The DOI matches its Crossref record; 38 of the 38 references it cites were found in a registry or an index.
Shapes and Positions of Black Hole Shadows in Accretion Disks and Spin Parameters of Black Holes
Open accessAbstract
Can we determine the spin parameter of a black hole by observing the black hole's shadow on an accretion disk? To answer this question, we make qualitative and quantitative analyses of the shape and position of the shadow cast by a rotating black hole on an optically thick accretion disk and its dependence on the angular momentum of the black hole. We consider two types of inner edges of accretion disks, an event horizon and a marginally stable orbit. We have found black hole shadows of quite similar sizes and shapes for very different black hole spin parameters and the same black hole mass. Thus, in practice it is difficult to determine the spin parameter of a black hole from the size and shape of its shadow on an accretion disk. On the other hand, a frame-dragging effect in the vicinity of a black hole causes a displacement of the shadow from the rotation axis of the black hole. The extent of the displacement largely depends on the black hole's spin parameter. However, it is difficult to determine the position of the rotation axis of a black hole observationally. So, we cannot practically use the displacement of the rotation axis of a black hole shadow to measure the spin parameter. We here introduce a bisector axis of black hole shadows that we call the "shadow axis." We define this as the bisector perpendicular to a line segment of the maximum width of a black hole shadow. We can determine the position of a shadow axis through observation of a black hole shadow. For a nonrotating black hole, the minimum interval between the mass center of a black hole and the shadow axis is null. On the other hand, for a rotating black hole the shape and position of the shadow are not symmetric with respect to its rotation axis. So, in this case the minimum interval between the mass center of the black hole and the shadow axis is finite. The extent of this minimum interval is roughly proportional to the spin parameter of a black hole for a fixed inclination angle between a rotation axis and the direction of an observer. The maximum extent of these minimum intervals is about 1.5 r g . Here r g is a gravitational radius. This is realized in the case of a maximum inclination angle and maximally rotating black hole in an accretion disk in which the inner edge is an event horizon. In order to measure the spin parameter of a black hole, if the shadow axis is determined observationally, it is crucially important to determine the position of the mass center in a region of the shadow. We also discuss how to determine a mass center of a black hole by observation of the shadow on an accretion disk.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
The Mathematical Theory of Black Holes
Chandrasekhar, S. (1984) · General Relativity and Gravitation · doi:10.1007/978-94-009-6469-3_2 · Cited by 3,191
Bardeen, J. M., Press, W. H., & Teukolsky, S. A. (1972) · The Astrophysical Journal · doi:10.1086/151796 · Cited by 2,628
Global Structure of the Kerr Family of Gravitational Fields
Carter, B. (1968) · Physical Review · doi:10.1103/physrev.174.1559 · Cited by 2,294
The Mathematical Theory of Black Holes
Chandrasekhar, S., & Janis, A. I. (1984) · Physics Today · doi:10.1063/1.2916327 · Cited by 2,244
Viewing the Shadow of the Black Hole at the Galactic Center
Falcke, H. D., Melia, F., & Agol, E. (2000) · The Astrophysical Journal · doi:10.1086/312423 · Cited by 1,150
Tanaka, Y., Nandra, K., Fabian, A. C., Inoue, H., Otani, C., Dotani, T., Hayashida, K., Iwasawa, K., Kii, T., Kunieda, H., et al. (1995) · Nature · doi:10.1038/375659a0 · Cited by 1,033
Near-infrared flares from accreting gas around the supermassive black hole at the Galactic Centre
Genzel, R., Schödel, R., Ott, T., Eckart, A., Alexander, T., Lacombe, F., Rouan, D., & Aschenbach, B. (2003) · Nature · doi:10.1038/nature02065 · Cited by 688
The effects of redshifts and focusing on the spectrum of an accretion disk around a Kerr black hole
Cunningham, C. T. (1975) · The Astrophysical Journal · doi:10.1086/154033 · Cited by 384
Formation of the radio jet in M87 at 100 Schwarzschild radii from the central black hole
Junor, W., Biretta, J. A., & Livio, M. (1999) · Nature · doi:10.1038/44780 · Cited by 383
The Optical Appearance of a Star Orbiting an Extreme Kerr Black Hole
Bardeen, C. T., & Cunningham, J. M. (1973) · The Astrophysical Journal · doi:10.1086/152223 · Cited by 302
Flagged first, then by citations
Research works printed but not linked: 8
- Fabian A. C., 1995, MNRAS, 277, L11
- Fukue J., 1988, PASJ, 40, 15
- Kindl, C. 1995, PH.D. thesis, Univ. Heidelberg (IWR)
- Luminet J.-P., 1979, A&A, 75, 228
- Perez C. A., 1991, BAAS, 23, 945
- Quien N., 1996, Pour la Science, 223, 40
- Shakura N. I., 1973, A&A, 24, 337
- Sikora M., 1979, Acta Astron., 29, 87
Cited by
Sorted by citations
First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
The Event Horizon Telescope Collaboration, Akiyama, K., Alberdi, A., Alef, W., Asada, K., Azulay, R., Baczko, A.-K., Ball, D., Baloković, M., Barrett, J., et al. (2019) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ab0ec7 · Cited by 4,205
First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
Akiyama, K., Alberdi, A., Alef, W., Asada, K., Azulay, R., Baczko, A.-K., Ball, D. R., Baloković, M., Barrett, J., Bintley, D., et al. (2019) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ab1141 · Cited by 1,904
First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring
The Event Horizon Telescope Collaboration, Akiyama, K., Alberdi, A., Alef, W., Asada, K., Azulay, R., Baczko, A.-K., Ball, D., Baloković, M., Barrett, J., et al. (2019) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ab0f43 · Cited by 1,424
First M87 Event Horizon Telescope Results. II. Array and Instrumentation
Akiyama, K., Alberdi, A., Alef, W., Asada, K., Azulay, R., Baczko, A.-K., Ball, D. R., Baloković, M., Barrett, J., Bintley, D., et al. (2019) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ab0c96 · Cited by 1,209
Vagnozzi, S., Roy, R., Tsai, Y.-D., Visinelli, L., Afrin, M., Allahyari, A., Bambhaniya, P., Dey, D., Ghosh, S. G., Joshi, P. S., et al. (2023) · Classical and Quantum Gravity · doi:10.1088/1361-6382/acd97b · Cited by 924
Metadata
- Authors
- Takahashi, R.
- Affiliations
- Kyoto University (JP)
- Corresponding author
- Takahashi, Rohta
- ORCID
- Takahashi, Rohta
- Venue
- The Astrophysical Journal
- Publisher
- American Astronomical Society
- Published
- 2004-08-20
- Volume
- 611
- Issue
- 2
- Pages
- 996-1004
- ISSN
- 0004-637X (ISSN-L)
- 1538-4357
- OpenAlex
- W2067381051
- Cited by
- 305
- References
- 38
- Citations by year
- 2026: 10 · 2025: 26 · 2024: 27 · 2023: 22 · 2022: 33 · 2021: 20 · 2020: 19 · 2019: 17 · 2018: 18 · 2017: 11 · 2016: 17 · 2015: 13 · 2014: 11 · 2013: 8 · 2012: 5
- FWCI
- 3.53
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Astrophysical Journal (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Astrophysical Phenomena and Observations
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Pulsars and Gravitational Waves Research
- Keywords
- black hole shadow, black hole spin, accretion disks, rotating black holes, frame-dragging, event horizon, marginally stable orbit, gravitational radius, inclination angle, optically thick accretion disk, Kerr metric
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
