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

TL;DR

This paper investigates how to determine a black hole's mass, distance, and inclination angle solely from observations of its shadow and accretion disk, considering finite observer distance, and shows that additional known parameters can resolve degeneracies.

Contribution

It demonstrates a method to uniquely determine black hole parameters from shadow and disk observations, including finite observer distance, and explores parameter degeneracies.

Findings

Black hole parameters can be inferred from shadow size and shape.

Knowing accretion rate or mass helps resolve parameter degeneracies.

Finite observer distance affects parameter determination methods.

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.