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The Event Horizon Telescope Collaboration, Recent developments in compact object astrophysics, especially the discovery of merging neutron stars by LIGO, the imaging of the black hole in M87 by the Event Horizon Telescope, and high- precision astrometry of the Galactic Center at close to the event horizon scale by the GRAVITY experiment motivate the development of numerical source models that solve the equations of general relativistic magnetohydrodynamics (GRMHD). Here we compare GRMHD solutions for the evolution of a magnetized accretion flow where turbulence is promoted by the magnetorotational instability from a set of nine GRMHD codes: Athena++, BHAC, Cosmos++, ECHO, H-AMR, iharm3D, HARM-Noble, IllinoisGRMHD, and KORAL. Agreement among the codes improves as resolution increases, as measured by a consistently applied, specially developed set of code performance metrics. We conclude that the community of GRMHD codes is mature, capable, and consistent on these test problems. © 2019. The American Astronomical Society. All rights reserved., R.N. thanks the National Science Foundation (NSF; grants OISE-1743747, AST-1816420) and acknowledges computational support from the NSF via XSEDE resources (grant TG-AST080026N). L.D.Z. acknowledges support from the PRIN-MIUR project Multi-scale Simulations of High-Energy Astrophysical Plasmas (Prot. 2015L5EE2Y) and from the INFN-TEONGRAV initiative. C.J.W. made use of thComision Nacional de Investigacion Cientifica y Tecnologica (CONICYT, ChileComision Nacional de Investigacion Cientifica y Tecnologica (CONICYT, Chilee Extreme Science and Engineering Discovery Environment (XSEDE) Comet at the San Diego Supercomputer Center through allocation AST170012. The H-AMR high-resolution simulation was made possible by NSF PRAC award Nos. 1615281 and OAC-1811605 at the Blue Waters sustained-petascale computing project and supported in part under grant No. NSF PHY-1125915 (PI A. Tchekhovskoy). K.C. and S.M. are supported by the Netherlands Organization for Scientific Research (NWO) VICI grant (No. 639.043.513); M.L. is supported by the NWO Spinoza Prize (PI M.B.M. van der Klis). The HARM-Noble simulations were made possible by NSF PRAC award No. NSF OAC-1515969, OAC-1811228 at the Blue Waters sustained-petascale computing project, and supported in part under grant No. NSF PHY-1125915. The BHAC CKS-GRMHD simulations were performed on the Dutch National Supercomputing cluster Cartesius and are funded by the NWO computing grant 16431. S.C.N. was supported by an appointment to the NASA Postdoctoral Program at the Goddard Space Flight Center administered by USRA through a contract with NASA. Y.M., H.O., O.P., and L.R. acknowledge support from the ERC synergy grant >BlackHoleCam: Imaging the Event Horizon of Black Holes> (grant No. 610058). M.B. acknowledges support from the European Research Council (grant No. 715368-MagBURST) and from the Gauss Centre for Supercomputing e.V. (www.Gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (www.lrz.de).P.C.F.was supported by NSF grant AST-1616185 and used resources from the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF grant No. ACI-1548562. Work by P.A. was performed in part under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. The authors of the present paper further thank the following organizations and programs: the Academy of Finland (projects 274477, 284495, 312496); 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; the Black Hole Initiative at Harvard University, through a grant (60477) from the John Templeton Foundation; the China Scholarship Council; Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT, Chile, via PIA ACT172033, Fondecyt 1171506, BASAL AFB-170002, ALMA-conicyt 31140007); Consejo Nacional de Ciencia y Tecnologia (CONACYT, Mexico, projects 104497, 275201, 279006, 281692); the Delaney Family via the Delaney Family John A. Wheeler Chair at Perimeter Institute; Direccion General de Asuntos del Personal Academico-Universidad Nacional Autonoma de Mexico (DGAPA-UNAM, project IN112417); the European Research Council Synergy Grant >BlackHoleCam: Imaging the Event Horizon of Black Holes> (grant 610058); the Generalitat Valenciana postdoctoral grant APOSTD/2018/177; 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); 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, QYZDJ-SSW-SYS008); 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 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); the National Aeronautics and Space Administration (NASA, Fermi Guest Investigator grant 80NSSC17K0649); 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-1312651, AST-1337663, AST-1440254, AST-1555365, AST-1715061, AST-1615796, AST-1716327, OISE-1743747, AST-1816420); the Natural Science Foundation of China (grants 11573051, 11633006, 11650110427, 10625314, 11721303, 11725312); 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); the Netherlands Organization for Scientific Research (NWO) VICI award (grant 639.043. 513) and Spinoza 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 Russian Science Foundation (grant 17-12-01029); the Spanish Ministerio de Economia y Competitividad (grants AYA2015-63939-C2-1-P, AYA2016-80889-P); the State Agency for Research of the Spanish MCIU through the >Center of Excellence Severo Ochoa> award for the Instituto de Astrofisica de Andalucia (SEV-2017-0709); the Toray Science Foundation; 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 Universita e Ricerca through the grant Progetti Premiali 2012-iALMA (CUP C52I13000140001); the European Union's Horizon 2020 research and innovation programme under grant agreement No. 730562 RadioNet; ALMA North America Development Fund; the Academia Sinica; and Chandra TM6-17006X. 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), Calcul Quebec (http://www.calculquebec.ca), and Compute Canada (http://www.computecanada.ca).

