Global dynamics of advection-dominated accretion revisited

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 flow Rs and the integration constant in angular momentum equation j as free parameters and integrate the equations from the sonic point inward to see if the solution can extend supersonically to the black hole horizon and outward to see if and where an acceptable outer boundary of the flow can be found. We recover the ADAF-thin disk solution constructed by Narayan, Kato, & Honma in a paper representative of previous works on global ADAF solutions, although in that paper an apparently very different procedure was adopted. The use of our method has the following advantages. First, we obtain all the solutions belonging to the ADAF-thin disk class, not only some examples, as in the paper by Narayan and colleagues. Second, we find other classes of solutions that were not noticed by these authors, namely, an ADAF-thick disk solution, in which an ADAF connects outward to a thick disk, and an α-type solution, which can extend either only to the black hole horizon or only to the outer boundary. The ADAF-thick disk solution may have astrophysical implications in view of the fact that in some cases models based on the ADAF-thin disk solution encounter some difficulties. The α-type solution is also worth studying, in the sense that such a solution could be a part of a shock-included global solution. Apart from all these classes of solutions, there are definite ranges of incorrect values of Rs and j for which no solutions exist at all. Taking all these results together, we obtain a complete picture in the form of Rs-j parameter space, which sums up the situation of ADAF solution at a glance. For comparison we also present the distribution of global solutions for inviscid flows in the Rs-j space, which supports the view that there should be some similarities between the dynamical behavior of ADAFs and that of adiabatic flows, and that there should be a continuous change from the properties of viscous flows to those of inviscid ones.