Determining parameters of a spherical black hole with a thin accretion disk by observing its shadow
Determining parameters of a spherical black hole with a thin accretion disk by observing its shadow
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DOI：
10.1103/physrevd.107.044042
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发表时间：
2022-10
影响因子：
5
通讯作者：
Kenta Hioki;U. Miyamoto
中科院分区：
文献类型：
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作者：
Kenta Hioki;U. Miyamoto
我们重温了广义相对论中球对称黑洞的经典系统（即，一个史瓦西黑洞）被一个几何上薄的吸积盘所包围。我们的目的是检查是否可以确定该系统的三个参数（即，黑洞质量M、黑洞与观测者的距离r_o、黑洞的倾角i）。我们分析中的一个要点是允许r_o是有限的，而在大多数相关研究中，r_o是无限的。首先，证明了由阴影的大小和形状可以确定$（r_o/M，i）$的值，其中$M/r_o$是所谓的引力角半径。然后，证明了如果我们通过任何独立的理论或观测方法另外知道吸积率$\dot{M}$（相应地，质量$M$），那么原则上，我们可以从吸积盘上任意点的通量值确定$（M，r_o，i）$ [相应地，$（\dot{M}，r_o，i）$]的值而不发生简并。
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.