Comparison of polarized radiative transfer codes used by the EHT collaboration
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Date
Authors
Prather, Ben S.
Dexter, Jason
Moscibrodzka, Monika
Pu, Hung-Yi
Bronzwaer, Thomas
Davelaar, Jordy
Younsi, Ziri
Gammie, Charles F.
Gold, Roman
Wong, George N.
Journal Title
Journal ISSN
Volume Title
Publisher
American Astronomical Society
Abstract
Interpretation of resolved polarized images of black holes by the Event Horizon Telescope (EHT) requires
predictions of the polarized emission observable by an Earth-based instrument for a particular model of the black
hole accretion system. Such predictions are generated by general relativistic radiative transfer (GRRT) codes,
which integrate the equations of polarized radiative transfer in curved spacetime. A selection of ray-tracing GRRT
codes used within the EHT Collaboration is evaluated for accuracy and consistency in producing a selection of test
images, demonstrating that the various methods and implementations of radiative transfer calculations are highly
consistent. When imaging an analytic accretion model, we find that all codes produce images similar within a
pixel-wise normalized mean squared error (NMSE) of 0.012 in the worst case. When imaging a snapshot from a
cell-based magnetohydrodynamic simulation, we find all test images to be similar within NMSEs of 0.02, 0.04,
0.04, and 0.12 in Stokes I, Q, U, and V, respectively. We additionally find the values of several image metrics
relevant to published EHT results to be in agreement to much better precision than measurement uncertainties.
Description
ACKNOWLEDGEMENTS : The Event Horizon Telescope Collaboration thanks the
following organizations and programs: the Academia Sinica; the
Academy of Finland (projects 274477, 284495, 312496, 315721);
the Agencia Nacional de Investigación y Desarrollo (ANID),
Chile via NCN19058 (TITANs) and Fondecyt 1221421, 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 ALMA North
America Development Fund; the Black Hole Initiative, which is
funded by grants from the John Templeton Foundation and the
Gordon and Betty Moore Foundation (although the opinions expressed in this work are those of the author(s) and do not
necessarily reflect the views of these Foundations); the Brinson
Foundation; Chandra DD7-18089X and TM6-17006X; the China
Scholarship Council; the China Postdoctoral Science Foundation
fellowships (2020M671266, 2022M712084); Consejo Nacional
de Ciencia y Tecnología (CONACYT, Mexico, projects U0004-
246083, U0004-259839, F0003-272050, M0037-279006, F0003-
281692, 104497, 275201, 263356); 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 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 Dutch Organization for Scientific
Research (NWO) for VICI award (grant 639.043.513), grant
OCENW.KLEIN.113 and the Dutch Black Hole Consortium
(with project No. NWA 1292.19.202) of the research program the
National Science Agenda; the Dutch National Supercomputers,
Cartesius and Snellius (NWO grant 2021.013); the EACOA
Fellowship awarded by the East Asia Core Observatories
Association, which consists of the Academia Sinica Institute of
Astronomy and Astrophysics, the National Astronomical Observatory
of Japan, Center for Astronomical Mega-Science, Chinese
Academy of Sciences, and the Korea Astronomy and Space
Science Institute; the European Research Council (ERC) Synergy
Grant “BlackHoleCam: Imaging the Event Horizon of Black
Holes” (grant 610058); the European Union Horizon 2020
research and innovation program under grant agreements Radio-
Net (No. 730562) and M2FINDERS (No. 101018682); the
Horizon ERC Grants 2021 program under grant agreement No.
101040021; the Generalitat Valenciana postdoctoral grant
APOSTD/2018/177 and GenT Program (project CIDEGENT/
2018/021); MICINN Research Project PID2019-108995GB-C22;
the European Research Council for advanced grant “JETSET:
Launching, propagation and emission of relativistic jets from
binary mergers and across mass scales” (grant No. 884631); the
Institute for Advanced Study; 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; DFG research grant “Jet physics on horizon scales and
beyond” (grant No. FR 4069/2-1); Joint Columbia/Flatiron
Postdoctoral Fellowship (research at the Flatiron Institute is
supported by the Simons Foundation); the Japan Ministry of
Education, Culture, Sports, Science and Technology (MEXT;
grant JPMXP1020200109); the Japanese Government (Monbukagakusho:
MEXT) Scholarship; the Japan Society for the
Promotion of Science (JSPS) Grant-in-Aid for JSPS Research
Fellowship (JP17J08829); the Joint Institute for Computational
Fundamental Science, Japan; 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, JP21H01137, JP18H03721,
JP18K13594, 18K03709, JP19K14761, 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 (103-
2119-M-001-010-MY2, 105-2112-M-001-025-MY3, 105-2119-
M-001-042, 106-2112-M-001-011, 106-2119-M-001-013, 106-
2119-M-001-027, 106-2923-M-001-005, 107-2119-M-001-017,
107-2119-M-001-020, 107-2119-M-001-041, 107-2119-M-110-
005, 107-2923-M-001-009, 108-2112-M-001-048, 108-2112-M-
001-051, 108-2923-M-001-002, 109-2112-M-001-025, 109-2124-
M-001-005, 109-2923-M-001-001, 110-2112-M-003-007-MY2,
110-2112-M-001-033, 110-2124-M-001-007, and 110-2923-M-
001-001); the Ministry of Education (MoE) of Taiwan Yushan
Young Scholar Program; the Physics Division, National Center
for Theoretical Sciences of Taiwan; the National Aeronautics and
Space Administration (NASA, Fermi Guest Investigator grant
80NSSC20K1567, NASA Astrophysics Theory Program grant
80NSSC20K0527, NASA NuSTAR award 80NSSC20K0645);
NASA Hubble Fellowship grants HST-HF2-51431.001-A, HSTHF2-
51482.001-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, 2017YFA0402703,
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-
1440254, AST-1555365, AST-1614868, AST-1615796, AST-
