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

Line emission from an accretion disk and a corotating hotspot 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 $6 G M/c^2$. 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 also consider lightcurves and frequency shifts in line emission as a function of time for corotating hotspots in extreme Kerr and Schwarzschild geometries. The frequency shift profile is an excellent measure of orbital parameters and might possibly be used to detect frame dragging even at radii approaching $6 G M/c^2$ if the inclination angle of the orbital plane is large. The lightcurve from a hotspot shows differences as well; although, these too are pronounced only at large inclination angles. This work is based on a parallel ray-tracing code which generated accretion disk images by generating the geodesics for those null rays which intersect the disk plane. The typical resolution of the images was $1000 \times 1000$ pixels. A set of images or templates generated at this resolution are suitable for fitting real line-emission data which can be expected from the next generation of X-ray satellites.