基于下落气体环通量变化的黑洞自旋测量新方法
New method for black-hole spin measurement based on flux variation from an infalling gas ring
摘要：
提出了一种测量黑洞自旋的新方法。在这种方法中，我们考虑一个气体团或环从边缘稳定轨道落到黑洞上，保持其初始轨道角动量。我们计算气体运动和光子的克尔时空轨迹，并假设气体团或环发出单色辐射，仔细检查它是如何观察到一个遥远的观察者。由于引力透镜和聚束效应导致的通量周期性增强，轨道气体团的光变曲线由许多峰组成。此外，每个峰的强度首先由于光子圆形轨道周围的聚焦效应而随着时间逐渐增加，然后由于引力红移而迅速减小，因为气体团接近事件视界。气体环的光变曲线相当于具有不同初始轨道相位的斑点的光变曲线的叠加，因此它是连续的，没有峰值。通量首先逐渐增加，然后迅速衰减，如在斑点模型中。流量变化的时间尺度依赖于黑洞的自旋，与黑洞的倾角无关，而时间平均频移则依赖于这两种效应。因此，我们原则上可以从观测中确定自旋和倾角。观测的影响和未来的问题进行了简要讨论。
英文摘要：
We propose a new method for black hole spin measurement. In this method, we consider a gas blob or ring falling onto a black hole from the marginally stable orbit, keeping its initial orbital angular momentum. We calculate the gas motion and photon trajectories in the Kerr space-time and, assuming that the gas blob or ring emits monochromatic radiation, carefully examine how it is observed by a distant observer. The light curve of the orbiting gas blob is composed of many peaks because of periodic enhancement of the flux due to the gravitational lensing and beaming effects. Further, the intensity of each peak first gradually increases with time due to the focusing effect around the photon circular orbit and then rapidly decreases due to the gravitational redshift, as the gas blob approaches the event horizon. The light curve of the gas ring is equivalent to a superposition of those of the blobs with various initial orbital phases, and so it is continuous and with no peaks. The flux first gradually increases and then rapidly decays, as in the blob model. The flux variation timescale depends on the black hole spin and is independent from the inclination angle, while time averaged frequency shift have dependences of both effects. We can thus, in principle, determine spin and inclination angle from observations. The observational implications and future issues are briefly discussed.
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