Previous
abstract 
Next
abstract
The coupled hydrodynamic equations governing equatorial flows in thin disk accretion in the Schwarzschild metric are developed and studied under isothermal conditions. The transonic solutions representing physically allowed accretion onto black holes and the location of the sonic point are investigated. For a certain range of angular momentum, there exist two physical sonic points. A shock can occur between the two sonic points. The entire solution with a shock still satisfies the condition for black hole accretion, which requires supersonic flow near the black hole horizon.
The jump condition across the shock will be modified by the relativistic effects only when the sound speed is comparable to the speed of light. The necessary condition for the presence of a shock is also changed from the classical condition $M>1$ where $M$ is the Mach number to the relativistic condition $M>M_{c}$ where $M_{c}>1$ is a value depending on the ratio of the sound speed to the speed of light. Stability analysis shows that only one of the two possible shocks between the two sonic points is stable. Isothermal shocks are used to explain the QPO behavior in black hole candidates such as Cygnus X-1, Nova Muscae and GX339-4.