Full list of authors: Issaoun, Sara; Wielgus, Maciek; Jorstad, Svetlana; Krichbaum, Thomas P.; Blackburn, Lindy; Janssen, Michael; Chan, Chi-kwan; Pesce, Dominic W.; Gomez, Jose L.; Akiyama, Kazunori; Moscibrodzka, Monika; Marti-Vidal, Ivan; Chael, Andrew; Lico, Rocco; Liu, Jun; Ramakrishnan, Venkatessh; Lisakov, Mikhail; Fuentes, Antonio; Zhao, Guang-Yao; Moriyama, Kotaro; Broderick, Avery E.; Tiede, Paul; MacDonald, Nicholas R.; Mizuno, Yosuke; Traianou, Efthalia; Loinard, Laurent; Davelaar, Jordy; Gurwell, Mark; Lu, Ru-Sen; Alberdi, Antxon; Alef, Walter; Algaba, Juan Carlos; Anantua, Richard; Asada, Keiichi; Azulay, Rebecca; Bach, Uwe; Baczko, Anne-Kathrin; Ball, David; Balokovic, Mislac; Barrett, John; Baubock, Michi; Benson, Bradford A.; Bintley, Dan; Blundell, Raymond; Boland, Wilfred; Bouman, Katherine L.; Bower, Geoffrey C.; Boyce, Hope; Bremer, Michael; Brinkerink, Christiaan D.; Brissenden, Roger; Britzen, Silke; Broguiere, Dominique; Bronzwaer, Thomas; Bustamante, Sandra; Byun, Do-Young; Carlstrom, John E.; Ceccobello, Chiara; Chatterjee, Koushik; Chatterjee, Shami; Chen, Ming-Tang; Chen, Yongjun; Cho, Ilje; Christian, Pierre; Conroy, Nicholas S.; Conway, John E.; Cordes, James M.; Crawford, Thomas M.; Crew, Geoffrey B.; Cruz-Osorio, Alejandro; Cui, Yuzhu; De Laurentis, Mariafelicia; Deane, Roger; Dempsey, Jessica; Desvignes, Gregory; Dexter, Jason; Doeleman, Sheperd S.; Dhruv, Vedant; Quijano, Sergio Abraham Dzib; Eatough, Ralph P.; Emami, Razieh; Falcke, Heino; Farah, Joseph; Fish, Vincent L.; Fomalont, Ed; Ford, H. Alyson; Fraga-Encinas, Raquel; Freeman, William T.; Friberg, Per; Fromm, Christian M.; Galison, Peter; Gammie, Charles F.; Garcia, Roberto; Gentaz, Olivier; Georgiev, Boris; Goddi, Ciriaco; Gold, Roman; Gomez-Ruiz, Arturo, I; Gu, Minfeng; Hada, Kazuhiro; Haggard, Daryl; Hecht, Michael H.; Hesper, Ronald; Ho, Luis C.; Ho, Paul; Honma, Mareki; Huang, Chih-Wei L.; Huang, Lei; Hughes, David H.; Ikeda, Shiro; Impellizzeri, C. M. Violette; Inoue, Makoto; James, David J.; Jannuzi, Buell T.; Jeter, Britton; Jiang, Wu; Jimenez-Rosales, Alejandra; Johnson, Michael D.; Joshi, Abhishek, V; Jung, Taehyun; Karami, Mansour; Karuppusamy, Ramesh; Kawashima, Tomohisa; Keating, Garrett K.; Kettenis, Mark; Kim, Dong-Jin; Kim, Jae-Young; Kim, Jongsoo; Kim, Junhan; Kino, Motoki; Koay, Jun Yi; Kocherlakota, Prashant; Kofuji, Yutaro; Koch, Patrick M.; Koyama, Shoko; Kramer, Carsten; Kramer, Michael; Kuo, Cheng-Yu; La Bella, Noemi; Lauer, Tod R.; Lee, Daeyoung; Lee, Sang-Sung; Leung, Po Kin; Levis, Aviad; Li, Zhiyuan; Lindahl, Greg; Lindqvist, Michael; Liu, Kuo; Liuzzo, Elisabetta; Lo, Wen-Ping; Lobanov, Andrei P.; Lonsdale, Colin; Mao, Jirong; Marchili, Nicola; Markoff, Sera; Marrone, Daniel P.; Marscher, Alan P.; Matsushita, Satoki; Matthews, Lynn D.; Medeiros, Lia; Menten, Karl M.; Michalik, Daniel; Mizuno, Izumi; Mizuno, Yosuke; Moran, James M.; Mueller, Cornelia; Mus, Alejandro; Musoke, Gibwa; Myserlis, Ioannis; Nadolski, Andrew; Nagai, Hiroshi; Nagar, Neil M.; Nakamura, Masanori; Narayan, Ramesh; Narayanan, Gopal; Natarajan, Iniyan; Nathanail, Antonios; Neilsen, Joey; Neri, Roberto; Ni, Chunchong; Noutsos, Aristeidis; Nowak, Michael A.; Oh, Junghwan; Okino, Hiroki; Olivares, Hector; Ortiz-Leon, Gisela N.; Oyama, Tomoaki; Ozel, Feryal; Palumbo, Daniel C. M.; Paraschos, Georgios Filippos; Park, Jongho; Parsons, Harriet; Patel, Nimesh; Pen, Ue-Li; Pietu, Vincent; Plambeck, Richard; PopStefanija, Aleksandar; Porth, Oliver; Potzl, Felix M.; Prather, Ben; Preciado-Lopez, Jorge A.; Psaltis, Dimitrios; Pu, Hung-Yi; Rao, Ramprasad; Rawlings, Mark G.; Raymond, Alexander W.; Rezzolla, Luciano; Ricarte, Angelo; Ripperda, Bart; Roelofs, Freek; Rogers, Alan; Ros, Eduardo; Romero-Canizales, Cristina; Roshanineshat, Arash; Rottmann, Helge; Roy, Alan L.; Ruiz, Ignacio; Ruszczyk, Chet; Rygl, Kazi L. J.; Sanchez, Salvador; Sanchez-Arguelles, David; Sanchez-Portal, Miguel; Sasada, Mahito; Satapathy, Kaushik; Savolainen, Tuomas; Schloerb, F. Peter; Schuster, Karl-Friedrich; Shao, Lijing; Shen, Zhiqiang; Small, Des; Sohn, Bong Won; SooHoo, Jason; Souccar, Kamal; Sun, He; Tazaki, Fumie; Tetarenko, Alexandra J.; Tilanus, Remo P. J.; Titus, Michael; Torne, Pablo; Trent, Tyler; Trippe, Sascha; van Bemmel, Ilse; van Langevelde, Huib Jan; van Rossum, Daniel R.; Vos, Jesse; Wagner, Jan; Ward-Thompson, Derek; Wardle, John; Weintroub, Jonathan; Wex, Norbert; Wharton, Robert; Wiik, Kaj; Witzel, Gunther; Wondrak, Michael; Wong, George N.; Wu, Qingwen; Yamaguchi, Paul; Yoon, Doosoo; Young, Andre; Young, Ken; Younsi, Ziri; Yuan, Feng; Yuan, Ye-Fei; Zensus, J. Anton; Zhang, Shuo; Zhao, Shan-Shan.-- This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited., The blazar J1924–2914 is a primary Event Horizon Telescope (EHT) calibrator for the Galactic center's black hole Sagittarius A*. Here we present the first total and linearly polarized intensity images of this source obtained with the unprecedented 20 μas resolution of the EHT. J1924–2914 is a very compact flat-spectrum radio source with strong optical variability and polarization. In April 2017 the source was observed quasi-simultaneously with the EHT (April 5–11), the Global Millimeter VLBI Array (April 3), and the Very Long Baseline Array (April 28), giving a novel view of the source at four observing frequencies, 230, 86, 8.7, and 2.3 GHz. These observations probe jet properties from the subparsec to 100 pc scales. We combine the multifrequency images of J1924–2914 to study the source morphology. We find that the jet exhibits a characteristic bending, with a gradual clockwise rotation of the jet projected position angle of about 90° between 2.3 and 230 GHz. Linearly polarized intensity images of J1924–2914 with the extremely fine resolution of the EHT provide evidence for ordered toroidal magnetic fields in the blazar compact core. © 2022. The Author(s). Published by the American Astronomical Society., The Event Horizon Telescope Collaboration thanks the following organizations and programs: the Academy of Finland (projects 274477, 284495, 312496, 315721); the Agencia Nacional de Investigación y Desarrollo (ANID), Chile via NCN19_058 (TITANs) and Fondecyt 3190878, 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; 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 (grant GBMF-3561); 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; 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, 107-2119-M-110-005, 108-2112-M-001-048, and 109-2124-M-001-005); the National Aeronautics and Space Administration (NASA, Fermi Guest Investigator grant 80NSSC20K1567, NASA Astrophysics Theory Program grant 80NSSC20K0527, NASA NuSTAR award 80NSSC20K0645); 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-1555365,AST-1615796, AST-1715061, AST-1716327, AST-1903847,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 Spinoza 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 European Union's Horizon 2020 research and innovation program under grant agreement No 730562 RadioNet; ALMA North America Development Fund; the Academia Sinica; Chandra DD7-18089X and TM6-17006X; the GenT Program (Generalitat Valenciana) Project CIDEGENT/2018/021. 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), Calcul Quebec (http://www.calculquebec.ca) and Compute Canada (http://www.computecanada.ca).

