Shapes and Positions of Black Hole Shadows in Accretion Disks and Spin Parameters of Black Holes

Takahashi, Rohta

doi:10.1086/422403

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

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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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: 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

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Shapes and Positions of Black Hole Shadows in Accretion Disks and Spin Parameters of Black Holes

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