Multitemperature Blackbody Spectrum of a Thin Accretion Disk around a Kerr Black Hole: Model Computations and Comparison with Observations

We use a ray-tracing technique to compute the observed spectrum of a thinaccretion disk around a Kerr black hole. We include all relativistic effectssuch as frame-dragging, Doppler boost, gravitational redshift, and bending oflight by the gravity of the black hole. We also include self-irradiation of thedisk as a result of light deflection. Assuming that the disk emission islocally blackbody, we show how the observed spectrum depends on the spin of theblack hole, the inclination of the disk, and the torque at the inner edge ofthe disk. We find that the effect of a nonzero torque on the spectrum can, to agood approximation, be absorbed into a zero-torque model by adjusting the massaccretion rate and the normalization. We describe a computer model, calledKERRBB, which we have developed for fitting the spectra of black hole X-raybinaries. Using KERRBB within the X-ray data reduction package XSPEC, andassuming a spectral hardening factor f_col = 1.7, we analyze the spectra ofthree black hole X-ray binaries: 4U1543-47, XTE J1550-564, and GRO J1655-40. Weestimate the spin parameters of the black holes in 4U1543-47 and GRO J1655-40to be a/M ~ 0.6 and ~ 0.6-0.7, respectively. If f_col ~ 1.5-1.6, as in a recentstudy, then we find a/M ~ 0.7-0.8 and ~ 0.8-0.9, respectively. These estimatesare subject to additional uncertainties in the assumed black hole masses,distances and disk inclinations.