We show that most of hot, optically thin accretion disk models which ignore advective cooling are not self-consistent. We have found new types of optically thin disk solutions where cooling is dominated by radial advection of heat. These new solutions are thermally and viscously stable.

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 amplification of disk oscillations resulting from non-linear resonant couplings between the oscillations and a warp is examined. The disks are geometrically thin and general relativistic with non-rotating central objects. By using a Lagrangian formulation, a general stability criterion is derived. The criterion is applied to horizontal and vertical resonances of g-mode oscillations and to horizontal resonances of p-mode oscillations. The results of analyses show that g-mode oscillations (including p-mode oscillations of n = 0) are amplified by horizontal resonances with the warp. Other modes of oscillations with other resonances are all damped by resonances. The amplified g-mode oscillations are located around the radius 4r g , the radius of the epicyclic frequency being maximum, i.e., κ max . The frequencies of amplified oscillations are harmonics of κ max , and well explain the 2 : 3 pairs of observed QPOs for reasonable masses (and spins) of the central objects.

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In this paper oscillations on geometrically thin disks are reviewed, focusing on two issues. One is the characteristics of disk oscillations. The other is possible excitation mechanisms of these oscillations. The main purpose of this paper is to clarify the physics and dynamics involved in these issues. We consider both Newtonian and general-relativistic disks, since a comparison of the oscillations on both disks clarifies the differences among these two oscillations and is helpful for understanding the unique properties of relativistic disks. Furthermore, we sometimes refer to stellar oscillations, since a comparison with stellar oscillations is helpful to have a deeper understanding of the disk oscillations, especially of the excitation mechanisms.

Twin quasi-periodic millisecond modulations of the X-ray flux (kHz QPOs) have recently been reported from an accreting 2.5 ms X-ray pulsar. We identify modes of disk oscillations whose frequencies are in agreement with the observed ones when the rotating neutron star is modeled with realistic equations of state. The frequency difference of the twin QPOs, equal to about one half of the neutron-star spin rate, clearly indicates that resonant oscillations of the accretion disk have been observed. Similar non-linear resonances may also be spontaneously excited in the accretion disk. The two QPO frequencies in the pulsar system are close to a 5:7 ratio and this suggests a link with the QPOs in black hole systems, where frequency ratios of 2:3 and 3:5 have been reported.

The "radiation inner edge" of an accretion disk is defined as the inner boundary of the region from which most of the luminosity emerges. Similarly, the "reflection edge" is the smallest radius capable of producing a significant X-ray reflection of the fluorescent iron line. For black hole accretion disks with very sub-Eddington luminosities these and all other "inner edges" coexist at the innermost stable circular orbit (ISCO). Thus, in this case, one may rightly consider ISCO as the unique inner edge of the black hole accretion disk. However, even at moderate luminosities, there is no such unique inner edge because differently defined edges are located at different places. Several of them are significantly closer to the black hole than ISCO. These differences grow with the increasing luminosity. For nearly Eddington luminosities, they are so huge that the notion of the inner edge loses all practical significance.