Quasi-viscous accretion flow - I. Equilibrium conditions and asymptotic behaviour

Abstract

In a novel approach to studying viscous accretion flows, viscosity has been introduced as a perturbative effect, involving a first-order correction in the α-viscosity parameter. This method reduces the problem of solving a second-order non-linear differential equation (Navier–Stokes equation) to that of an effective first-order equation. Viscosity breaks down the invariance of the equilibrium conditions for stationary inflow and outflow solutions, and distinguishes accretion from wind. Under a dynamical systems classification, the only feasible critical points of this ‘quasi-viscous’ flow are saddle points and spirals. On large spatial scales of the disc, where a linearized and radially propagating time-dependent perturbation is known to cause a secular instability, the velocity evolution equation of the quasi-viscous flow has been transformed to bear a formal closeness with Schrödinger's equation with a repulsive potential. Compatible with the transport of angular momentum to the outer regions of the disc, a viscosity-limited length-scale has been defined for the full spatial extent over which the accretion process would be viable.