Global Structure and Dynamics of Advection-Dominated Accretion Flows   Around Black Holes
  We present global solutions that describe advection-dominated accretion flows around black holes. The solutions are obtained by numerically solving a set of coupled ordinary differential equations corresponding to a steady axisymmetric height-integrated flow. The solutions satisfy consistent boundary conditions at both ends. We obtain well-behaved transonic solutions for a wide range of values of the viscosity parameter $\alpha$, from 0.001 to 0.3. We do not find any need for shocks in our solutions, and disagree with previous claims that viscous accretion flows with low values of $\alpha$ must have shocks. We see a qualitative difference between solutions with low values of the viscosity parameter, $\alpha\ \sles\ 0.01$, and those with large values, $\alpha\sgreat\ 0.01$. The solutions with low $\alpha$ have their sonic transitions occurring close to the radius of the marginally bound orbit. These flows are characterized by regions of super-Keplerian rotation, and have pressure maxima outside the sonic point. The solutions are similar in many respects to the hydrostatic thick tori developed previously as models of active galactic nuclei. In contrast, the solutions with large $\alpha$ have sonic transitions farther out, close to or beyond the marginally stable orbit, and have no super-Keplerian rotation or pressure maxima. We believe these flows will be nearly quasi-spherical down to the sonic radius and will not have empty funnels along the rotation axis. The large $\alpha$ solutions are more likely to be representative of real systems. 
Ramesh Narayan, Shoji Kato and Fumio Honma