4.6 Article

Observational appearance of inefficient accretion flows and jets in 3D GRMHD simulations: Application to Sagittarius A

期刊

ASTRONOMY & ASTROPHYSICS
卷 570, 期 -, 页码 -

出版社

EDP SCIENCES S A
DOI: 10.1051/0004-6361/201424358

关键词

accretion, accretion disks; black hole physics; magnetohydrodynamics (MHD); radiative transfer; Galaxy: center; galaxies: jets

资金

  1. NWO Spinoza Price
  2. ERC
  3. US NSF [AST 07-09246, AST 13-33612]
  4. NASA [NNX10AD03G]
  5. NSF [ACI-1053575]
  6. NASA [135909, NNX10AD03G] Funding Source: Federal RePORTER
  7. Direct For Mathematical & Physical Scien [1333682] Funding Source: National Science Foundation
  8. Division Of Astronomical Sciences [1333682] Funding Source: National Science Foundation
  9. Division Of Astronomical Sciences
  10. Direct For Mathematical & Physical Scien [1333091, 1333612] Funding Source: National Science Foundation

向作者/读者索取更多资源

Context. Radiatively inefficient accretion flows (RIAFs) are believed to power supermassive black holes in the underluminous cores of galaxies. Such black holes are typically accompanied by flat-spectrum radio cores indicating the presence of moderately relativistic jets. One of the best constrained RIAFs is associated with the supermassive black hole in the Galactic center, Sgr A*. Aims. Since the plasma in RIAFs is only weakly collisional, the dynamics and the radiative properties of these systems are very uncertain. Here we want to study the impact of varying electron temperature on the appearance of accretion flows and jets. Methods. Using three-dimensional general relativistic magnetohydrodynamics accretion flow simulations, we use ray tracing methods to predict spectra and radio images of RIAFs allowing for different electron heating mechanisms in the in-and outflowing parts of the simulations. Results. We find that small changes in the electron temperature can result in dramatic differences in the relative dominance of jets and accretion flows. Application to Sgr A* shows that radio spectrum and size of this source can be well reproduced with a model where electrons are more efficiently heated in the jet. The X-ray emission is sensitive to the electron heating mechanism in the jets and disk and therefore X-ray observations put strong constraints on electron temperatures and geometry of the accretion flow and jet. For Sgr A*, the jet model also predicts a significant frequency-dependent core shift which could place independent constraints on the model once measured accurately. Conclusions. We conclude that more sophisticated models for electron distribution functions are crucial for constraining GRMHD simulations with actual observations. For Sgr A*, the radio appearance may well be dominated by the outflowing plasma. Nonetheless, at the highest radio frequencies, the shadow of the event horizon should still be detectable with future Very Long Baseline Interferometric observations.

