Multi-Temperature 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 thin accretion disk around a Kerr black hole. We include all relativistic effects such as frame-dragging, Doppler boost, gravitational redshift, and bending of light by the gravity of the black hole. We also include self-irradiation of the disk as a result of light deflection. Assuming that the disk emission is locally blackbody, we show how the observed spectrum depends on the spin of the black hole, the inclination of the disk, and the torque at the inner edge of the disk. We find that the effect of a nonzero torque on the spectrum can, to a good approximation, be absorbed into a zero-torque model by adjusting the mass accretion rate and the normalization. We describe a computer model, called KERRBB, which we have developed for fitting the spectra of black hole X-ray binaries. Using KERRBB within the X-ray data reduction package XSPEC, and assuming a spectral hardening factor f_col = 1.7, we analyze the spectra of three black hole X-ray binaries: 4U1543-47, XTE J1550-564, and GRO J1655-40. We estimate the spin parameters of the black holes in 4U1543-47 and GRO J1655-40 to be a/M ~ 0.6 and ~ 0.6-0.7, respectively. If f_col ~ 1.5-1.6, as in a recent study, then we find a/M ~ 0.7-0.8 and ~ 0.8-0.9, respectively. These estimates are subject to additional uncertainties in the assumed black hole masses, distances and disk inclinations.