Ja n 20 06 Radiation Transport Around Kerr Black Holes

This Thesis describes the basic framework of a relativistic ray-tracing code for analyzing accretion processes around Kerr black holes. We begin in Chapter 1 with a brief historical summary of the major advances in black hole astrophysics over the past few decades and outline some of the important questions still open today. In Chapter 2 we present a detailed description of the ray-tracing code, which integrates the geodesic equations of motion for massless particles, tabulating the position and momentum along each photon trajectory. Coupled with an independent model for the emission and absorption at each point in spacetime, time-dependent images and spectra can be produced by integrating the radiative transfer equation along these geodesic photon paths. This approach can be used to calculate the transfer function between the plane of the accretion disk and the detector plane, an important tool for modeling relativistically broadened emission lines. Observations from the Rossi X-Ray Timing Explorer have shown the existence of high frequency quasi-periodic oscillations (HFQPOs) in a growing number of black hole binary systems. In Chapter 3, we employ a simple “hot spot” model to explain the position and amplitude of these HFQPO peaks. Using the exact geodesic equations of motion for the Kerr metric, we calculate the trajectories of massive test particles, which are treated as isotropic, monochromatic emitters in their rest frames, imaged with the ray-tracing code described above. The power spectrum of the periodic X-ray light curve consists of multiple peaks located at integral combinations of the black hole coordinate frequencies. Additionally, we model the effects of shearing the hot spot in the disk, producing an arc of emission that also follows a geodesic orbit. By including non-planar orbits that experience Lense-Thirring precession, we investigate the possible connection between high and low frequency QPOs. In Chapter 4, we introduce additional features to the hot spot model to explain the broadening of the QPO peaks as well as the damping of higher frequency harmonics in the power spectrum. We present a number of analytic results that agree closely with more detailed numerical calculations. Three primary pieces are developed: the addition of multiple hot spots with random phases, a finite width in the distribution of geodesic orbits, and the scattering of photons from the hot spot through a corona