Full list of authors: Goddi, Ciriaco; Martí-Vidal, Iván; Messias, Hugo; Bower, Geoffrey C.; Broderick, Avery E.; Dexter, Jason; Marrone, Daniel P.; Moscibrodzka, Monika; Nagai, Hiroshi; Algaba, Juan Carlos; Asada, Keiichi; Crew, Geoffrey B.; Gómez, José L.; Impellizzeri, C. M. Violette; Janssen, Michael; Kadler, Matthias; Krichbaum, Thomas P.; Lico, Rocco; Matthews, Lynn D.; Nathanail, Antonios Ricarte, Angelo; Ros, Eduardo; Younsi, Ziri; Akiyama, Kazunori; Alberdi, Antxon; Alef, Walter; Anantua, Richard; Azulay, Rebecca; Baczko, Anne-Kathrin; Ball, David; Baloković, Mislav; Barrett, John; Benson, Bradford A.; Bintley, Dan; Blackburn, Lindy; Blundell, Raymond; Boland, Wilfred; Bouman, Katherine L.; Boyce, Hope; Bremer, Michael; Brinkerink, Christiaan D.; Brissenden, Roger; Britzen, Silke; Broguiere, Dominique; Bronzwaer, Thomas; Byun, Do-Young; Carlstrom, John E.; Chael, Andrew; Chan, Chi-kwan; Chatterjee, Shami; Chatterjee, Koushik; Chen, Ming-Tang; Chen, Yongjun; Chesler, Paul M.; Cho, Ilje; Christian, Pierre; Conway, John E.; Cordes, James M.; Crawford, Thomas M.; Cruz-Osorio, Alejandro; Cui, Yuzhu; Davelaar, Jordy; De Laurentis, Mariafelicia; Deane, Roger; Dempsey, Jessica; Desvignes, Gregory; Doeleman, Sheperd S.; Eatough, Ralph P.; Falcke, Heino; Farah, Joseph; Fish, Vincent L.; Fomalont, Ed; Ford, H. Alyson; Fraga-Encinas, Raquel; Freeman, William T.; Friberg, Per; Fromm, Christian M.; Fuentes, Antonio; Galison, Peter; Gammie, Charles F.; García, Roberto; Gentaz, Olivier; Georgiev, Boris; Gold, Roman; Gómez-Ruiz, Arturo I.; Gu, Minfeng; Gurwell, Mark; Hada, Kazuhiro; Haggard, Daryl; Hecht, Michael H.; Hesper, Ronald; Ho, Luis C.; Ho, Paul; Honma, Mareki; Huang, Chih-Wei L.; Huang, Lei; Hughes, David H.; Inoue, Makoto; Issaoun, Sara; James, David J.; Jannuzi, Buell T.; Jeter, Britton; Jiang, Wu; Jimenez-Rosales, Alejandra; Johnson, Michael D.; Jorstad, Svetlana; Jung, Taehyun; Karami, Mansour; Karuppusamy, Ramesh; Kawashima, Tomohisa; Keating, Garrett K.; Kettenis, Mark; Kim, Dong-Jin; Kim, Jae-Young; Kim, Jongsoo; Kim, Junhan; Kino, Motoki; Koay, Jun Yi; Kofuji, Yutaro; Koch, Patrick M.; Koyama, Shoko; Kramer, Michael; Kramer, Carsten; Kuo, Cheng-Yu; Lauer, Tod R.; Lee, Sang-Sung; Levis, Aviad; Li, Yan-Rong; Li, Zhiyuan; Lindqvist, Michael; Lindahl, Greg; Liu, Jun; Liu, Kuo; Liuzzo, Elisabetta; Lo, Wen-Ping; Lobanov, Andrei P.; Loinard, Laurent; Lonsdale, Colin; Lu, Ru-Sen; MacDonald, Nicholas R.; Mao, Jirong; Marchili, Nicola; Markoff, Sera; Marscher, Alan P.; Matsushita, Satoki; Medeiros, Lia; Menten, Karl M.; Mizuno, Izumi; Mizuno, Yosuke; Moran, James M.; Moriyama, Kotaro; Müller, Cornelia; Musoke, Gibwa; Mejías, Alejandro Mus; Nagar, Neil M.; Nakamura, Masanori; Narayan, Ramesh; Narayanan, Gopal; Natarajan, Iniyan; Neilsen, Joey; Neri, Roberto; Ni, Chunchong; Noutsos, Aristeidis; Nowak, Michael A.; Okino, Hiroki; Olivares, Héctor; Ortiz-León, Gisela N.; Oyama, Tomoaki; Özel, Feryal; Palumbo, Daniel C. M.; Park, Jongho; Patel, Nimesh; Pen, Ue-Li; Pesce, Dominic W.; Piétu, Vincent; Plambeck, Richard; PopStefanija, Aleksandar; Porth, Oliver; Pötzl, Felix M.; Prather, Ben; Preciado-López, Jorge A.; Psaltis, Dimitrios; Pu, Hung-Yi; Ramakrishnan, Venkatessh; Rao, Ramprasad; Rawlings, Mark G.; Raymond, Alexander W.; Rezzolla, Luciano; Ripperda, Bart; Roelofs, Freek; Rogers, Alan; Rose, Mel; Roshanineshat, Arash; Rottmann, Helge; Roy, Alan L.; Ruszczyk, Chet; Rygl, Kazi L. J.; Sánchez, Salvador; Sánchez-Arguelles, David; Sasada, Mahito; Savolainen, Tuomas; Schloerb, F. Peter; Schuster, Karl-Friedrich; Shao, Lijing; Shen, Zhiqiang; Small, Des; Sohn, Bong Won; SooHoo, Jason; Sun, He; Tazaki, Fumie; Tetarenko, Alexandra J.; Tiede, Paul; Tilanus, Remo P. J.; Titus, Michael; Toma, Kenji; Torne, Pablo; Trent, Tyler; Traianou, Efthalia; Trippe, Sascha; van Bemmel, Ilse; van Langevelde, Huib Jan; van Rossum, Daniel R.; Wagner, Jan; Ward-Thompson, Derek; Wardle, John; Weintroub, Jonathan; Wex, Norbert; Wharton, Robert; Wielgus, Maciek; Wong, George N.; Wu, Qingwen; Yoon, Doosoo; Young, André; Young, Ken; Yuan, Feng; Yuan, Ye-Fei; Zensus, J. Anton; Zhao, Guang-Yao; Zhao, Shan-Shan; Bruni, Gabriele; Gopakumar, A.; Hernández-Gómez, Antonio; Herrero-Illana, Ruben; Ingram, Adam; Komossa, S.; Kovalev, Y. Y.; Muders, Dirk; Perucho, Manel; Rösch, Florian; Valtonen, Mauri.-- This is an open access article, original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI., 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 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. © 2021. The American Astronomical Society., ALMA is a partnership of the European Southern Observatory (ESO; Europe, representing its member states), NSF, andNational 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 Investigacion y Desarrollo (ANID), Chile via NCN19_058 (TITANs) and Fondecyt 3190878; Consejo Nacional de Ciencia y Tecnologia (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; Direccion General de Asuntos del Personal AcademicoUniversidad Nacional Autonoma de Mexico (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-SSWSLH057, QYZDJSSW-SYS008, ZDBS-LY-SLH011); the Leverhulme Trust Early Career Research Fellowship; the MaxPlanck-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-001020, 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-HF251431.001-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, 2015R1D1A1A01056807, 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 Spinoza 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 Economia y Competitividad (grants PGC2018098915-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 Astrofisica de Andalucia (SEV-2017-0709); the Toray Science Foundation; the Consejeria de Economia, Conocimiento, Empresas y Universidad of the Junta de Andalucia (grant P18-FR-1769), the Consejo Superior de Investigaciones Cientificas (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 Universita e Ricerca through the grant Progetti Premiali 2012-iALMA (CUP C52I13000140001); 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), Calcul 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 fur 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 Astrofisica, Optica, y Electronica (Mexico) and the University of Massachusetts at Amherst (USA). The IRAM 30m 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 Geografico 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 Electronics 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 Valenciana through grant PROMETEU/2019/071.

