Line Emission from an Accretion Disk around a Rotating Black Hole: Toward a Measurement of Frame Dragging

Abstract

Line emission from an accretion disk and a corotating hot spot about a rotating black hole are considered for possible signatures of the frame-dragging effect. We explicitly compare integrated line profiles from a geometrically thin disk about a Schwarzschild and an extreme Kerr black hole, and show that the line profile differences are small if the inner radius of the disk is near or above the Schwarzschild stable-orbit limit of radius 6GM/c². However, if the inner disk radius extends below this limit, as is possible in the extreme Kerr spacetime, then differences can become significant, especially if the disk emissivity is stronger near the inner regions. We demonstrate that the first three moments of a line profile define a three-dimensional space in which the presence of material at small radii becomes quantitatively evident in broad classes of disk models. In the context of the simple, thin disk paradigm, this moment-mapping scheme suggests formally that the iron line detected by the Advanced Satellite for Cosmology and Astrophysics mission from MCG -6-30-15 (Tanaka et al.) is ~3 times more likely to originate from a disk about a rotating black hole than from a Schwarzschild system. A statistically significant detection of black hole rotation in this way may be achieved after only modest improvements in the quality of data. We also consider light curves and frequency shifts in line emission as a function of time for corotating hot spots in extreme Kerr and Schwarzschild geometries. The frequency-shift profile is a valuable measure of orbital parameters and might possibly be used to detect frame dragging even at radii approaching 6GM/c² if the inclination angle of the orbital plane is large. The light curve from a hot spot shows differences as well, although these too are pronounced only at large inclination angles.