We describe three-dimensional general relativistic magnetohydrodynamic simulations of a geometrically thin accretion disk around a non-spinning black hole. The disk has a thickness $h/rsim0.05-0.1$ over the radial range $(2-20)GM/c^2$. In steady stat
e, the specific angular momentum profile of the inflowing magnetized gas deviates by less than 2% from that of the standard thin disk model of Novikov & Thorne (1973). Also, the magnetic torque at the radius of the innermost stable circular orbit (ISCO) is only $sim2%$ of the inward flux of angular momentum at this radius. Both results indicate that magnetic coupling across the ISCO is relatively unimportant for geometrically thin disks.
We consider a simple Newtonian model of a steady accretion disk around a black hole. The model is based on height-integrated hydrodynamic equations, alpha-viscosity, and a pseudo-Newtonian potential that results in an innermost stable circular orbit
(ISCO) that closely approximates the one predicted by GR. We find that the hydrodynamic models exhibit increasing deviations from the standard disk model of Shakura & Sunyaev as disk thickness H/R or the value of alpha increases. The latter is an analytical model in which the viscous torque is assumed to vanish at the ISCO. We consider the implications of the results for attempts to estimate black hole spin by using the standard disk model to fit continuum spectra of black hole accretion disks. We find that the error in the spin estimate is quite modest so long as H/R < 0.1 and alpha < 0.2. At worst the error in the estimated value of the spin parameter is 0.1 for a non-spinning black hole; the error is much less for a rapidly spinning hole. We also consider the density and disk thickness contrast between the gas in the disk and that inside the ISCO. The contrast needs to be large if black hole spin is to be successfully estimated by fitting the relativistically-broadened X-ray line profile of fluorescent iron emission from reflection off an accretion disk. In our hydrodynamic models, the contrast in density and thickness is low when H/R>0.1, sugesting that the iron line technique may be most reliable in extemely thin disks. We caution that these results have been obtained with a viscous hydrodynamic model and need to be confirmed with MHD simulations of radiatively cooled thin disks.
We have used the Novikov-Thorne thin disk model to fit the continuum X-ray spectra of three transient black hole X-ray binaries in the thermal state. From the fits we estimate the dimensionless spin parameters of the black holes to be: 4U 1543-47, a*
= a/M = 0.7-0.85; GRO J1655-40, a* = 0.65-0.8; GRS 1915+105, a* = 0.98-1. We plan to expand the sample of spin estimates to about a dozen over the next several years. Some unresolved theoretical issues are briefly discussed.
