1207.1070 (Sourav Sen et al.)

Implications of nonlinearity for spherically symmetric accretion    [PDF]

Sourav Sen, Arnab K. Ray

Stationary solutions of spherically symmetric accretion processes have been subjected to a time-dependent radial perturbation, whose equation includes nonlinearity to any arbitrary order. Regardless of the order of nonlinearity, the equation of the perturbation bears a form that is remarkably similar to the metric equation of an analogue acoustic black hole. Casting the perturbation as a standing wave and maintaining nonlinearity in it up to the second order, brings out the time-dependence of the perturbation in the form of a Lienard system. A dynamical systems analysis of this Lienard 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 may also adversely affect the temporal evolution of the flow towards a final stable transonic state.

View original: http://arxiv.org/abs/1207.1070