Full list of authors: Narayan, Ramesh; Palumbo, Daniel C. M.; Johnson, Michael D.; Gelles, Zachary; Himwich, Elizabeth; Chang, Dominic O.; Ricarte, Angelo; Dexter, Jason; Gammie, Charles F.; Chael, Andrew A.; Event Horizon Telescope Collaboration; Akiyama, Kazunori; Alberdi, Antxon; Alef, Walter; Algaba, Juan Carlos; Anantua, Richard; Asada, Keiichi; Azulay, Rebecca; Baczko, Anne-Kathrin; Ball, David Baloković, Mislav; Barrett, John; Benson, Bradford A.; Bintley, Dan; Blackburn, Lindy; Blundell, Raymond; Boland, Wilfred; Bouman, Katherine L.; Bower, Geoffrey C.; Boyce, Hope; Bremer, Michael; Brinkerink, Christiaan D.; Brissenden, Roger; Britzen, Silke; Broderick, Avery E.; Broguiere, Dominique; Bronzwaer, Thomas; Byun, Do-Young; Carlstrom, John E.; Chan, Chi-kwan; Chatterjee, Shami; Chatterjee, Koushik; Chen, Ming-Tang; Chen, Yongjun; Chesler, Paul M.; Cho, Ilje; Christian, Pierre; Conway, John E.; Cordes, James M.; Crawford, Thomas M.; Crew, Geoffrey B.; Cruz-Osorio, Alejandro; Cui, Yuzhu; Davelaar, Jordy; De Laurentis, Mariafelicia; Deane, Roger; Dempsey, Jessica; Desvignes, Gregory; Doeleman, Sheperd S.; Eatough, Ralph P.; Falcke, Heino; Farah, Joseph; Fish, Vincent L.; Fomalont, Ed; Ford, H. Alyson; Fraga-Encinas, Raquel; Friberg, Per; Fromm, Christian M.; Fuentes, Antonio; Galison, Peter; García, Roberto; Gentaz, Olivier; Georgiev, Boris; Goddi, Ciriaco; Gold, Roman; Gómez, José L.; Gómez-Ruiz, Arturo I.; Gu, Minfeng; Gurwell, Mark; Hada, Kazuhiro; Haggard, Daryl; Hecht, Michael H.; Hesper, Ronald; Ho, Luis C.; Ho, Paul; Honma, Mareki; Huang, Chih-Wei L.; Huang, Lei; Hughes, David H.; Ikeda, Shiro; Inoue, Makoto; Issaoun, Sara; James, David J.; Jannuzi, Buell T.; Janssen, Michael; Jeter, Britton; Jiang, Wu; Jimenez-Rosales, Alejandra; Jorstad, Svetlana; Jung, Taehyun; Karami, Mansour; Karuppusamy, Ramesh; Kawashima, Tomohisa; Keating, Garrett K.; Kettenis, Mark; Kim, Dong-Jin; Kim, Jae-Young; Kim, Jongsoo; Kim, Junhan; Kino, Motoki; Koay, Jun Yi; Kofuji, Yutaro; Koch, Patrick M.; Koyama, Shoko; Kramer, Michael; Kramer, Carsten; Krichbaum, Thomas P.; Kuo, Cheng-Yu; Lauer, Tod R.; Lee, Sang-Sung; Levis, Aviad; Li, Yan-Rong; Li, Zhiyuan; Lindqvist, Michael; Lico, Rocco; Lindahl, Greg; Liu, Jun; Liu, Kuo; Liuzzo, Elisabetta; Lo, Wen-Ping; Lobanov, Andrei P.; Loinard, Laurent; Lonsdale, Colin; Lu, Ru-Sen; MacDonald, Nicholas R.; Mao, Jirong; Marchili, Nicola; Markoff, Sera; Marrone, Daniel P.; Marscher, Alan P.; Martí-Vidal, Iván; Matsushita, Satoki; Matthews, Lynn D.; Medeiros, Lia; Menten, Karl M.; Mizuno, Izumi; Mizuno, Yosuke; Moran, James M.; Moriyama, Kotaro; Moscibrodzka, Monika; Müller, Cornelia; Musoke, Gibwa; Mejías, Alejandro Mus; Nagai, Hiroshi; Nagar, Neil M.; Nakamura, Masanori; Narayanan, Gopal; Natarajan, Iniyan; Nathanail, Antonios; Neilsen, Joey; Neri, Roberto; Ni, Chunchong; Noutsos, Aristeidis; Nowak, Michael A.; Okino, Hiroki; Olivares, Héctor; Ortiz-León, Gisela N.; Oyama, Tomoaki; Özel, Feryal; Park, Jongho; Patel, Nimesh; Pen, Ue-Li; Pesce, Dominic W.; Piétu, Vincent; Plambeck, Richard; PopStefanija, Aleksandar; Porth, Oliver; Pötzl, Felix M.; Prather, Ben; Preciado-López, Jorge A.; Psaltis, Dimitrios; Pu, Hung-Yi; Ramakrishnan, Venkatessh; Rao, Ramprasad; Rawlings, Mark G.; Raymond, Alexander W.; Rezzolla, Luciano; Ripperda, Bart; Roelofs, Freek; Rogers, Alan; Ros, Eduardo; Rose, Mel; Roshanineshat, Arash; Rottmann, Helge; Roy, Alan L.; Ruszczyk, Chet; Rygl, Kazi L. J.; Sánchez, Salvador; Sánchez-Arguelles, David; Sasada, Mahito; Savolainen, Tuomas; Schloerb, F. Peter; Schuster, Karl-Friedrich; Shao, Lijing; Shen, Zhiqiang; Small, Des; Sohn, Bong Won; SooHoo, Jason; Sun, He; Tazaki, Fumie; Tetarenko, Alexandra J.; Tiede, Paul; Tilanus, Remo P. J.; Titus, Michael; Toma, Kenji; Torne, Pablo; Trent, Tyler; Traianou, Efthalia; Trippe, Sascha; van Bemmel, Ilse; van Langevelde, Huib Jan; van Rossum, Daniel R.; Wagner, Jan; Ward-Thompson, Derek; Wardle, John; Weintroub, Jonathan; Wex, Norbert; Wharton, Robert; Wielgus, Maciek; Wong, George N.; Wu, Qingwen; Yoon, Doosoo; Young, André; Young, Ken; Younsi, Ziri; Yuan, Feng; Yuan, Ye-Fei; Zensus, J. Anton; Zhao, Guang-Yao; Zhao, Shan-Shan.--This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI., Synchrotron radiation from hot gas near a black hole results in a polarized image. The image polarization is determined by effects including the orientation of the magnetic field in the emitting region, relativistic motion of the gas, strong gravitational lensing by the black hole, and parallel transport in the curved spacetime. We explore these effects using a simple model of an axisymmetric, equatorial accretion disk around a Schwarzschild black hole. By using an approximate expression for the null geodesics derived by Beloborodov and conservation of the Walker–Penrose constant, we provide analytic estimates for the image polarization. We test this model using currently favored general relativistic magnetohydrodynamic simulations of M87*, using ring parameters given by the simulations. For a subset of these with modest