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Tilanus, Michael Titus, Pablo Torne, Efthalia Traianou, Tyler Trent, Sascha Trippe, Matthew Turk, Ilse van Bemmel, Huib Jan van Langevelde, Daniel R. van Rossum, Jesse Vos, Jan Wagner, Derek Ward-Thompson, John Wardle, Jonathan Weintroub, Norbert Wex, Robert Wharton, Maciek Wielgus, Kaj Wiik, Gunther Witzel, Michael F. Wondrak, George N. Wong, Qingwen Wu, Paul Yamaguchi, Doosoo Yoon, Andre Young, Ken Young, Ziri Younsi, Feng Yuan, Ye-Fei Yuan, J. Anton Zensus, Shuo Zhang, Guang-Yao Zhao, Shan-Shan Zhao, Feryal Ozel, Claudio Agurto, Alexander Allardi, Rodrigo Amestica, Juan Pablo Araneda, Oriel Arriagada, Jennie L. Berghuis, Alessandra Bertarini, Ryan Berthold, Jay Blanchard, Ken Brown, Mauricio Cardenas, Michael Cantzler, Patricio Caro, Edgar Castillo-Dominguez, Tin Lok Chan, Chih-Cheng Chang, Dominic O. Chang, Shu-Hao Chang, Song-Chu Chang, Chung-Chen Chen, Ryan Chilson, Tim C. Chuter, Miroslaw Ciechanowicz, Edgar Colin-Beltran, Iain M. Coulson, Joseph Crowley, Nathalie Degenaar, Sven Dornbusch, Carlos A. Duran, Wendeline B. Everett, Aaron Faber, Karl Forster, Miriam M. Fuchs, David M. Gale, Gertie Geertsema, Edouard Gonzalez, Dave Graham, Frederic Gueth, Nils W. Halverson, Chih-Chiang Han, Kuo-Chang Han, Yutaka Hasegawa, Jose Luis Hernandez-Rebollar, Cristian Herrera, Ruben Herrero-Illana, Stefan Heyminck, Akihiko Hirota, James Hoge, Shelbi R. Hostler Schimpf, Ryan E. Howie, Yau-De Huang, Homin Jiang, Hao Jinchi, David John, Kimihiro Kimura, Thomas Klein, Derek Kubo, John Kuroda, Caleb Kwon, Richard Lacasse, Robert Laing, Erik M. Leitch, Chao-Te Li, Ching-Tang Liu, Kuan-Yu Liu, Lupin C-C Lin, Li-Ming Lu, Felipe Mac-Auliffe, Pierre Martin-Cocher, Callie Matulonis, John K. Maute, Hugo Messias, Zheng Meyer-Zhao, Alfredo Montana, Francisco Montenegro-Montes, William Montgomerie, Marcos Emir Moreno Nolasco, Dirk Muders, Hiroaki Nishioka, Timothy J. Norton, George Nystrom, Hideo Ogawa, Rodrigo Olivares, Peter Oshiro, Juan Pablo Perez-Beaupuits, Rodrigo Parra, Neil M. Phillips, Michael Poirier, Nicolas Pradel, Richard Qiu, Philippe A. Raffin, Alexandra S. Rahlin, Jorge Ramirez, Sean Ressler, Mark Reynolds, Ivan Rodriguez-Montoya, Alejandro F. Saez-Madain, Jorge Santana, Paul Shaw, Leslie E. Shirkey, Kevin M. Silva, William Snow, Don Sousa, T. K. Sridharan, William Stahm, Anthony A. Stark, John Test, Karl Torstensson, Paulina Venegas, Craig Walther, Ta-Shun Wei, Chris White, Gundolf Wieching, Rudy Wijnands, Jan G. A. Wouterloot, Chen-Yu Yu, Wei Yu, Milagros Zeballos

Summary: This study presents the first observations of Sagittarius A* using the Event Horizon Telescope. The data supports the presence of a supermassive black hole at the center of the Milky Way, with an image that is consistent with the expected appearance of a Kerr black hole. The results also connect dynamical measurements of stellar orbits to event-horizon-scale images.

ASTROPHYSICAL JOURNAL LETTERS (2022)

