UPPER LIMIT OF THE VISCOSITY PARAMETER IN ACCRETION FLOWS AROUND A BLACK HOLE WITH SHOCK WAVES

Black hole accretion is necessarily transonic; thus, flows must become supersonic and, therefore, sub-Keplerian before they enter into the black hole. The viscous timescale is much longer than the infall timescale close to a black hole. Hence, the angular momentum remains almost constant and the centrifugal force similar to l(2)/r(3) becomes increasingly dominant over the gravitational force similar to 1/r(2). The slowed down matter piles creating an accretion shock. The flow between shock and inner sonic point is puffed up and behaves like a boundary layer. This socalled Comptonizing cloud/corona produces hard X-rays and jets/outflows and, therefore, is an important component of black hole astrophysics. In this paper, we study steady state viscous, axisymmetric, transonic accretion flows around a Schwarzschild black hole. We adopt a viscosity parameter a and compute the highest possible value of alpha (namely, alpha(cr)) for each pair of two inner boundary parameters (namely, specific angular momentum carried to horizon, l(in) and specific energy at inner sonic point, E(x(in))) which is still capable of producing a standing or oscillating shock. We find that while such possibilities exist for a as high as alpha(cr) = 0.3 in very small regions of the flow parameter space, typical acr appears to be about similar to 0.05-0.1. Coincidentally, this also happens to be the typical viscosity parameter achieved by simulations of magnetorotational instabilities in accretion flows. We therefore believe that all realistic accretion flows are likely to have centrifugal pressure supported shocks unless the viscosity parameter everywhere is higher than a(cr).