Schwarzschild和Kerr几何中的吸积盘照明：拟合公式
Accretion Disk Illumination in Schwarzschild and Kerr Geometries: Fitting Formulae
摘要：
我们描述的方法和计算的照明几何薄吸积盘周围的黑洞的任意自旋参数$a$暴露于辐射的点状，各向同性源在任意高度以上的磁盘上的对称轴。然后，我们提供了解析拟合公式作为源高度$h$和黑洞角动量$a$的函数的照明。我们发现，对于一个源上的磁盘对称轴和$h/M > 3$，参数$a$的主要影响是允许磁盘扩展到更小的半径（接近$r/M \to 1$作为$a/M \to 1$），从而允许照明的区域更高的旋转速度和红移。我们还计算了与源相对于吸积盘的运动相关的各向异性发射的照明轮廓，并给出了$a/M=0$和$a/M=0.99$的各向同性和各向异性发射的被黑洞吸收、被吸积盘拦截或逃逸到无穷远的光子的分数。随着各向异性（接近圆盘的源的各向异性）的增加，照明轮廓（近似）减小到单一的幂律，其指数$q$由于黑洞对光束光子的吸收而饱和到不高于$q \gtrsim 3$的值。最后，我们计算了与特定照明相关的荧光Fe线轮廓，并在各种情况下进行了比较。
英文摘要：
We describe the methodology and compute the illumination of geometrically thin accretion disks around black holes of arbitrary spin parameter $a$ exposed to the radiation of a point-like, isotropic source at arbitrary height above the disk on its symmetry axis. We then provide analytic fitting formulae for the illumination as a function of the source height $h$ and the black hole angular momentum $a$. We find that for a source on the disk symmetry axis and $h/M > 3$, the main effect of the parameter $a$ is allowing the disk to extend to smaller radii (approaching $r/M \to 1$ as $a/M \to 1$) and thus allow the illumination of regions of much higher rotational velocity and redshift. We also compute the illumination profiles for anisotropic emission associated with the motion of the source relative to the accretion disk and present the fractions of photons absorbed by the black hole, intercepted by the disk or escaping to infinity for both isotropic and anisotropic emission for $a/M=0$ and $a/M=0.99$. As the anisotropy (of a source approaching the disk) increases the illumination profile reduces (approximately) to a single power-law, whose index, $q$, because of absorption of the beamed photons by the black hole, saturates to a value no higher than $q \gtrsim 3$. Finally, we compute the fluorescence Fe line profiles associated with the specific illumination and compare them among various cases.
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