMFIT.

<sup>b</sup> The values reported in columns are ratios between the method referred in the first column and UVMF, with the latter being in the denominator.

<sup>c</sup> The EVPA column shows the angle difference (in deg) between the methods.

<sup>d</sup> In each instance, three values are displayed: the median value of the distribution; the median absolute deviation or MAD (the value in brackets); the percentage of cases farther from the median than five times the MAD in quadrature with the measurement error (the value in the second row).

generally comparable (in absolute terms) to the 0.03% of Stokes *I* leakage onto *Q* and *U*. The EVPA shows a MAD value of ~0.1 deg, which results in a MAD value of up to 10% in the RM (note these are comparable or better than the observed statistical uncertainties—see Tables E1 and E2 in Appendix E). The poorer results for Stokes *V* are induced by the low level of CP in the sample (although the MAD is still comfortably around 4%).

Table C1 reports a fraction of “outliers” in the distributions (those cases that are 5σ away from the sample median). These are generally associated with the sources with the most prominent extended emission (other outliers are associated to parameters estimated at low-significance values). In order to better assess the magnitude of these outliers, in Figure C1 we show a detailed comparison between the uv-based and the 3 × 3 image-based methods for M87 (upper panels) and Sgr A* (lower panels), respectively. Analogously to Table C1, individual panels show the ratio of the four Stokes parameters, the LP, and the RM (3 × 3/UVMF), and the difference of the EVPA in degrees (3 × 3-UVMF); the results are reported per day and SPW.

In the case of M87, the two methods exhibit an excellent agreement, except for Stokes *U*. This is due to a combination of faint *U* emission at the core and appreciable emission from knots A and B. The discrepancy in Stokes *U* results generally in ΔEVPA ≲ 0.4° comparable with the uncertainties quoted in Table E2 in Appendix E, with one single case of ΔEVPA ~ 0.6° (on April 11 SPW = 1). Given the consistency in RM (within 1σ), this worst-case scenario discrepancies in EVPA do not affect the results of the analysis of this Letter.

In the case of Sgr A*, the discrepancies are much more pronounced in most parameters. Despite the prominence of the

mini-spiral (see Section 3.1 and Figure B1), Stokes *I* values actually agree within less than 1% between the two methods. It is however noteworthy that Flux(3 × 3)>Flux(UVMF) (i.e., the opposite trend with respect to Table C1). This inverted trend is due to a flux-decrement in the visibility amplitudes at around 25–30 kλ affecting most prominently UVMFIT on April 11 (this can be assessed by inspecting amplitude versus baseline-length uv-plots—not shown here—for the parallel hands on all days). Unlike Stokes *I*, Stokes *QU* are heavily affected, up to 20%–30% in the worst cases, resulting in LP differences up to 10% and EVPA offsets up to 2°. These large deviations in Stokes *QU* are systematic since all four SPWs appear to deviate in each day by an approximate amount. This in turn results in consistent RM values within 1σ. We note that we do not observe the same systematic offset either in M87 or J1924–2914, which were also calibrated using 3C 279 as the polarization-calibrator (on April 6 and 11), hence we discard calibration issues as being responsible for these systematics. One possible explanation is differential Stokes *I* leakage onto *Q* and *U* from extended unpolarized emission (see the spurious EVPA vectors matching the spiral-arms in Figure B1). Note also that such unpolarized emission extends farther than the inner third of the image field of view, where beam-squash (Hull et al. 2020) combined with leakage may induce significant deviations.

