Multi-transonic Black Hole Accretion Discs with Dissipative Standing Shocks

In this work we would like to address the issue of shock formation in black hole accretion discs. We provide a {\it generalized two parameter solution scheme} for multi-transonic, isothermal accretion and wind around Schwarzschild black holes, by mainly concentrating on accretion solutions which may contain steady, standing dissipative shocks. By `dissipative' shock, we mean a shock solution which conserves flow temperature in expense of energy dissipation at shock location. Unlike previous works in this field, our calculation is {\it not} restricted to any particular kind of post-Newtonian gravitational potentials, rather we use {\it all} available pseudo-Schwarzschild potentials to formulate and solve the equations governing the accretion and wind only in terms of flow temperature $T$ and specific angular momentum $\lambda$ of the flow. Our generalized formalism assures that the shock formation is not just an artifact of a particular type of gravitational potential, rather inclusion of all available black-hole potentials allows a substantially extended zone of parameter space allowing for the possibility of shock formation. We thus arrive at the conclusion that the dissipative standing shocks are essential ingredients in rotating advective accretion flows of isothermal fluid around a non-spinning astrophysical black hole. We clearly identify {\it all} possible shock solution which may be present in isothermal disc accretion and throughly study the dependence of various shock parameters on fundamental dynamical variables governing the accretion flow for {\it all} possible initial boundary conditions. The results are discussed in connection to other astrophysical phenomena of related interest, the QPO behaviour of galactic black hole candidates for example.