Radial Shocks in Advection-Dominated Accretion FlowsAround Black Holes

We have solved the set of equations for advection-dominated accretion flows (ADAFs) around black holes, and found a new class of global solutions with standing radial shocks.Such α-X-type shocks may exist in flows when 0 ≤ α < 0.05. An example solution is given explicitly, for which α=0.01 and γ=1.5. The shock position is R_sh=8.68R_g, which is between the inner sonic point R_s1=3.88R_g and the outer sonic point R_s2=85.92R_g.