Given the results from this comparative analysis, we conclude that, for the purpose of the polarimetric analysis conducted in this Letter, the uv-fitting method provides sufficiently accurate flux values of Stokes *IQU* in all cases, although for Sgr A* we observe deviations in Stokes *QU* when comparing the two flux extraction methods.
<figure><img src="image_17.png" /></figure>

**Figure C1.** Comparison between image-based and uv-based flux-extraction methods for the two sources with the most prominent extended emission in our sample: M87 (top panels), and Sgr A* (bottom panels). The two methods being compared are UVMULTIFIT (UVMF) and the sum of the nine central pixels (3 × 3) of the model image. All parameters are compared via ratios, except for the EVPA (showing the difference in degrees). The errorbar in each data point is the combination in quadrature of the statistical error from each flux extraction method. The vertical dotted line and the shaded region show the median and MAD from Table C1. The labels in the Y-axis indicate the observing day in 2017 April (5, 6, 7, 10, 11) and the observing SPW (s1, s2, s3, s4); the RM panel shows only the days. Non-detections in the images are indicated with a cross. Note that the plotted uncertainties are not those of individual measurements but ratios or differences between the two methods. Therefore the errors on LP and EVPA for M87 on April 10/11 appear comparable to other days despite the large error bars and/or non-detections in Stokes U (i.e., the errors in U displayed do not propagate in the LP and EVPA plots).

## Appendix D
### Comparison of Stokes Parameters with the AMAPOLA Polarimetric Grid Survey

For the purposes of absolute flux calibration, ALMA monitors the flux of bright sources (mainly blazars or QSOs)

spread over the full range in R.A. (the Grid) by observing them together with solar system objects, the so-called Grid Survey (GS), with a period of approximately 10 days. These observations are executed with the ACA, in Bands 3, 6, and 7. Since full-polarization mode is adopted, it is possible to retrieve
<figure><img src="image_18.png" /></figure>

**Figure D1.** Comparison with time between the polarimetric results obtained for all the sources observed in the ALMA-VLBI campaign and those retrieved from the AMAPOLA polarimetric analysis of Grid Survey (GS) data. Each row shows a parameter (from top to bottom: Stokes Q, U, and V, LP, and EVPA) while each column corresponds to a source (from left to right: 3C 279, OJ 287, J1924–2914, and 4C 01.28; see Figure D2 for more). Only sources with entries in the ALMA archive (close in time to the observations, i.e., between end of March and 2017 April) are displayed. The measured flux values during the ALMA-VLBI observations are indicated as data points and corresponding errorbars (blue and green for Band 3 and 6 observations, respectively). The shaded regions indicate AMAPOLA’s ±1σ uncertainty in Band 3 (97.5 GHz; blue shade) and Band 7 (343.4 GHz; red shade), respectively. These are obtained from the ACA GS and their time evolution (lines) are obtained by interpolating between these measurements.

polarimetry information from the GS sources. This is done with AMAPOLA,<fnref n="150" /> a set of CASA-friendly Python scripts used to reduce the full-Stokes polarimetry of GS observations with ACA. Some of our targets are part of the GS, including: 3C 273 (J1229+0203); 3C 279 (J1256-0547); 4C 01.28 (J1058+0133); 4C 09.57 (J1751+0939); J0510+1800; OJ 287 (J0854+2006); J0006-0623; J1733-1304; and J1924-2914. Although the reported values by AMAPOLA are used for observation planning and the two arrays cover different uv-

ranges, it is still useful to make a comparison with this database to assess any systematics or clear inconsistent variability within a week's time-frame.

Figures D1 and D2 show the observed polarimetry parameters for the 2017 VLBI sessions (data points and errorbars), specifically Q, U, and V Stokes parameters, LP, and EVPA. The shaded ±1σ regions highlight the time variance of the same parameters as measured by AMAPOLA (an inflection in the trend means a time of GS observation). The color-coding is such that blue refers to Band 3 measurements, green to Band 6, and red to Band 7 ones. These figures show that most

<footnote n="150">150 http://www.alma.cl/~skameno/AMAPOLA/</footnote>
<figure><img src="image_19.png" /><figcaption>**Figure D2.** Same as Figure D1, but for different sources (from left to right: 3C 273, J0006-0623, NRAO 530, 4C 09.57). We note that source J0006-0623 was observed on April 7 but the calibrated data were of poor quality and were flagged before analysis (see Section 2.2).</figcaption></figure>