Faraday effects, we show that the ring model broadly reproduces the polarimetric image morphology. Our model also predicts the polarization evolution for compact flaring regions, such as those observed from Sgr A* with GRAVITY. With suitably chosen parameters, our simple model can reproduce the EVPA pattern and relative polarized intensity in Event Horizon Telescope images of M87*. Under the physically motivated assumption that the magnetic field trails the fluid velocity, this comparison is consistent with the clockwise rotation inferred from total intensity images. © 2021 The Author(s). Published by the American Astronomical Society., We thank the National Science Foundation (awards OISE1743747, AST-1816420, AST-1716536, AST-1440254, AST1935980) and the Gordon and Betty Moore Foundation (GBMF-5278) for financial support of this work. This work was supported in part by the black hole Initiative, which is funded by grants from the John Templeton Foundation and the Gordon and Betty Moore Foundation to Harvard University. Support for this work was also provided by the NASA 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 Event Horizon Telescope Collaboration thanks the following organizations and programs: the Academy of Finland (projects 274477, 284495, 312496, 315721); the Agencia Nacional de Investigacion y Desarrollo (ANID), Chile via NCN19_058 (TITANs) and Fondecyt 3190878, 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; Consejo Nacional de Ciencia y Tecnologia (CONACYT, Mexico, projects U0004-246083, U0004-259839, F0003-272050, M0037279006, F0003-281692, 104497, 275201, 263356); the Delaney Family via the Delaney Family John A. Wheeler Chair at Perimeter Institute; Direccion General de Asuntos del Personal Academico-Universidad Nacional Autonoma de Mexico (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 (grant GBMF-3561; 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; 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 and JP19H01943); the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (CAS, grants QYZDJ-SSW-SLH057, QYZDJSSW-SYS008, ZDBS-LYSLH011); 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-001017, 107-2119-M-001-020,107-2119-M-110-005, 108-2112-M001-048, and 109-2124-M-001-005); the National Aeronautics and SpaceAdministration (NASA grant NNX17AL82G, Fermi Guest Investigator grant 80NSSC20K1567, NASA Astrophysics Theory Program grant 80NSSC20K0527, NASA NuSTAR award 80NSSC20K0645); 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-1555365, AST-1615796, AST-1715061, AST-1716327, AST-1903847, 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 Research Foundation of Korea (the Global PhD Fellowship Grant: grants NRF-2015H1A2A1033752, 2015R1D1A1A01056807, 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 Spinoza 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 Innovation (DSI) of South Africa; the South African Research Chairs Initiative of the Department of Science and Innovation and National Research Foundation; 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 201700648) 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 Economia 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 Astrofisica de Andalucia (SEV-2017-0709); the Toray Science Foundation; the Consejeria de Economia, Conocimiento, Empresas y Universidad of the Junta de Andalucia (grant P18-FR-1769), the Consejo Superior de Investigaciones Cientificas (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 European Union's Horizon 2020 research and innovation program under grant agreement No. 730562 RadioNet; ALMA North America Development Fund; the Academia Sinica; Chandra DD7-18089X and TM6-17006X; the GenT Program (Generalitat Valenciana) Project CIDEGENT/2018/021. 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 TGAST170024 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), Calcul Quebec (http://www.calculquebec.ca) and Compute Canada (http://www.computecanada.ca).We thank the staff at the participating observatories, correlation centers, and institutions for their enthusiastic support. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2016.1.01154.V. 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. APEX is a collaboration between the Max-Planck-Institut fur Radioastronomie (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 Astrofisica, Optica, y Electronica (Mexico) and the University of Massachusetts at Amherst (USA), with financial support from the Consejo Nacional de Ciencia y Tecnologia and the National Science Foundation. The IRAM 30m telescope on Pico Veleta, Spain is operated by IRAM and supported by CNRS (Centre National de la Recherche Scientifique, France), MPG (MaxPlanck-Gesellschaft, Germany) and IGN (Instituto Geografico 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 Electronics 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 EHTspecific support with the use of DiFX. We acknowledge the significance that Maunakea, where the SMA and JCMT EHT stations are located, has for the indigenous Hawaiian people.

