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

By R. Takahashi. 2004

261 citations recorded by the source corpus.

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 1.5rg. Here rg 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.

Subfields: Astronomy and Astrophysics, Biomedical Engineering

View Paper: https://www.semanticscholar.org/paper/99e6dd1f0f0507112b1953ccc1a821c004cdb4ae

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Biomedical Engineering

Citations in the corpus

Imaging optically-thin hotspots near the black hole horizon of Sgr A* at radio and near-infrared wavelengths (2005, background): “In contrast, a number of researchers have suggested that imaging an optically-thin background accretion flow could provide a direct test of strong gravity (see, e.g. Falcke, Melia & Agol 2000; Takahashi 2004, 2005; Broderick & Loeb 2006).”
First Sagittarius A* Event Horizon Telescope Results. IV. Variability, Morphology, and Black Hole Mass (2022, background): “26g If the observations were directly sensitive to the critical curve bounding the black hole shadow, then α could be determined analytically and would take on a value ranging from ∼9.6 to 10.4 depending on the black hole spin and inclination (Bardeen 1973; Takahashi 2004).”
Calculating black hole shadows: Review of analytical studies (2021, background): “Takahashi [96] x and y (8) and (9) p and q(2) —”
Observing the Inner Shadow of a Black Hole: A Direct View of the Event Horizon (2021, methodology): “The inner shadow of a Kerr black hole has a significantly different dependence on its parameters than the critical curve (Takahashi 2004).”
Measuring the spins of accreting black holes (2011, methodology): “Meanwhile, several other methods of measuring spin have been proposed or applied (e.g., Takahashi 2004, Barai et al 2004, Huang et al 2007, Suleimanov et al 2008, Shcherbakov and Huang 2011).”
Extreme gravitational lensing near rotating black holes (2004, methodology): “…recent papers have emphasised that the true size of the shadow of the event horizon (in effect the impact parameter of the orbiting photons, given fairly accurately by our second order image) is rather similar in both Schwarzchild and Kerr (Falcke, Melia, & Agol 2000; Fukue 2003; Takahashi 2004).”
Imaging bright-spots in the accretion flow near the black hole horizon of Sgr A* (2005, unknown): “These may be compared to calculations that assume a C© 2005 RAS, MNRAS 363, 353–362 Downloaded from https://academic.oup.com/mnras/article-abstract/363/2/353/1123264 by guest on 27 July 2018 uniform and steady accretion flow (e.g. Falcke et al. 2000; Takahashi 2004, 2005).”
A coordinate-independent characterization of a black hole shadow (2015, background): “…black holes, the observation of the black hole shadow and of the deformations resulting in the case of nonzero spin, is also expected to help determine many of the black hole properties (see e.g. Chandrasekhar 1998; Falcke & Markoff 2013; Takahashi 2004; Falcke et al. 2000; Doeleman et al. 2009).”
RADIATIVE MODELS OF SGR A* FROM GRMHD SIMULATIONS (2009, background): “This small number of baselines does not permit imaging of the emitting region or the “silhouette” of the BH (Bardeen 1973; Chandrasekhar 1983; Falcke et al. 2000; Takahashi 2004), but it does constrain models of the emitting region.”
PHOTON RINGS AROUND KERR AND KERR-LIKE BLACK HOLES (2013, methodology): “(36) Takahashi (2004) calculated the ring displacement as a function of the spin for several inclination angles and determined approximately the maximum ring diameter (across the geometric center of the ring) from a set of calculated ring images.”
Shadows of spherically symmetric black holes and naked singularities (2018, background): “Many authors (Synge 1966; Zakharov 2014; Takahashi 2004; Hioki & Maeda 2009; Takahashi 2005; deVries 2000; Young 1976; Yumoto et al. 2012; Shipley & Dolan 2016) have studied the characteristics of shadows cast by various black holes.”