The Polarized Image of a Synchrotron-emitting Ring of Gas Orbiting a Black Hole
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. ,   The 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 陈永 Yongjun 军 , 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 顾敏 Minfeng 峰 , Gurwell Mark , Hada Kazuhiro , Haggard Daryl , Hecht Michael H. , Hesper Ronald , Ho 何子 Luis C. 山 , Ho Paul , Honma Mareki , Huang Chih-Wei L. , Huang 黄 Lei 磊 , Hughes David H. , Ikeda Shiro , Inoue Makoto , Issaoun Sara , James David J. , Jannuzi Buell T. , Janssen Michael , Jeter Britton , Jiang 江 Wu 悟 , 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 李彦 Yan-Rong 荣 , Li 李志 Zhiyuan 远 , Lindqvist Michael , Lico Rocco , Lindahl Greg , Liu 刘 Jun 俊 , Liu Kuo , Liuzzo Elisabetta , Lo Wen-Ping , Lobanov Andrei P. , Loinard Laurent , Lonsdale Colin , Lu 路如 Ru-Sen 森 , MacDonald Nicholas R. , Mao 毛基 Jirong 荣 , 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 沈志 Zhiqiang 强 , Small Des , Sohn Bong Won , SooHoo Jason , Sun 孙 He 赫 , 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 吴庆 Qingwen 文 , Yoon Doosoo , Young André , Young Ken , Younsi Ziri , Yuan 袁 Feng 峰 , Yuan 袁业 Ye-Fei 飞 , Zensus J. Anton , Zhao Guang-Yao , Zhao Shan-Shan 
Published: May 2021

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.