A systematic study of the standing shocks in astrophysical flows near a compact object

We have systematically studied both standing dissipative and non-dissipative shocks and isentropic compression waves in thin, rotating, adiabatic astrophysical flows, such as the accretion or winds near black holes and neutron stars. The flow is assumed to be in transverse equilibrium and the dissipation is allowed only at the shocks. We classify the whole parameter space spanned by the accretion rate (M), the energy (E), and the angular momentum (λ) according to whether a shock solution can exist or not. Apart from conserving the baryon flux and the net momentum flux, flows at these discontinuities (collectively referred to as 'shocks') may conserve energy (Rankine-Hugoniot shocks), entropy (isentropic compression waves), or just be isothermal (isothermal shocks) according to three extreme physical processes which may take place near the shocks. We also show that for given pre- and post-shock parameters the shock locations are not unique. We derive an invariant Mach number relation at the shock and from this show that the shocks in this model cannot be arbitrarily weak. We perform a local stability analysis to show that some of the shocks are unstable. In most cases, the local analysis is not capable of resolving the issue concerning the non-uniqueness of shock locations. (author)