Article Astronomy & Astrophysics

Selective Dynamical Imaging of Interferometric Data

Joseph Farah, Peter Galison, Kazunori Akiyama, Katherine L. Bouman, Geoffrey C. Bower, Andrew Chael, Antonio Fuentes, Jose L. Gomez, Mareki Honma, Michael D. Johnson, Yutaro Kofuji, Daniel P. Marrone, Kotaro Moriyama, Ramesh Narayan, Dominic W. Pesce, Paul Tiede, Maciek Wielgus, Guang-Yao Zhao, Antxon Alberdi, Walter Alef, Juan Carlos Algaba, Richard Anantua, Keiichi Asada, Rebecca Azulay, Anne-Kathrin Baczkovic, David Ball, Mislay Balokovic, John Barrett, Bradford A. Benson, Dan Bintley, Lindy Blackburn, Raymond Blundell, Wilfred Boland, Hope Boyce, Michael Bremer, Christiaan D. Brinkerink, Roger Brissenden, Silke Britzen, Avery E. Broderick, Dominique Broguiere, Thomas Bronzwaer, Sandra Bustamente, Do-Young Byun, John E. Carlstrom, Chi-kwan Chan, Koushik Chatterjee, Shami Chatterjee, Ming-Tang Chen, Yongjun Chen, Ilje Cho, Pierre Christian, John E. Conway, James M. Cordes, Thomas M. Crawford, Geoffrey B. Crew, Alejandro Cruz-Osorio, Yuzhu Cui, Jordy Davelaar, Mariafelicia De Laurentis, Roger Deane, Jessica Dempsey, Gregory Desvignes, Sheperd S. Doeleman, Ralph P. Eatough, Heino Falcke, Vincent L. Fish, Ed Fomalont, H. Alyson Ford, Raquel Fraga-Encinas, Per Friberg, Christian M. Fromm, Charles F. Gammie, Roberto Garc'a, Olivier Gentaz, Ciriaco Goddi, Roman Gold, Arturo Gomez-Ruiz, Minfeng Gu, Mark Gurwell, Kazuhiro Hada, Daryl Haggard, Michael H. Hecht, Ronald Hesper, Luis C. Ho, Paul Ho, Chih-Wei L. Huang, Lei Huang, David H. Hughes, Shiro Ikeda, Makoto Inoue, Sara Issaoun, David J. James, Buell T. Jannuzi, Michael Janssen, Britton Jeter, Wu Jiang, Alejandra Jimenez-Rosales, Svetlana Jorstad, Taehyun Jung, Mansour Karami, Ramesh Karuppusamy, Tomohisa Kawashima, Garrett K. Keating, Mark Kettenis, Dong-Jin Kim, Jae-Young Kim, Jongsoo Kim, Junhan Kim, Motoki Kino, Jun Yi Koay, Patrick M. Koch, Shoko Koyama, Carsten Kramer, Michael Kramer, Thomas P. Krichbaum, Cheng-Yu Kuo, Tod R. Lauer, Sang-Sung Lee, Aviad Levis, Yan-Rong Li, Zhiyuan Li, Rocco Lico, Greg Lindahl, Michael Lindqvist, Jun Liu, Kuo Liu, Elisabetta Liuzzo, Wen-Ping Lo, Andrei P. Lobanov, Laurent Loinard, Colin Lonsdale, Ru-Sen Lu, Nicholas R. MacDonald, Jirong Mao, Nicola Marchili, Sera Markoff, Alan P. Marscher, Ivan Marti-Vidal, Satoki Matsushita, Lynn D. Matthews, Lia Medeiros, Karl M. Menten, Izumi Mizuno, Yosuke Mizuno, James M. Moran, Monika Moscibrodzka, Cornelia Muller, Alejandro Mus Mejas, Gibwa Musoke, Hiroshi Nagai, Neil M. Nagar, Masanori Nakamura, Gopal Narayanan, Iniyan Natarajan, Antonios Nathanail, Joey Neilsen, Roberto Neri, Chunchong Ni, Aristeidis Noutsos, Michael A. Nowak, Hiroki Okino, Hector Olivares, Gisela N. Ortiz-Leon, Tomoaki Oyama, Feryal Zel, Daniel C. M. Palumbo, Jongho Park, Nimesh Patel, Ue-Li Pen, Vincent Pietu, Richard Plambeck, Aleksandar PopStefanija, Oliver Porth, Felix M. Potzl, Ben Prather, Jorge A. Preciado-Lopez, Dimitrios Psaltis, Hung-Yi Pu, Venkatessh Ramakrishnan, Ramprasad Rao, Mark G. Rawlings, Alexander W. Raymond, Luciano Rezzolla, Bart Ripperda, Freek Roelofs, Alan Rogers, Eduardo Ros, Mel Rose, Arash Roshanineshat, Helge Rottmann, Alan L. Roy, Chet Ruszczyk, Kazi L. J. Rygl, Salvador Sanchez, David Sanchez-Arguelles, Mahito Sasada, Tuomas Savolainen, F. Peter Schloerb, Karl-Friedrich Schuster, Lijing Shao, Zhiqiang Shen, Des Small, Bong Won Sohn, Jason SooHoo, He Sun, Fumie Tazaki, Alexandra J. Tetarenko, Remo P. J. Tilanus, Michael Titus, Kenji Toma, Pablo Torne, Efthalia Traianou, Tyler Trent, Sascha Trippe, Ilse van Bemmel, Huib Jan van Langevelde, Daniel R. van Rossum, Jan Wagner, Derek Ward-Thompson, John Wardle, Jonathan Weintroub, Norbert Wex, Robert Wharton, Kaj Wiik, George N. Wong, Qingwen Wu, Doosoo Yoon, Andre Young, Ken Young, Ziri Younsi, Feng Yuan, Ye-Fei Yuan, J. Anton Zensus, Shan-Shan Zhao

Summary: Recent advancements in VLBI have enabled the EHT to observe and analyze the inner accretion flows of large supermassive black holes. The sparse coverage of the EHT poses a challenge in resolving highly time-variable sources. However, the changing coverage of the EHT can contain time regions within a single observation that facilitate dynamic imaging. A metric based on baseline isotropy and density is introduced to rank array configurations for accurate dynamic reconstructions.

