Locations of Sonic Points in Advection Dominated Accretion Flows Around Black Holes

The global transonic solutions describing advection dominated accretion flows around black holes are obtained by directly integrating the set of differential equations from the sonic point inward to the horizon and outward.The results show that the sonic points can locate themselves at almost any radius,regardless of the viscous parameter a and polytropic indexγ.This result is greatly different with previous ones.Example solutions with very different values of R_(s)from 4.3 to 300R_(g) and withγ=1.5,5/3 are given explicitly.The consistency between this result and that in inviscid flows is emphasized.