Full list of authors: Akiyama, Kazunori; Algaba, Juan Carlos; Alberdi, Antxon; Alef, Walter; Anantua, Richard; Asada, Keiichi; Azulay, Rebecca; Baczko, Anne-Kathrin; Ball, David; Baloković, Mislav; Barrett, John; Benson, Bradford A.; Bintley, Dan; Blackburn, Lindy; Blundell, Raymond; Boland, Wilfred; Bouman, Katherine L.; Bower, Geoffrey C.; Boyce, Hope Bremer, Michael; Brinkerink, Christiaan D.; Brissenden, Roger; Britzen, Silke; Broderick, Avery E.; Broguiere, Dominique; Bronzwaer, Thomas; Byun, Do-Young; Carlstrom, John E.; Chael, Andrew; Chan, Chi-kwan; Chatterjee, Shami; Chatterjee, Koushik; Chen, Ming-Tang; Chen, Yongjun; Chesler, Paul M.; Cho, Ilje; Christian, Pierre; Conway, John E.; Cordes, James M.; Crawford, Thomas M.; Crew, Geoffrey B.; Cruz-Osorio, Alejandro; Cui, Yuzhu; Davelaar, Jordy; De Laurentis, Mariafelicia; Deane, Roger; Dempsey, Jessica; Desvignes, Gregory; Dexter, Jason; Doeleman, Sheperd S.; Eatough, Ralph P.; Falcke, Heino; Farah, Joseph; Fish, Vincent L.; Fomalont, Ed; Ford, H. Alyson; Fraga-Encinas, Raquel; Freeman, William T.; Friberg, Per; Fromm, Christian M.; Fuentes, Antonio; Galison, Peter; Gammie, Charles F.; García, Roberto; Gentaz, Olivier; Georgiev, Boris; Goddi, Ciriaco; Gold, Roman; Gómez, José L.; Gómez-Ruiz, Arturo I.; Gu, Minfeng; Gurwell, Mark; Hada, Kazuhiro; Haggard, Daryl; Hecht, Michael H.; Hesper, Ronald; Ho, Luis C.; Ho, Paul; Honma, Mareki; Huang, Chih-Wei L.; Huang, Lei; Hughes, David H.; Ikeda, Shiro; Inoue, Makoto; Issaoun, Sara; James, David J.; Jannuzi, Buell T.; Janssen, Michael; Jeter, Britton; Jiang, Wu; Jimenez-Rosales, Alejandra; Johnson, Michael D.; Jorstad, Svetlana; Jung, Taehyun; Karami, Mansour; Karuppusamy, Ramesh; Kawashima, Tomohisa; Keating, Garrett K.; Kettenis, Mark; Kim, Dong-Jin; Kim, Jae-Young; Kim, Jongsoo; Kim, Junhan; Kino, Motoki; Koay, Jun Yi; Kofuji, Yutaro; Koch, Patrick M.; Koyama, Shoko; Kramer, Michael; Kramer, Carsten; Krichbaum, Thomas P.; Kuo, Cheng-Yu; Lauer, Tod R.; Lee, Sang-Sung; Levis, Aviad; Li, Yan-Rong; Li, Zhiyuan; Lindqvist, Michael; Lico, Rocco; Lindahl, Greg; Liu, Jun; Liu, Kuo; Liuzzo, Elisabetta; Lo, Wen-Ping; Lobanov, Andrei P.; Loinard, Laurent; Lonsdale, Colin; Lu, Ru-Sen; MacDonald, Nicholas R.; Mao, Jirong; Marchili, Nicola; Markoff, Sera; Marrone, Daniel P.; Marscher, Alan P.; Martí-Vidal, Iván; Matsushita, Satoki; Matthews, Lynn D.; Medeiros, Lia; Menten, Karl M.; Mizuno, Izumi; Mizuno, Yosuke; Moran, James M.; Moriyama, Kotaro; Moscibrodzka, Monika; Müller, Cornelia; Musoke, Gibwa; Mejías, Alejandro Mus; Michalik, Daniel; Nadolski, Andrew; Nagai, Hiroshi; Nagar, Neil M.; Nakamura, Masanori; Narayan, Ramesh; Narayanan, Gopal; Natarajan, Iniyan; Nathanail, Antonios; Neilsen, Joey; Neri, Roberto; Ni, Chunchong; Noutsos, Aristeidis; Nowak, Michael A.; Okino, Hiroki; Olivares, Héctor; Ortiz-León, Gisela N.; Oyama, Tomoaki; Özel, Feryal; Palumbo, Daniel C. M.; Park, Jongho; Patel, Nimesh; Pen, Ue-Li; Pesce, Dominic W.; Piétu, Vincent; Plambeck, Richard; PopStefanija, Aleksandar; Porth, Oliver; Pötzl, Felix M.; Prather, Ben; Preciado-López, Jorge A.; Psaltis, Dimitrios; Pu, Hung-Yi; Ramakrishnan, Venkatessh; Rao, Ramprasad; Rawlings, Mark G.; Raymond, Alexander W.; Rezzolla, Luciano; Ricarte, Angelo; Ripperda, Bart; Roelofs, Freek; Rogers, Alan; Ros, Eduardo; Rose, Mel; Roshanineshat, Arash; Rottmann, Helge; Roy, Alan L.; Ruszczyk, Chet; Rygl, Kazi L. J.; Sánchez, Salvador; Sánchez-Arguelles, David; Sasada, Mahito; Savolainen, Tuomas; Schloerb, F. Peter; Schuster, Karl-Friedrich; Shao, Lijing; Shen, Zhiqiang; Small, Des; Sohn, Bong Won; SooHoo, Jason; Sun, He; Tazaki, Fumie; Tetarenko, Alexandra J.; Tiede, Paul; Tilanus, Remo P. J.; Titus, Michael; Toma, Kenji; Torne, Pablo; Trent, Tyler; Traianou, Efthalia; Trippe, Sascha; van Bemmel, Ilse; van Langevelde, Huib Jan; van Rossum, Daniel R.; Wagner, Jan; Ward-Thompson, Derek; Wardle, John; Weintroub, Jonathan; Wex, Norbert; Wharton, Robert; Wielgus, Maciek; Wong, George N.; Wu, Qingwen; Yoon, Doosoo; Young, André; Young, Ken; Younsi, Ziri; Yuan, Feng; Yuan, Ye-Fei; Zensus, J. Anton; Zhao, Guang-Yao; Zhao, Shan-Shan; Event Horizon Telescope Collaboration.-- This is an open access article, original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI., In 2017 April, the Event Horizon Telescope (EHT) observed the near-horizon region around the supermassive black hole at the core of the M87 galaxy. These 1.3 mm wavelength observations revealed a compact asymmetric ring-like source morphology. This structure originates from synchrotron emission produced by relativistic plasma located in the immediate vicinity of the black hole. Here we present the corresponding linear-polarimetric EHT images of the center of M87. We find that only a part of the ring is significantly polarized. The resolved fractional linear polarization has a maximum located in the southwest part of the ring, where it rises to the level of ∼15%. The polarization position angles are arranged in a nearly azimuthal pattern. We perform quantitative measurements of relevant polarimetric properties of the compact emission and find evidence for the temporal evolution of the polarized source structure over one week of EHT observations. The details of the polarimetric data reduction and calibration methodology are provided. We carry out the data analysis using multiple independent imaging and modeling techniques, each of which is validated against a suite of synthetic data sets. The gross polarimetric structure and its apparent evolution with time are insensitive to the method used to reconstruct the image. These polarimetric images carry information about the structure of the magnetic fields responsible for the synchrotron emission. Their physical interpretation is discussed in an accompanying publication. © 2021. The Author(s). Published by the American Astronomical Society., The authors of the present Letter thank the following organizations and programs: the Academy of Finland (projects 274477, 284495, 312496, 315721); the Alexander von Humboldt Stiftung; Agencia Nacional de Investigacion y Desarrollo (ANID), Chile via NCN19_058 (TITANs), and Fondecyt 3190878; 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; Consejo Nacional de Ciencia y Tecnologia (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; Direccion General de Asuntos del Personal Academico-Universidad Nacional Autonoma de Mexico (DGAPA-UNAM, projects IN112417 and IN112820); the EACOA Fellowship of the East Asia Core Observatories Association; 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; 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-PlanckGesellschaft (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-001025-MY3, 106-2112-M-001-011, 106-2119-M-001-027, 1072119-M-001-017, 107-2119-M-001-020, 107-2119-M-110-005, 108-2112-M-001-048, and 109-2124-M-001-005); the National Aeronautics and Space Administration (NASA, Fermi Guest Investigator grant 80NSSC20K1567 and 80NSSC20K1567, NASA Astrophysics Theory Program grant 80NSSC20K0527, NASA NuSTAR award 80NSSC20K0645, NASA grant NNX17AL82G, and Hubble Fellowship grant HST-HF251431.001-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, AST0521233, AST-0705062, AST-0905844, AST-0922984, AST1126433, AST-1140030, DGE-1144085, AST-1207704, AST1207730, AST-1207752, MRI-1228509, OPP-1248097, AST1310896, AST-1337663, AST-1440254, AST-1555365, AST1615796, AST-1715061, AST-1716327, AST-1716536, OISE1743747, AST-1816420, AST-1903847, AST-1935980, AST2034306); 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 Research Foundation of Korea (the Global PhD Fellowship Grant: grants 2014H1A2A1018695, NRF2015H1A2A1033752, 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 Spinoza 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 Innovation (DSI) of South Africa; the South African Research Chairs Initiative of the Department of Science and Innovation and National Research Foundation; 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 Ciencia e Innovacion (grants PGC2018-098915-B-C21, AYA2016-80889-P; PID2019108995GB-C21, PGC2018-098915-B-C21); the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award for the Instituto de Astrofisica de Andalucia (SEV-2017-0709); the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award for the Instituto de Astrofisica de Andalucia (SEV-2017-0709); the Toray Science Foundation; the Consejeria de Economia, Conocimiento, Empresas y Universidad of the Junta de Andalucia (grant P18-FR-1769), the Consejo Superior de Investigaciones Cientificas (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 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; 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 DBI1743442. 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), Calcul Quebec (http://www.calculquebec.ca) and Compute Canada (http://www.computecanada.ca).We thank the staff at the participating observatories, correlation centers, and institutions for their enthusiastic support. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2016.1.01154.V. 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 paper has made use of the following APEX data: Project ID T-091.F-0006-2013. APEX is a collaboration between the Max-Planck-Institut fur Radioastronomie (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 Astrofisica, Optica, y Electronica (Mexico) and the University of Massachusetts at Amherst (USA), with financial support from the Consejo Nacional de Ciencia y Tecnologia and the National Science Foundation. 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 (MaxPlanck-Gesellschaft, Germany) and IGN (Instituto Geografico 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 Electronics 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 acknowledge the significance that Maunakea, where the SMA and JCMT EHT stations are located, has for the indigenous Hawaiian people.

Full list of authors: Akiyama, Kazunori; Algaba, Juan Carlos; Alberdi, Antxon; Alef, Walter; Anantua, Richard; Asada, Keiichi; Azulay, Rebecca; Baczko, Anne-Kathrin; Ball, David; Baloković, Mislav; Barrett, John; Benson, Bradford A.; Bintley, Dan; Blackburn, Lindy; Blundell, Raymond; Boland, Wilfred; Bouman, Katherine L.; Bower, Geoffrey C.; Boyce, Hope Bremer, Michael; Brinkerink, Christiaan D.; Brissenden, Roger; Britzen, Silke; Broderick, Avery E.; Broguiere, Dominique; Bronzwaer, Thomas; Byun, Do-Young; Carlstrom, John E.; Chael, Andrew; Chan, Chi-kwan; Chatterjee, Shami; Chatterjee, Koushik; Chen, Ming-Tang; Chen, Yongjun; Chesler, Paul M.; Cho, Ilje; Christian, Pierre; Conway, John E.; Cordes, James M.; Crawford, Thomas M.; Crew, Geoffrey B.; Cruz-Osorio, Alejandro; Cui, Yuzhu; Davelaar, Jordy; De Laurentis, Mariafelicia; Deane, Roger; Dempsey, Jessica; Desvignes, Gregory; Dexter, Jason; Doeleman, Sheperd S.; Eatough, Ralph P.; Falcke, Heino; Farah, Joseph; Fish, Vincent L.; Fomalont, Ed; Ford, H. Alyson; Fraga-Encinas, Raquel; Friberg, Per; Fromm, Christian M.; Fuentes, Antonio; Galison, Peter; Gammie, Charles F.; García, Roberto; Gelles, Zachary; Gentaz, Olivier; Georgiev, Boris; Goddi, Ciriaco; Gold, Roman; Gómez, José L.; Gómez-Ruiz, Arturo I.; Gu, Minfeng; Gurwell, Mark; Hada, Kazuhiro; Haggard, Daryl; Hecht, Michael H.; Hesper, Ronald; Himwich, Elizabeth; Ho, Luis C.; Ho, Paul; Honma, Mareki; Huang, Chih-Wei L.; Huang, Lei; Hughes, David H.; Ikeda, Shiro; Inoue, Makoto; Issaoun, Sara; James, David J.; Jannuzi, Buell T.; Janssen, Michael; Jeter, Britton; Jiang, Wu; Jimenez-Rosales, Alejandra; Johnson, Michael D.; Jorstad, Svetlana; Jung, Taehyun; Karami, Mansour; Karuppusamy, Ramesh; Kawashima, Tomohisa; Keating, Garrett K.; Kettenis, Mark; Kim, Dong-Jin; Kim, Jae-Young; Kim, Jongsoo; Kim, Junhan; Kino, Motoki; Koay, Jun Yi; Kofuji, Yutaro; Koch, Patrick M.; Koyama, Shoko; Kramer, Michael; Kramer, Carsten; Krichbaum, Thomas P.; Kuo, Cheng-Yu; Lauer, Tod R.; Lee, Sang-Sung; Levis, Aviad; Li, Yan-Rong; Li, Zhiyuan; Lindqvist, Michael; Lico, Rocco; Lindahl, Greg; Liu, Jun; Liu, Kuo; Liuzzo, Elisabetta; Lo, Wen-Ping; Lobanov, Andrei P.; Loinard, Laurent; Lonsdale, Colin; Lu, Ru-Sen; MacDonald, Nicholas R.; Mao, Jirong; Marchili, Nicola; Markoff, Sera; Marrone, Daniel P.; Marscher, Alan P.; Martí-Vidal, Iván; Matsushita, Satoki; Matthews, Lynn D.; Medeiros, Lia; Menten, Karl M.; Mizuno, Izumi; Mizuno, Yosuke; Moran, James M.; Moriyama, Kotaro; Moscibrodzka, Monika; Müller, Cornelia; Musoke, Gibwa; Mus Mejías, Alejandro; Michalik, Daniel; Nadolski, Andrew; Nagai, Hiroshi; Nagar, Neil M.; Nakamura, Masanori; Narayan, Ramesh; Narayanan, Gopal; Natarajan, Iniyan; Nathanail, Antonios; Neilsen, Joey; Neri, Roberto; Ni, Chunchong; Noutsos, Aristeidis; Nowak, Michael A.; Okino, Hiroki; Olivares, Héctor; Ortiz-León, Gisela N.; Oyama, Tomoaki; Özel, Feryal; Palumbo, Daniel C. M.; Park, Jongho; Patel, Nimesh; Pen, Ue-Li; Pesce, Dominic W.; Piétu, Vincent; Plambeck, Richard; PopStefanija, Aleksandar; Porth, Oliver; Pötzl, Felix M.; Prather, Ben; Preciado-López, Jorge A.; Psaltis, Dimitrios; Pu, Hung-Yi; Ramakrishnan, Venkatessh; Rao, Ramprasad; Rawlings, Mark G.; Raymond, Alexander W.; Rezzolla, Luciano; Ricarte, Angelo; Ripperda, Bart; Roelofs, Freek; Rogers, Alan; Ros, Eduardo; Rose, Mel; Roshanineshat, Arash; Rottmann, Helge; Roy, Alan L.; Ruszczyk, Chet; Rygl, Kazi L. J.; Sánchez, Salvador; Sánchez-Arguelles, David; Sasada, Mahito; Savolainen, Tuomas; Schloerb, F. Peter; Schuster, Karl-Friedrich; Shao, Lijing; Shen, Zhiqiang; Small, Des; Sohn, Bong Won; SooHoo, Jason; Sun, He; Tazaki, Fumie; Tetarenko, Alexandra J.; Tiede, Paul; Tilanus, Remo P. J.; Titus, Michael; Toma, Kenji; Torne, Pablo; Trent, Tyler; Traianou, Efthalia; Trippe, Sascha; van Bemmel, Ilse; van Langevelde, Huib Jan; van Rossum, Daniel R.; Wagner, Jan; Ward-Thompson, Derek; Wardle, John; Weintroub, Jonathan; Wex, Norbert; Wharton, Robert; Wielgus, Maciek; Wong, George N.; Wu, Qingwen; Yoon, Doosoo; Young, André; Young, Ken; Younsi, Ziri; Yuan, Feng; Yuan, Ye-Fei; Zensus, J. Anton; Zhao, Guang-Yao; Zhao, Shan-Shan; Event Horizon Telescope Collaboration.