A Precessing Ring Model for Low-Frequency Quasi-periodic Oscillations

We develop a simple physical model to describe the most common type of low-frequency quasi-periodic oscillations (QPOs) seen in a number of accreting black hole systems, as well as the shape of the relativistically broadened iron emission lines that often appear simultaneously in such sources. The model is based on an inclined ring of hot gas that orbits the black hole along geodesic trajectories. For spinning black holes, this ring will precess around the spin axis of the black hole at the Lense-Thirring (``frame-dragging'') frequency. Using a relativistic ray-tracing code, we calculate X-ray light curves and observed energy spectra as a function of the radius and tilt angle of the ring, the spin magnitude, and the inclination of the black hole. The model predicts higher-amplitude QPOs for systems with high inclinations, as seen in a growing number of black hole binary systems. We find that the Rossi X-ray Timing Explorer observations of low-frequency QPOs in GRS 1915+105 are consistent with a ring of radius R ~ 10M orbiting a black hole with spin a/M ~0.5 and inclination angle of i ~ 70 deg. Finally, we describe how future X-ray missions may be able to use simultaneous timing and spectroscopic observations to measure the black hole spin and probe the inner-most regions of the accretion disk.