Global solutions of advection-dominated accretion flows with two critical points

This paper presents global solutions of advection-dominated accretion flows (ADAFs) around black holes. The global solution passes through two critical points, the sonic point Rs and viscous point Rv and is thus naturally divided by these points into three radial zones: the subsonic, subviscous outer zone (R > Rv), the subsonic, superviscous middle zone (Rs < R < Rv), and the supersonic, superviscous inner zone (R < Rs). We have obtained a complete picture by means of the Rs — j parameter space which sums up the situation of ADAF solution at a glance. We find three classes of global solutions: the ADAF-thin disk solution, the ADAF-thick disk solution and the α — X type adiabatic shock-included solution. We also present the unique correspondences among Rs, Rv and Rout of the ADAF-thin disk solutions, where Rout is the outer boundary of ADAF. The adiabatic shock in the accretion flow connects the supersonic and superviscous zone of an X-type solution to the subsonic and superviscous zone of an α-type soultion. Because the shock occurs between two superviscous zones, it can exist for flows with either a low or a high viscosity.