We present global solutions that describe advection-dominated accretion ows around black holes. The solutions are obtained by numerically solving a set of coupled ordinary di erential equations corresponding to a steady axisymmetric height-integrated ow. The solutions satisfy consistent boundary conditions at both ends. On the inside, the ow passes through a sonic point and falls supersonically into the black hole with a zero-torque condition at the horizon. On the outside, the ow attaches to a normal thin accretion disk.We obtain consistent transonic solutions for a wide range of values of the viscosity parameter , from 0.001 to 0.3. We do not nd any need for shocks in our solutions, and disagree with previous claims that viscous accretion ows with low values of must have shocks.We compare the exact global solutions of this paper with a local self-similar solution which has been studied in the past. Although the self-similar solution makes signi cant errors close to the boundaries, we nd that it nevertheless provides a reasonable description of the overall properties of the ow. We also compare two di erent forms of viscosity; one is based on a di usion 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 di erence between solutions with low values of the viscosity parameter, < 0:01, and those with large values, > 0:01. The solutions with low have their sonic transitions occurring close to the radius of the marginally bound orbit. These ows 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 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 ows will be nearly quasi-spherical down to the sonic radius and will not have empty funnels along the rotation axis. The large solutions are more likely to be representative of real systems since most observations of advection-dominated ows in astrophysical sources indicate values of > 0:1.

The global structure of accretion disks around a stellar-mass black hole is examined while taking into account the energy transport by means of diffusion, as well as that by means of radial flow. It is shown that the model can have two types of solutions: In one type, the whole disk is cool and is optically thick; in the other, the disk has a hot optically thin inner region. The structure of the hot inner region of the latter is examined and an analytic formula for the location of the interface of the hot and cold region is obtained. The stability of the latter is also discussed briefly. This behavior of the model can be a possible explanation for the bimodal behavior observed in the X-ray spectra of black hole candidates.

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A b s t r a c t . The innermost region of slim accretion disks with standard a viscosity is unstable against axisymmetric radial inertial acoustic perturbations under certain conditions. Numerical simulations are performed in order to demonstrate behaviors of such unstable disks. It is shown that oscillations with the period of ~ 1 0 -3 ( M B H / -M © ) S can be excited near the inner edge of the disks, where MBH is the mass of the central object. This kind of unstable disks is a possible origin of the periodic X-ray time variabilities with period of ~ 10 4 s observed in a Seyfert galaxy NGC 6814.

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