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 solving numerically a set of coupled ordinary differential equations corresponding to a steady axisymmetric height-integrated flow. The solutions satisfy consistent boundary conditions at both ends. On the inside, the flow passes through a sonic point and falls supersonically into the black hole with a zero-torque condition at the horizon. On the outside, the how attaches to a normal thin accretion disk. We obtain consistent transonic solutions for a wide range of values of the viscosity parameter a, from 0.001 to 0.3. We do not find any need for shocks in our solutions, and we disagree with previous claims that viscous accretion flows with low values of alpha must have shocks. We compare the exact global solutions of this paper with a local self-similar solution that has been studied in the past. Although the self-similar solution makes significant errors close to the boundaries, we find that it provides nevertheless a reasonable description of the overall properties of the how. We compare also two different forms of viscosity: one is based on a diffusion prescription, while the other takes the shear stress to be simply proportional to the pressure. The results with the two prescriptions are similar. We see a qualitative difference between solutions with low values of the visocity parameter, alpha less than or similar to 0.01, and those with large values, alpha greater than or similar to 0.01. The solutions with low a 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, since most observations of astrophysical systems are best fit, within the context of advection-dominated theories, with values of alpha greater than or similar to 0.1.