New method for black-hole spin measurement based on flux variation from an infalling gas ring

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 of the inclination angle, while time-averaged frequency shift has dependence on both effects. We can thus, in principle, determine spin and inclination angle from observations. The observational implications and future issues are briefly discussed.