The Polarized Image of a Synchrotron-emitting Ring of Gas Orbiting a Black Hole

Creators: 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.; 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

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Abstract

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.

Additional Information

© 2021 The Author(s). Published by the American Astronomical Society. 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. Received 2021 January 31; revised 2021 March 18; accepted 2021 March 21; published 2021 May 3. We thank the National Science Foundation (awards OISE-1743747, AST-1816420, AST-1716536, AST-1440254, AST-1935980) 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 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 and JP19H01943); 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 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, 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 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). 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 für 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 Astrofísica, Óptica, y Electrónica (Mexico) and the University of Massachusetts at Amherst (USA), with financial support from the Consejo Nacional de Ciencia y Tecnología 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 (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 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.

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