ASTROPHYSICAL JOURNAL LETTERS (2022)

Article Astronomy & Astrophysics

PATOKA: Simulating Electromagnetic Observables of Black Hole Accretion

George N. Wong, Ben S. Prather, Vedant Dhruv, Benjamin R. Ryan, Monika Moscibrodzka, Chi-kwan Chan, Abhishek V. Joshi, Ricardo Yarza, Angelo Ricarte, Hotaka Shiokawa, Joshua C. Dolence, Scott C. Noble, Jonathan C. McKinney, Charles F. Gammie

Summary: The article describes the analysis of reconstructed images of millimeter emission near the supermassive black hole in the center of the M87 galaxy by the Event Horizon Telescope (EHT). The analysis utilized a synthetic black hole image and spectrum library produced through numerical simulations and polarized ray tracing. The article provides a detailed description of the PATOKA pipeline used to generate the simulation library, as well as an overview of the numerical codes iharm, ipole, and igrmonty. The simulated data produced by PATOKA are briefly introduced, and limitations and future directions are discussed.

ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES (2022)

Article Astronomy & Astrophysics

Resolving the Inner Parsec of the Blazar J1924-2914 with the Event Horizon Telescope

Sara Issaoun, Maciek Wielgus, Svetlana Jorstad, Thomas P. Krichbaum, Lindy Blackburn, Michael Janssen, Chi-kwan Chan, Dominic W. Pesce, Jose L. Gomez, Kazunori Akiyama, Monika Moscibrodzka, Ivan Marti-Vidal, Andrew Chael, Rocco Lico, Jun Liu, Venkatessh Ramakrishnan, Mikhail Lisakov, Antonio Fuentes, Guang-Yao Zhao, Kotaro Moriyama, Avery E. Broderick, Paul Tiede, Nicholas R. MacDonald, Yosuke Mizuno, Efthalia Traianou, Laurent Loinard, Jordy Davelaar, Mark Gurwell, Ru-Sen Lu, Antxon Alberdi, Walter Alef, Juan Carlos Algaba, Richard Anantua, Keiichi Asada, Rebecca Azulay, Uwe Bach, Anne-Kathrin Baczko, David Ball, Mislac Balokovic, John Barrett, Michi Baubock, Bradford A. Benson, Dan Bintley, Raymond Blundell, Wilfred Boland, Katherine L. Bouman, Geoffrey C. Bower, Hope Boyce, Michael Bremer, Christiaan D. Brinkerink, Roger Brissenden, Silke Britzen, Dominique Broguiere, Thomas Bronzwaer, Sandra Bustamante, Do-Young Byun, John E. Carlstrom, Chiara Ceccobello, Koushik Chatterjee, Shami Chatterjee, Ming-Tang Chen, Yongjun Chen, Ilje Cho, Pierre Christian, Nicholas S. Conroy, John E. Conway, James M. Cordes, Thomas M. Crawford, Geoffrey B. Crew, Alejandro Cruz-Osorio, Yuzhu Cui, Mariafelicia De Laurentis, Roger Deane, Jessica Dempsey, Gregory Desvignes, Jason Dexter, Sheperd S. Doeleman, Vedant Dhruv, Sergio Abraham Dzib Quijano, Ralph P. Eatough, Razieh Emami, Heino Falcke, Joseph Farah, Vincent L. Fish, Ed Fomalont, H. Alyson Ford, Raquel Fraga-Encinas, William T. Freeman, Per Friberg, Christian M. Fromm, Peter Galison, Charles F. Gammie, Roberto Garcia, Olivier Gentaz, Boris Georgiev, Ciriaco Goddi, Roman Gold, Arturo Gomez-Ruiz, Minfeng Gu, Kazuhiro Hada, Daryl Haggard, Michael H. Hecht, Ronald Hesper, Luis C. Ho, Paul Ho, Mareki Honma, Chih-Wei L. Huang, Lei