The structure and stability of transonic accretion disks surrounding black holes

Stationary transonic α-viscosity models of accretion disks surrounding nonrotating black holes have been investigated. The viscosity is modified such that it vanishes in the supersonic region to ensure its effect does not violate the causality condition. In contrast to previous studies, the viscous stress is taken to be explicitly proportional to the angular velocity gradient, dΩ/dr, and is not assumed to depend solely on the local pressure in the disk. The numerical results reveal that the structure of the innermost regions of the disk are more sensitive to the modified form of the viscosity than to the form of the viscous stress. The critical sonic point is located inside the innermost stable circular orbit of a test particle at 3 Schwarzschild radii. In these solutions, the transition from subsonic to supersonic flow results from pressure effects and not viscous effects. The linear stability of these disks has been examined in the local approximation. It is found that radiative energy transport and viscous stresses in the radial direction can have important effects. As a result, it is shown that the growth rate of the inertial-acoustic mode reaches a maximum (∼1-4αΩ_K, where Ω_K is the local Keplerian angular velocity) at a critical wavelength, λ_c (with λ_c ∼ 5-10H, where H is the local scale height of the disk). For wavelengths shorter than ∼3-5H, the inertial-acoustic mode is stabilized.