Global Dynamics of Advection-dominated Accretion Revisited

We numerically solve the set of dynamical equations describing advectiondominated accretion flows (ADAF) around black holes, using a method similar to that of Chakrabarti (1996a). 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 inwards to see if the solution can extend supersonically to the black hole horizon, and outwards to see if and where an acceptable outer boundary of the flow can be found. We recover the ADAF-thin disk solution constructed in Narayan, Kato, & Honma (1997, NKH97), an representative paper of the 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 NKH97. Second, we find other classes of solutions that were not noticed in NKH97, namely the ADAF-thick disk solution in which an ADAF connects outwards to a thick disk, and the 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 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