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

Abstract

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 R s and viscous point R v and is thus naturally divided by these points into three radial zones: the subsonic, subviscous outer zone ( R > R v ), the subsonic, superviscous middle zone ( R s < R < R v ), and the supersonic, superviscous inner zone ( R < R s ). We have obtained a complete picture by means of the R s — 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 R s , R v and R out of the ADAF-thin disk solutions, where R out 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.