Determining parameters of a spherical black hole with a thin accretion disk by observing its shadow

Abstract

We revisit the classic system of a spherically symmetric black hole in general relativity (i.e., a Schwarzschild black hole) surrounded by a geometrically thin accretion disk. Our purpose is to examine whether one can determine three parameters of this system (i.e., black hole mass $M$, distance between the black hole and an observer $r_o$, inclination angle $i$) solely by observing the accretion disk and the black hole shadow. A point in our analysis is to allow $r_o$ to be finite, which is set to be infinite in most relevant studies. First, it is shown that one can determine the values of $(r_o/M,i)$, where $M/r_o$ is the so-called angular gravitational radius, from the size and shape of shadow. Then, it is shown that if one additionally knows the accretion rate $\dot{M}$ (respectively, mass $M$) by any independent theoretical or observational approach, one can determine the values of $(M,r_o,i)$ [respectively, $(\dot{M},r_o,i)$] without degeneracy, in principle, from the value of flux at any point on the accretion disk.

28 pages, 11 figures, title modified, sec 6 added, accepted for publication in Physical Review D

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Cited by in corpus (5)

• Image of the Kerr-Newman black hole surrounded by a thin accretion disk
• Constraints on the black-hole charges of M87* and Sagittarius A* by changing rates of photon spheres can be relaxed
• Research on high-frequency quasi-periodic oscillations in black bounce-type spacetime
• Determining parameters of Kerr black holes at finite distance by shadow observation
• Determining parameters of Kerr-Newman black holes by shadow observation from finite distance and spatial infinity