Global dynamics of advection-dominated accretion revisited

We numerically solve the set of dynamical equations describing advection-do minated accretion flows (ADAFs) around black holes, using a method similar to that of Chakrabarti. We choose the sonic radius of the flow R-s 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 a nd where an acceptable outer boundary of the how can be found. We recover t he ADAF-thin disk solution constructed by Narayan, Kato, & Honma in a paper representative of previous works on global ADAF solutions, although in tha t paper an apparently very different procedure was adopted. The use of our method has the following advantages. First, we obtain all the solutions bel onging to the ADAF-thin disk. class, not only some examples, as in the pape r by Narayan and colleagues. Second, we find other classes of solutions tha t were not noticed by these authors, namely, an ADAF-thick disk solution, i n which an ADAF connects outward to a thick disk, and an alpha-type solutio n, which can extend either only to the black hole horizon or only to the ou ter boundary; The ADAF-thick disk solution may have astrophysical implicati ons in view of the fact that in some cases models based on the ADAF-thin di sk solution encounter some difficulties. The alpha-type solution is also wo rth 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 R-s and j for which no solution s exist at all. Taking all these results together, we obtain a complete pic ture in the form of R-s-j parameter space, which sums up the situation of A DAF solution at a glance. For comparison we also present the distribution o f global solutions for inviscid hows in the R-s-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 continuou s change from the properties of viscous flows to those of inviscid ones.