Viscous Torque and Dissipation in the Inner Regions of a Thin Accretion Disk: Implications for Measuring Black Hole Spin

We consider a simple Newtonian model of a steady accretion disk around a black hole. The model is based on height-integrated hydrodynamic equations, α-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 α 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 α ≤ 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. We find that the contrast in density and thickness in the hydrodynamic models is low for H/R ∼ 0.1. This suggests that the iron line technique requires an extremely thin disk for reliable results. Subject headings: X-ray: stars — binaries: close — accretion, accretion disks — black hole physics Harvard University, Department of Physics, 17 Oxford Street, Cambridge, MA 02138 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138