We obtain global solutions for radiatively inefficiently accretion flows around black holes. Whether and where convection develops in a flow are self-consistently determined by mixinglength theory. The solutions can be divided into three types according to the strength of normal viscosity. Type I solutions correspond to large viscosity parameter α 0.1-they are purely advection-dominated with no convection; they have been extensively studied in the literature. Type II solutions are for moderate α 0.01, and have a three-zone structure. The inner zone is advection-dominated, the middle zone is convection-dominated and ranges from a few tens to a few thousands of gravitational radii, and the outer zone is convectively stable and outwardly matches a Keplerian disc. The net energy flux throughout the flow is inward, as in type I solutions. Type III solutions, which are for small α 0.001, consist of two zones as Abramowicz et al. suggested previously: an inner advection-dominated zone and an outer convection-dominated zone, separated at a radius of a few tens of gravitational radii. This type of solution has an outward net energy flux. In both type II and type III solutions, the radial density profile is between the 1/2 law of the self-similar convection-dominated accretion flow model and the 3/2 law of the self-similar advection-dominated accretion flow model, and the efficiency of energy release is found to be extremely low. Our results are in good agreement with those of recent numerical simulations.

We numerically solve the set of dynamical equations describing advection-dominated accretion flows (ADAFs) around black holes, using a method similar to that of Chakrabarti. We choose the sonic radius of the

This paper presents global solutions of adiabatic accretion flows with isothermal shocks in Kerr black hole geometry. It is known that in the previously studied cases, where the flow including the shock is either entirely adiabatic or entirely isothermal, there can be no more than one stable shock solution, and the solution can only be of a-x type. However, the solution topology in the present case shows remarkable new characteristics: for the same flow parameters there can be two stable shock solutions satisfying physical boundary conditions, and the solution can be of three types, namely a-x, x-a and a-a type. In addition, shocks in the present case occur for a parameter region different from that for Rankine-Hugoniot shocks. These results greatly increase the possibilities of shock formation in astrophysical flows. It is also significant that the effects of frame-dragging of a rapid Kerr black hole on the shock formation are discovered. Finally, a brief comparison is made between shocked inviscid flows and two types of shock-free viscous flows, namely those of Shakura & Sunyaev and Narayan & Yi, and some comments are made about the fact that numerous authors who have studied transonic global solutions of accretion flows have found no shocks.

This paper presents a fully relativistic study on the standing shock formation in thin, stationary, axisymmetric, adiabatic fluid flows in Kerr geometry. Wend out the energyangular momentum parameter space for which the flow may develop shocks. The multiplicity of the formal shock location is removed by employing the boundary conditions and stability analysis: the stable shock location is practically unique. The effects of the frame-dragging of a rapid rotating black hole on the shock properties are pointed out. Finally, we discuss the validity of the assumptions made about the flow and conclude that shocks are likely to be common in astrophysical flows.

This paper presents global solutions of adiabatic accretion flows with isothermal shocks in the potential of a non-rotating black hole. It is known that in the previously studied cases, where flow including shock is either entirely adiabatic or entirely isothermal, there can be no more than one stable shock solution, and the solution can only be of the a-x type; however, the solution topology in the present case shows new remarkable characteristics: for the same flow parameters there can be two stable shock solutions satisfying the physical boundary conditions, and the solution can be of three types, namely a-x, x-a, and a-a type. In addition, shocks in the present case occur for a parameter region that is different from that for RankineHugoniot shocks to occur. These results greatly increase the possibilities of shock formation in astrophysical flows. It is also noted that in the present case the efficiency of energy release at the shock can be as high as a few percent. Finally, a brief comparison is made between shocked inviscid flows and two types of shock-free viscous flow, namely that of Shakura and Sunyaev (1973, AAA 09.066.049) and that of Narayan and Yi (1994, AAA 61.064.083).

We clarify the concept of Keplerian circular motion of fluidsin the theory of general relativity, showing how it overlaps with as well as differs from the counterpart in the particle case. Applying the concept to the study of accretion disks, we prove a constraint on the sonic transition of accretion flows.

The motion of adiabatic jets propagating along the symmetry axis of a Kerr black hole is studied in the case where the outflowing matter possesses angular momentum. A simple parametrization is used for the cross-sectional area of the jets and the results applied to conical and paraboloidal jets. Inclusion of angular momentum in the outflowing material has the effect of shifting the critical point inward closer to the black hole, thus contributing to the radial acceleration of the flow. When the black hole is rotating, this inward shift is more pronounced for direct flows than retrograde ones: for a maximally rotating Kerr hole, the relative shift (with respect to a Schwarzschild black hole) varies from about 12% to 30% for the range of values of angular momentum considered. Rotation in the outflowing matter has the effect of reducing the mass outflow rate. Other parameters being the same, conical jets have their critical points considerably closer to the black hole than paraboloidal jets.

The disk-driven precession model, proposed originally for SS 433 by Sarazin et al. (1980), is applied to extragalactic radio jets. Byeresenting a statistical relationship between the precession period and optical luminosity fo the sources, it is shown that the observational evidence is in favor of the model.

Transonic motion of adiabatic jets from funnels of thick accretion disks around Kerr black holes is studied. Provided the matter at the bottom of the funnel possesses a high enough enthalpy, the location of the sonic point of the flow can be very close to its lower limit, and an extremely relativistic terminal velocity can be achieved.

Received September 10, 1984; accepted February 12, 1985 Summary. The fact that the adiabatic transonic accretion of rotating matter onto a black hole has non-unique, bimodal, solution was demonstrated previously only in terms of an approximate, Newtonian, model. Here the correct generalrelativistic equations are used to prove the bimodal character of accretion onto a Schwarzschild black hole.