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Cited by 305Astrophysical Phenomena and ObservationsBlack Holes and Theoretical PhysicsPulsars and Gravitational Waves Research

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

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Takahashi, Rohta·2004·The Astrophysical Journal
DOI 10.1086/422403
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Abstract

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.

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Research works printed but not linked: 8

  1. Fabian A. C., 1995, MNRAS, 277, L11
  2. Fukue J., 1988, PASJ, 40, 15
  3. Kindl, C. 1995, PH.D. thesis, Univ. Heidelberg (IWR)
  4. Luminet J.-P., 1979, A&A, 75, 228
  5. Perez C. A., 1991, BAAS, 23, 945
  6. Quien N., 1996, Pour la Science, 223, 40
  7. Shakura N. I., 1973, A&A, 24, 337
  8. Sikora M., 1979, Acta Astron., 29, 87

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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
DOI
10.1086/422403
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
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

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