Transition of accretion flow from Keplerian phase to advective phase as a dynamical system

A model for the transition of Keplerian accretion flow to advective phase is proposed. The advective fluid particle in the Keplerian accretion background is modelled using two-phase hydrodynamics. The hydrodynamic equations for the advective phase is reduced to a non-linear dynamical system. For small fluctuation of advective nature for sufficiently small time, a linearized dynamical system in density and radial velocity is obtained. The fluctuation is found to be linearly growing for suitable choice of the values of free parameters. The linear growth is studied as a function of the angular Mach number of the background Keplerian accretion flow. The other parameters of the dynamical system are the radial Mach number of the Keplerian accretion flow, viscosity parameters and gas constants of the Keplerian phase as well as the advective phase and the angular velocity profile of the advective fluid particle. The location of the transition region between Keplerian accretion flow and advective accretion flow is parametrized by the radial Mach number and the angular Mach number of the Keplerian accretion flow. The Keplerian accretion flow is found to be linearly unstable against transition to advective phase only if the radial Mach number greater than or of the order of 10−3. Since radial velocity has no dynamical relevance in Keplerian accretion flow (radial Mach number is very small, and the radial velocity comes only as a drift velocity in the equation of continuity), this means that such a transition is possible only at much inner part of the accretion disc. Appreciable linear growth of the advective fluctuation is possible only if the viscosity parameter of the advective phase has high or intermediate value. This could severely restrict the plausible branches of global solution of the inner advective accretion disc.