1715061, AST-1716327, AST-1716536, OISE-1743747, AST-
1816420, AST-1935980, AST-2034306); NSF Astronomy and
Astrophysics Postdoctoral Fellowship (AST-1903847); the Natural
Science Foundation of China (grants 11650110427,
10625314, 11721303, 11725312, 11873028, 11933007,
11991052, 11991053, 12192220, 12192223); 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, the Korea Research Fellowship
Program: NRF-2015H1D3A1066561, Brain Pool
Program: 2019H1D3A1A01102564, Basic Research Support
Grant 2019R1F1A1059721, 2021R1A6A3A01086420,
2022R1C1C1005255); Netherlands Research School for Astronomy
(NOVA) Virtual Institute of Accretion (VIA) postdoctoral
fellowships; 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 Princeton Gravity Initiative; the Spanish Ministerio
de Ciencia e Innovación (grants PGC2018-098915-B-C21,
AYA2016-80889-P, PID2019-108995GB-C21, PID2020-
117404GB-C21); the University of Pretoria for financial aid in
the provision of the new Cluster Server nodes and SuperMicro
(USA) for a SEEDING GRANT approved toward these nodes in
2020; the Shanghai Pilot Program for Basic Research, Chinese
Academy of Science, Shanghai Branch (JCYJ-SHFY-2021-013);
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 Spinoza Prize
SPI 78-409; the South African Research Chairs Initiative, through
the South African Radio Astronomy Observatory (SARAO, grant
ID 77948), which is a facility of the National Research
Foundation (NRF), an agency of the Department of Science and
Innovation (DSI) of South Africa; the Toray Science Foundation;
the Swedish Research Council (VR); 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 YCAA Prize Postdoctoral Fellowship;
and the Astrophysics and High Energy Physics program by
MCIN (with funding from European Union NextGenerationEU,
PRTR-C17I1).
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 research used
resources of the Oak Ridge Leadership Computing Facility at
the Oak Ridge National Laboratory, which is supported by the
Office of Science of the U.S. Department of Energy under
contract No. DE-AC05-00OR22725. We also thank the Center
for Computational Astrophysics, National Astronomical Observatory
of Japan. The computing cluster of Shanghai VLBI
correlator supported by the Special Fund for Astronomy from
the Ministry of Finance in China is acknowledged. This work
was supported by FAPESP (Fundacao de Amparo a Pesquisa
do Estado de Sao Paulo) under grant 2021/01183-8.
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 Research and Development
Program (No. 2017YFA0402700) of China and Natural
Science Foundation of China grant 11873028. Additional
funding support for the JCMT is provided by the Science and
Technologies Facility Council (UK) and participating universities
in the UK and Canada. The LMT is a project operated
by the Instituto Nacional de Astrófisica, Óptica, y Electrónica
(Mexico) and the University of Massachusetts at Amherst
(USA). The IRAM 30 m telescope on Pico Veleta, Spain is
operated by IRAM and supported by CNRS (Centre National
de la Recherche Scientifique, France), MPG (Max-Planck-
Gesellschaft, Germany), and IGN (Instituto Geográfico Nacional,
Spain). The SMT is operated by the Arizona Radio
Observatory, a part of the Steward Observatory of the
University of Arizona, with financial support of operations
from the State of Arizona and financial support for instrumentation
development from the NSF. Support for SPT participation
in the EHT is provided by the National Science Foundation
through award OPP-1852617 to the University of Chicago.
Partial support is also provided by the Kavli Institute of
Cosmological Physics at the University of Chicago. The SPT
hydrogen maser was provided on loan from the GLT, courtesy
of ASIAA.
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. This research is part of the
Frontera computing project at the Texas Advanced Computing
Center through the Frontera Large-Scale Community Partnerships
allocation AST20023. Frontera is made possible by National
Science Foundation award OAC-1818253. This research was
done using services provided by the OSG Consortium (Pordes
et al. 2007; Sfiligoi et al. 2009), which is supported by the
National Science Foundation award Nos. 2030508 and 1836650.
This research was carried out using resources provided by the
Open Science Grid, which is supported by the National Science
Foundation and the U.S. Department of Energy Office of Science.
Additional work used ABACUS2.0, which is part of the eScience
center at Southern Denmark University. Simulations were also
performed on the SuperMUC cluster at the LRZ in Garching, on
the LOEWE cluster in CSC in Frankfurt, on the HazelHen cluster
at the HLRS in Stuttgart, and on the Pi2.0 and Siyuan Mark-I at
Shanghai Jiao Tong University. The computer resources of the
Finnish IT Center for Science (CSC) and the Finnish Computing
Competence Infrastructure (FCCI) project are acknowledged.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).
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 opensource
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,
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 Martin Shepherd for the addition of
extra features in the Difmap software that were used for the
CLEAN imaging results presented in this paper. We acknowledge
the significance that Maunakea, where the SMA and
JCMT EHT stations are located, has for the indigenous
Hawaiian people.
Keywords
Supermassive black holes, Radiative transfer simulations, Astronomy software, Event Horizon Telescope (EHT), General relativistic radiative transfer (GRRT)
Sustainable Development Goals
None
Citation
Prather, B.S., Dexter, J., Moscibrodzka, M. et al. 2023, 'Comparison of polarized radiative transfer codes used by the EHT collaboration', The Astrophysical Journal, vol. 950, no. 35, pp. 1-23. https://DOI.org/10.3847/1538-4357/acc586.