Band 3 ALMA-VLBI measurements fall within the blue regions, while most Band 6 measurements fall in between the blue and red regions, indicating that our measurements are broadly consistent with the AMAPOLA trends. Some potential conflicts can still be consistent with the inter-GS-cadence variability or differential time variability between frequency bands (as also observed in some cases in the AMAPOLA monitoring). We conclude that, despite the different array specifications and data-reduction schemes, the ALMA-VLBI and AMAPOLA results are consistent between each other.

## Appendix E
### Stokes Parameters per ALMA Frequency Band (SPW)

We report the polarimetric quantities (Stokes *IQU*, LP, EVPA) per SPW in Tables E1 (GMVA sources) and E2 (EHT sources). The Stokes parameters were fitted directly on the visibilities using UVMULTIFIT (see Section 3.2). Uncertainties are assessed with MC simulations, as the standard deviation of 1000 MC simulations for each Stokes parameter. The quoted uncertainties include in quadrature the fitting error and the Stokes *I* leakage onto Stokes *QU* (0.03% of *I*), as
<table><caption>Table E1
Polarization Parameters of GMVA Sources per Frequency Band (SPW) and per Day</caption><thead><tr><th>Frequency<br>(GHz)</th><th>I<br>(mJy)</th><th>Q<br>(mJy)</th><th>U<br>(mJy)</th><th>LP<br>(%)</th><th>EVPA<br>(deg)</th></tr></thead><tbody><tr><td colspan="6" style="text-align:center;">Apr 2<br>OJ 287</td></tr><tr><td>86.3</td><td>6242.41 ± 0.26</td><td>-409.6 ± 1.9</td><td>-351.2 ± 1.9</td><td>8.643 ± 0.030</td><td>-69.69 ± 0.10</td></tr><tr><td>88.3</td><td>6170.33 ± 0.26</td><td>-410.2 ± 1.9</td><td>-347.5 ± 1.9</td><td>8.711 ± 0.030</td><td>-69.87 ± 0.10</td></tr><tr><td>98.3</td><td>5787.47 ± 0.28</td><td>-398.9 ± 1.7</td><td>-327.8 ± 1.7</td><td>8.919 ± 0.030</td><td>-70.30 ± 0.10</td></tr><tr><td>100.3</td><td>5674.69 ± 0.27</td><td>-392.4 ± 1.7</td><td>-324.2 ± 1.7</td><td>8.970 ± 0.030</td><td>-70.214 ± 0.093</td></tr><tr><td colspan="6" style="text-align:center;">J0510+1800</td></tr><tr><td>86.3</td><td>3259.30 ± 0.57</td><td>-127.5 ± 1.0</td><td>22.6 ± 1.0</td><td>3.976 ± 0.030</td><td>84.97 ± 0.21</td></tr><tr><td>88.3</td><td>3208.82 ± 0.59</td><td>-126.2 ± 1.0</td><td>31.9 ± 1.0</td><td>4.054 ± 0.030</td><td>82.91 ± 0.20</td></tr><tr><td>98.3</td><td>2996.03 ± 0.62</td><td>-120.30 ± 0.90</td><td>46.96 ± 0.91</td><td>4.311 ± 0.030</td><td>79.33 ± 0.20</td></tr><tr><td>100.3</td><td>2962.36 ± 0.63</td><td>-121.52 ± 0.90</td><td>43.17 ± 0.90</td><td>4.353 ± 0.030</td><td>80.22 ± 0.21</td></tr><tr><td colspan="6" style="text-align:center;">4C 01.28</td></tr><tr><td>86.3</td><td>5039.680 ± 0.072</td><td>90.9 ± 1.5</td><td>-195.6 ± 1.5</td><td>4.281 ± 0.030</td><td>-32.54 ± 0.20</td></tr><tr><td>88.3</td><td>4970.067 ± 0.055</td><td>93.2 ± 1.5</td><td>-192.6 ± 1.5</td><td>4.306 ± 0.030</td><td>-32.09 ± 0.20</td></tr><tr><td>98.3</td><td>4745.126 ± 0.053</td><td>92.5 ± 1.4</td><td>-194.1 ± 1.4</td><td>4.533 ± 0.030</td><td>-32.26 ± 0.20</td></tr><tr><td>100.3</td><td>4665.997 ± 0.054</td><td>92.1 ± 1.4</td><td>-192.1 ± 1.4</td><td>4.566 ± 0.030</td><td>-32.18 ± 0.18</td></tr><tr><td colspan="6" style="text-align:center;">Apr 3<br>Sgr A*</td></tr><tr><td>86.3</td><td>2574.84 ± 0.87</td><td>9.28 ± 0.77</td><td>-3.64 ± 0.77</td><td>0.388 ± 0.030</td><td>-10.7 ± 2.2</td></tr><tr><td>88.3</td><td>2480.44 ± 0.82</td><td>12.51 ± 0.74</td><td>-2.36 ± 0.74</td><td>0.513 ± 0.030</td><td>-5.3 ± 1.7</td></tr><tr><td>98.3</td><td>2514.64 ± 0.74</td><td>18.44 ± 0.75</td><td>16.77 ± 0.75</td><td>0.991 ± 0.030</td><td>21.10 ± 0.86</td></tr><tr><td>100.3</td><td>2504.04 ± 0.72</td><td>15.20 ± 0.75</td><td>21.41 ± 0.75</td><td>1.048 ± 0.030</td><td>27.31 ± 0.81</td></tr><tr><td colspan="6" style="text-align:center;">J1924-2914</td></tr><tr><td>86.3</td><td>5273.93 ± 0.18</td><td>-10.6 ± 1.6</td><td>-245.0 ± 1.6</td><td>4.650 ± 0.030</td><td>-46.25 ± 0.19</td></tr><tr><td>88.3</td><td>5244.90 ± 0.18</td><td>-12.7 ± 1.6</td><td>-248.9 ± 1.6</td><td>4.752 ± 0.030</td><td>-46.46 ± 0.18</td></tr><tr><td>98.3</td><td>4984.67 ± 0.19</td><td>-12.0 ± 1.5</td><td>-248.2 ± 1.5</td><td>4.986 ± 0.030</td><td>-46.39 ± 0.17</td></tr><tr><td>100.3</td><td>4920.17 ± 0.21</td><td>-12.3 ± 1.5</td><td>-244.6 ± 1.5</td><td>4.978 ± 0.030</td><td>-46.44 ± 0.18</td></tr><tr><td colspan="6" style="text-align:center;">NRAO 530</td></tr><tr><td>86.3</td><td>2857.621 ± 0.036</td><td>7.11 ± 0.86</td><td>24.37 ± 0.86</td><td>0.889 ± 0.030</td><td>36.8 ± 1.0</td></tr><tr><td>88.3</td><td>2826.545 ± 0.035</td><td>6.60 ± 0.85</td><td>24.53 ± 0.85</td><td>0.899 ± 0.030</td><td>37.4 ± 1.0</td></tr><tr><td>98.3</td><td>2649.116 ± 0.034</td><td>4.24 ± 0.80</td><td>24.59 ± 0.80</td><td>0.943 ± 0.030</td><td>40.08 ± 0.92</td></tr><tr><td>100.3</td><td>2618.629 ± 0.035</td><td>3.71 ± 0.79</td><td>24.62 ± 0.79</td><td>0.952 ± 0.030</td><td>40.73 ± 