On the Structure of Advective Accretion Disks at High Luminosity

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Abstract
Global solutions of optically thick advective accretion disks around black holes are constructed. The solutions are obtained by solving numerically a set of ordinary differential equations corresponding to a steady, axisymmetric, geometrically thin disk. We pay special attention to consistently satisfying the regularity conditions at singular points of the equations. For this reason, we analytically expand the solution at the singular point and use coefficients of the expansion in our iterative numerical procedure. We obtain consistent transonic solutions for a wide range of values of the viscosity parameter α and mass accretion rate. We compare results for two different prescriptions for the viscosity: the first is to assume that the shear stress is proportional to the pressure, and the other is to assume that it is proportional to the gradient of the angular velocity. We find that there are two singular points in the solutions corresponding to a shear stress proportional to the pressure. The inner singular point is located close to the last stable orbit around the black hole. This point changes its type from a saddle to node depending on the value of α and the accretion rate. The outer singular point is located at a larger radius and is always of the saddle type. We argue that, contrary to the previous investigations, a nodal-type inner singular point does not introduce multiple solutions. Only one integral curve, which corresponds to the unique global solution, simultaneously passes the inner and outer singular points independently of the type of inner singular point. Solutions for the case when shear stress is proportional to the angular velocity gradient have one singular point which is always of the saddle type and corresponds to the unique global solution. The structure of accretion disks corresponding to the two prescriptions for the viscous stress are similar.
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