Implications of nonlinearity for spherically symmetric accretion

Abstract

We subject the steady solutions of a spherically symmetric accretion flow to a time-dependent radial perturbation. The equation of the perturbation includes nonlinearity up to any arbitrary order, and bears a form that is very similar to the metric equation of an analogue acoustic black hole. Casting the perturbation as a standing wave on subsonic solutions, and maintaining nonlinearity in it up to the second order, we get the time-dependence of the perturbation in the form of a Liénard system. A dynamical systems analysis of the Liénard system reveals a saddle point in real time, with the implication that instabilities will develop in the accreting system when the perturbation is extended into the nonlinear regime. The instability of initial subsonic states also adversely affects the temporal evolution of the flow towards a final and stable transonic state.

14 pages, ReVTeX. Substantially revised with respect to the previous version. Three figures and a new section (Sec. VI) added

References in corpus (7)

• The theory of Hawking radiation in laboratory analogues
• On the stability of self-gravitating accreting flows
• Horizons and Ergoregions in Superfluids
• Critical properties of spherically symmetric black hole accretion in Schwarzschild geometry
• Perturbations on steady spherical accretion in Schwarzschild geometry
• Critical properties of spherically symmetric accretion in a fractal medium
• Acoustic horizons in nuclear fluids

Cited by in corpus (5)

• Perturbation of mass accretion rate, associated acoustic geometry and stability analysis
• Relativistic sonic geometry for isothermal accretion in the Schwarzschild metric
• Nonlinear variations in axisymmetric accretion
• Acoustic Analogue of Gravitational Wave
• Dissipation and acoustic tunnelling about the sonic horizon of Bondi accretion