-- This is an open access article, original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI., Event Horizon Telescope (EHT) observations at 230 GHz have now imaged polarized emission around the supermassive black hole in M87 on event-horizon scales. This polarized synchrotron radiation probes the structure of magnetic fields and the plasma properties near the black hole. Here we compare the resolved polarization structure observed by the EHT, along with simultaneous unresolved observations with the Atacama Large Millimeter/submillimeter Array, to expectations from theoretical models. The low fractional linear polarization in the resolved image suggests that the polarization is scrambled on scales smaller than the EHT beam, which we attribute to Faraday rotation internal to the emission region. We estimate the average density ne ~ 104–7 cm−3, magnetic field strength B ~ 1–30 G, and electron temperature Te ~ (1–12) × 1010 K of the radiating plasma in a simple one-zone emission model. We show that the net azimuthal linear polarization pattern may result from organized, poloidal magnetic fields in the emission region. In a quantitative comparison with a large library of simulated polarimetric images from general relativistic magnetohydrodynamic (GRMHD) simulations, we identify a subset of physical models that can explain critical features of the polarimetric EHT observations while producing a relativistic jet of sufficient power. The consistent GRMHD models are all of magnetically arrested accretion disks, where near-horizon magnetic fields are dynamically important. We use the models to infer a mass accretion rate onto the black hole in M87 of (3–20) × 10−4 M⊙ yr−1. © 2021. The Author(s). Published by the American Astronomical Society., The authors of the present Letter thank the following organizations and programs: the Academy of Finland (projects 274477, 284495, 312496, 315721); Agencia Nacional de Investigacion y Desarrollo (ANID), Chile via NCN19_058 (TITANs), and Fondecyt 3190878; 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; Consejo Nacional de Ciencia y Tecnologia (CONACYT, Mexico, projects U0004-246083, U0004-259839, F0003-272050, M0037-279006, F0003-281692, 104497, 275201, 263356, 57265507); the Delaney Family via the Delaney Family John A. Wheeler Chair at Perimeter Institute; Direccion General de Asuntos del Personal Academico-Universidad Nacional Autonoma de Mexico (DGAPA-UNAM, projects IN112417 and IN112820); the EACOA Fellowship of the East Asia Core Observatories Association; 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; 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). We further thank the Leverhulme Trust Early Career Research Fellowship; the Max-Planck-Gesellschaft (MPG); theMax Planck Partner Group of the MPG and the CAS; the MEXT/JSPS KAKENHI (grants 18KK0090, JP18K13594, JP18K03656, JP18H03721, 18K03709, 18H01245, JP19H01943, 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-M001-025-MY3, 106-2112-M-001-011, 106-2119-M-001-027, 107-2119-M-001-017, 107-2119-M-001-020, 107-2119-M-110005, 108-2112-M-001-048, and 109-2124-M-001-005); the National Aeronautics and Space Administration (NASA, Fermi Guest Investigator grant 80NSSC20K1567, NASA Astrophysics Theory Program grant 80NSSC20K0527, NASA grant NNX17AL82G, Hubble Fellowship grant HST-HF2-51431.001A 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, and NASA NuSTAR award 80NSSC20K0645); 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 Research Foundation of Korea (the Global PhD Fellowship Grant: grants 2014H1A2A1018695, NRF-2015H1A2A1033752, 2015-R1D1A1A01056807, the Korea Research Fellowship Program: NRF-2015H1D3A1066 561, Basic Research Support Grant 2019R1F1A1059721); the Netherlands Organization for Scientific Research (NWO) VICI award (grant 639.043. 513) and Spinoza 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 Innovation (DSI) of South Africa; the South African Research Chairs Initiative of the Department of Science and Innovation and National Research Foundation; 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 Economia y Competitividad (grants PGC2018098915-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 Astrofisica de Andalucia (SEV-2017-0709); the Toray Science Foundation; the Consejeria de Economia, Conocimiento, Empresas y Universidad of the Junta de Andalucia (grant P18FR-1769), the Consejo Superior de Investigaciones Cientificas (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 89233218CNA000 001); 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 and DD7-18089X; the GenT Program (Generalitat Valenciana) Project CIDEGENT/2018/021. 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 TGAST170024 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), Calcul Quebec (http://www.calculquebec.ca) and Compute Canada (http://www.computecanada.ca).We thank the staff at the participating observatories, correlation centers, and institutions for their enthusiastic support. This Letter makes use of the following ALMA data: ADS/JAO. ALMA#2016.1.01154.V. 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 paper has made use of the following APEX data: Project ID T-091.F-0006-2013. APEX is a collaboration between the Max-Planck-Institut fur Radioastronomie (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 Astrofisica, Optica, y Electronica (Mexico) and the University of Massachusetts at Amherst (USA), with financial support from the Consejo Nacional de Ciencia y Tecnologia and the National Science Foundation. The IRAM30-mtelescope 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 Geografico 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 Electronics 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 acknowledge the significance that Maunakea, where the SMA and JCMT EHT stations are located, has for the indigenous Hawaiian people.