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On the Structure of Advective Accretion Disks At High Luminosity
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 satisfy the
regularity conditions at singular points of the equations. For this reason we
analytically expand a solution at the singular point, and use coefficients of
the expansion in our iterative numerical procedure. We obtain consistent
transonic solutions in a wide range of values of the viscosity parameter alpha
and mass acretion rate. We compare two different form of viscosity: one takes
the shear stress to be proportional to the pressure, while the other uses the
angular velocity gradient-dependent stress.
We find that there are two singular points in solutions corresponding to the
pressure-proportional shear stress. The inner singular point locates close to
the last stable orbit around black hole. This point changes its type from a
saddle to node depending on values of alpha and accretion rate. The outer
singular point locates at larger radius and is always of a 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, passes simultaneously the
inner and outer singular points independently of the type of inner singular
point. Solutions with the angular velocity gradient-dependent shear stress have
one singular point which is always of a saddle-type and corresponds to the
unique global solution. The structure of accretion disks corresponding to both
viscosities are similar.Comment: 20 pages, 6 figures, submitted to Ap