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 $\alpha$-viscosity parameter. This method reduces the problem of solving a second-order nonlinear 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. A linearised and radially propagating time-dependent perturbation gives rise to secular instability on large spatial scales of the disc. Further, on these same length scales, 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.

15 pages

References in corpus (11)

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• Critical properties and stability of stationary solutions in multi-transonic pseudo-Schwarzschild accretion
• On the stability of self-gravitating accreting flows
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• Axisymmetric black hole accretion in the Kerr metric as an autonomous dynamical system
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• Secular instability in quasi-viscous disc accretion
• Critical properties of spherically symmetric accretion in a fractal medium
• Magnetohydrodynamic instability in differentially rotating compressible flow
• Hybrid viscosity and the magnetoviscous instability in hot, collisionless accretion disks

Cited by in corpus (9)

• Hysteresis effects and diagnostics of the shock formation in low angular momentum axisymmetric accretion in the Kerr metric
• The role of flow geometry in influencing the stability criteria for low angular momentum axisymmetric black hole accretion
• On Spin Dependence of Relativistic Acoustic Geometry
• Axially Symmetric Accretion of Fractal Medium onto Rotating Black Holes and the emergence of the Acoustic Manifold
• Nonlinear variations in axisymmetric accretion
• Carter-Penrose diagrams for emergent spacetime in axisymmetrically accreting black hole systems
• An Analytical Study on the Multi-critical Behaviour and Related Bifurcation Phenomena for Relativistic Black Hole Accretion
• Dissipation and acoustic tunnelling about the sonic horizon of Bondi accretion
• Transonicity in black hole accretion -- A mathematical study using the generalized Sturm chains