0.92</td></tr><tr><td colspan="6" style="text-align:center;">4C 09.57</td></tr><tr><td>86.3</td><td>2920.272 ± 0.085</td><td>65.23 ± 0.88</td><td>-98.94 ± 0.88</td><td>4.057 ± 0.030</td><td>-28.30 ± 0.21</td></tr><tr><td>88.3</td><td>2898.304 ± 0.073</td><td>65.59 ± 0.87</td><td>-96.53 ± 0.88</td><td>4.028 ± 0.030</td><td>-27.91 ± 0.22</td></tr><tr><td>98.3</td><td>2805.452 ± 0.071</td><td>61.49 ± 0.84</td><td>-96.65 ± 0.85</td><td>4.084 ± 0.030</td><td>-28.76 ± 0.21</td></tr><tr><td>100.3</td><td>2775.60 ± 0.48</td><td>60.67 ± 0.84</td><td>-96.55 ± 0.84</td><td>4.107 ± 0.030</td><td>-28.93 ± 0.22</td></tr><tr><td colspan="6" style="text-align:center;">Apr 4<br>3C 279</td></tr><tr><td>86.3</td><td>13309.65 ± 0.19</td><td>70.9 ± 4.0</td><td>1612.7 ± 4.0</td><td>12.129 ± 0.030</td><td>43.746 ± 0.071</td></tr><tr><td>88.3</td><td>13168.27 ± 0.19</td><td>67.6 ± 4.0</td><td>1596.6 ± 4.0</td><td>12.136 ± 0.030</td><td>43.791 ± 0.069</td></tr><tr><td>98.3</td><td>12671.78 ± 0.19</td><td>52.6 ± 3.8</td><td>1541.8 ± 3.8</td><td>12.175 ± 0.030</td><td>44.021 ± 0.070</td></tr><tr><td>100.3</td><td>12575.88 ± 0.19</td><td>49.9 ± 3.8</td><td>1533.0 ± 3.8</td><td>12.198 ± 0.030</td><td>44.067 ± 0.069</td></tr><tr><td colspan="6" style="text-align:center;">3C 273</td></tr><tr><td>86.3</td><td>10066.53 ± 0.38</td><td>-13.8 ± 3.0</td><td>-419.4 ± 3.0</td><td>4.167 ± 0.030</td><td>-45.95 ± 0.20</td></tr><tr><td>88.3</td><td>10013.63 ± 0.36</td><td>-12.3 ± 3.0</td><td>-405.9 ± 3.0</td><td>4.054 ± 0.030</td><td>-45.87 ± 0.21</td></tr><tr><td>98.3</td><td>9698.37 ± 0.31</td><td>-3.3 ± 2.9</td><td>-370.9 ± 2.9</td><td>3.826 ± 0.030</td><td>-45.25 ± 0.23</td></tr><tr><td>100.3</td><td>9645.14 ± 0.31</td><td>3.4 ± 2.9</td><td>-375.2 ± 2.9</td><td>3.891 ± 0.030</td><td>-44.74 ± 0.23</td></tr></tbody></table>

recommended by the ALMA observatory. The LP uncertainty is dominated by such systematic error, except for the weakest sources J0132–1654 and NGC 1052, for which the thermal noise starts to dominate.

In order to correct for the LP bias in the low-S/N regime, we estimate a *debias*ed LP as $\sqrt{LP^2 - \sigma_{LP}^2}$, where LP = $\sqrt{Q^2 + U^2}/I$.

$\sigma_{LP}$ can be estimated using propagation of errors:

$$ \sigma_{LP}^2 I^2 = \frac{(Q\sigma_Q)^2 + (U\sigma_U)^2 + 2QU\sigma_{QU}}{Q^2 + U^2} + \left[ \left(\frac{Q}{I}\right)^2 + \left(\frac{U}{I}\right)^2 \right] \sigma_I^2 - 2\frac{Q}{I}\sigma_{QI} - 2\frac{U}{I}\sigma_{UI} $$