Huang, David H. Hughes, Shiro Ikeda, C. M. Violette Impellizzeri, Makoto Inoue, David J. James, Buell T. Jannuzi, Britton Jeter, Wu Jiang, Alejandra Jimenez-Rosales, Michael D. Johnson, Abhishek Joshi, Taehyun Jung, Mansour Karami, Ramesh Karuppusamy, Tomohisa Kawashima, Garrett K. Keating, Mark Kettenis, Dong-Jin Kim, Jae-Young Kim, Jongsoo Kim, Junhan Kim, Motoki Kino, Jun Yi Koay, Prashant Kocherlakota, Yutaro Kofuji, Patrick M. Koch, Shoko Koyama, Carsten Kramer, Michael Kramer, Cheng-Yu Kuo, Noemi La Bella, Tod R. Lauer, Daeyoung Lee, Sang-Sung Lee, Po Kin Leung, Aviad Levis, Zhiyuan Li, Greg Lindahl, Michael Lindqvist, Kuo Liu, Elisabetta Liuzzo, Wen-Ping Lo, Andrei P. Lobanov, Colin Lonsdale, Jirong Mao, Nicola Marchili, Sera Markoff, Daniel P. Marrone, Alan P. Marscher, Satoki Matsushita, Lynn D. Matthews, Lia Medeiros, Karl M. Menten, Daniel Michalik, Izumi Mizuno, Yosuke Mizuno, James M. Moran, Cornelia Mueller, Alejandro Mus, Gibwa Musoke, Ioannis Myserlis, Andrew Nadolski, Hiroshi Nagai, Neil M. Nagar, Masanori Nakamura, Ramesh Narayan, Gopal Narayanan, Iniyan Natarajan, Antonios Nathanail, Joey Neilsen, Roberto Neri, Chunchong Ni, Aristeidis Noutsos, Michael A. Nowak, Junghwan Oh, Hiroki Okino, Hector Olivares, Gisela N. Ortiz-Leon, Tomoaki Oyama, Feryal Ozel, Daniel C. M. Palumbo, Georgios Filippos Paraschos, Jongho Park, Harriet Parsons, Nimesh Patel, Ue-Li Pen, Vincent Pietu, Richard Plambeck, Aleksandar PopStefanija, Oliver Porth, Felix M. Potzl, Ben Prather, Jorge A. Preciado-Lopez, Dimitrios Psaltis, Hung-Yi Pu, Ramprasad Rao, Mark G. Rawlings, Alexander W. Raymond, Luciano Rezzolla, Angelo Ricarte, Bart Ripperda, Freek Roelofs, Alan Rogers, Eduardo Ros, Cristina Romero-Canizales, Arash Roshanineshat, Helge Rottmann, Alan L. Roy, Ignacio Ruiz, Chet Ruszczyk, Kazi L. J. Rygl, Salvador Sanchez, David Sanchez-Arguelles, Miguel Sanchez-Portal, Mahito Sasada, Kaushik Satapathy, Tuomas Savolainen, F. Peter Schloerb, Karl-Friedrich Schuster, Lijing Shao, Zhiqiang Shen, Des Small, Bong Won Sohn, Jason SooHoo, Kamal Souccar, He Sun, Fumie Tazaki, Alexandra J. Tetarenko, Remo P. J. Tilanus, Michael Titus, Pablo Torne, Tyler Trent, Sascha Trippe, Ilse van Bemmel, Huib Jan van Langevelde, Daniel R. van Rossum, Jesse Vos, Jan Wagner, Derek Ward-Thompson, John Wardle, Jonathan Weintroub, Norbert Wex, Robert Wharton, Kaj Wiik, Gunther Witzel, Michael Wondrak, George N. Wong, Qingwen Wu, Paul Yamaguchi, Doosoo Yoon, Andre Young, Ken Young, Ziri Younsi, Feng Yuan, Ye-Fei Yuan, J. Anton Zensus, Shuo Zhang, Shan-Shan Zhao

Summary: We observed the calibrator source J1924-2914 for Sagittarius A*, the black hole at the center of the Milky Way, using the Event Horizon Telescope (EHT), and obtained the first high-resolution images. This compact radio source shows strong optical variability and polarization. Our observations reveal a characteristic bending in the jet and provide evidence for ordered toroidal magnetic fields in the core of the blazar.

