Disc accretion shocks with alpha viscosity

Abstract

ABSTRACT Shocks in rotating disc accretion flows under the vertically hydrostatic equilibrium are examined, taking into account the α viscosity. For the case that the stress tensor is proportional to the gas pressure, and neglects the effects of the mixture of gas and radiation pressure, we derive analytical expressions for jump conditions of disc accretion shocks with alpha viscosity; they would be useful for various disc accretion problems. As in the usual accretion disc, the alpha viscosity works as angular momentum transport and heat generation. When a steadily standing shock wave is generated in a disc, due to the viscous effect, the azimuthal velocity discontinuously decreases in the post-shock region inside the front. For sufficiently strong shocks, the post-shock azimuthal velocity vanishes; in other words, the rotating accretion flows turn to the radially accretion ones, after passing the shock front. This vanishing condition is roughly expressed as $\alpha {\cal M}_1/{\cal M}_{\varphi 1}$ 1, where α is the viscous alpha parameter, ${\cal M}_1$ the pre-shock radial Mach number, and ${\cal M}_{\varphi 1}$ the pre-shock azimuthal Mach number. Furthermore, due to the viscous heating, the disc height increases and the surface density decreases in the post-shock region, compared to the non-viscous case. This angular momentum transport via disc shocks would affect the accretion spin-up of the central objects and accretion problems in general.