ASTROPHYSICAL JOURNAL (2022)

Article Astronomy & Astrophysics

Polarimetric signatures of hot spots in black hole accretion flows

J. Vos, M. A. Moscibrodzka, M. Wielgus

Summary: This study investigates the flaring events observed in the Sagittarius A* supermassive black hole system and finds that they are attributed to the nonhomogeneous nature of the accretion flow. The research shows that the underlying magnetic field topology can be constrained by analyzing the polarimetric features of the emission.

ASTRONOMY & ASTROPHYSICS (2022)

Article Astronomy & Astrophysics

Effects of Hydrogen versus Helium on Electromagnetic Black Hole Observables

George N. Wong, Charles F. Gammie

Summary: This study uses analytical models and numerical simulations to investigate the impact of hydrogen/helium content on the polarimetric images and spectral energy distributions of black hole accretion. The results show that increasing the helium fraction leads to higher gas temperature and decreased electron density and magnetic field strength. The emission shifts from low to high plasma beta regions, altering the image morphology and reducing light curve variability. The gas composition also affects the linear polarization fraction and the spectra of helium-composition flows.

ASTROPHYSICAL JOURNAL (2022)

Article Astronomy & Astrophysics

Polarization-sensitive Compton Scattering by Accelerated Electrons

Monika A. A. Moscibrodzka

Summary: This article describes upgrades to a numerical code that calculates synchrotron and inverse-Compton emission from relativistic plasma, including full polarization. The upgraded code enables more accurate simulations of emissions from plasma jets associated with accreting compact objects.

ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES (2022)

Article Astronomy & Astrophysics

Probing plasma physics with spectral index maps of accreting black holes on event horizon scales

Angelo Ricarte, Charles Gammie, Ramesh Narayan, Ben S. Prather

Summary: The Event Horizon Telescope (EHT) collaboration has produced the first resolved images of supermassive black holes. They predict spectral index maps of M87* and Sgr A* and show that the spectral index increases with increasing magnetic field strength, electron temperature, and optical depth. Spectral index maps can be used to discriminate between different models if our understanding of plasma physics improves.

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY (2023)

Article Astronomy & Astrophysics

Jets and Rings in Images of Spinning Black Holes

Evan Papoutsis, Michi Baubock, Dominic Chang, Charles F. Gammie

Summary: We propose a dual-cone model to study millimeter wavelength emission near a rotating black hole. The model consists of luminous cones representing jet walls and results in a dominant thin ring image. We investigate the effect of the black hole's spin on the image and find that it displaces the ring perpendicular to the spin axis projection by 2a(*) in i + O(a(*)(3)), which can be detected with a positional reference. Additionally, we explore the ring substructure and show that features in the total intensity depend on the cone-opening angle.

ASTROPHYSICAL JOURNAL (2023)

Article Astronomy & Astrophysics

Prospects for Ray-tracing Light Intensity and Polarization in Models of Accreting Compact Objects Using a GPU

Monika A. Moscibrodzka, Aristomenis I. Yfantis

Summary: The Event Horizon Telescope (EHT) has released high-resolution images of accretion flows onto two supermassive black holes. This work focuses on speeding up radiative-transfer simulations used to create mock images of black holes for comparison with EHT observations. By porting a ray-tracing code onto a GPU, they achieved a significant reduction in computational time, with a speedup factor of up to approximately 1200. This speedup enables dynamic model fitting to the EHT data and reduces the carbon footprint of generating EHT image libraries.

ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES (2023)

Article Astronomy & Astrophysics

Blandford-Znajek process in quadratic gravity

Jameson Dong, Nicolas Patino, Yiqi Xie, Alejandro Cardenas-Avendano, Charles F. Gammie, Nicolas Yunes

Summary: This study investigates the impact of the Blandford-Znajek process on rotating black holes based on the scalar Gauss-Bonnet and dynamical Chern-Simons gravity theories. The results show that the extracted power is enhanced in scalar Gauss-Bonnet gravity and reduced in dynamical Chern-Simons gravity, compared to general relativity, under the conditions of small-coupling approximation and slow-rotation approximation.

PHYSICAL REVIEW D (2022)

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