Description |
Stationary spherically symmetric transonic (Bondi) accretion is a paradigm in
astrophysical fluid dynamics. We, however, show that in the stationary regime this process
cannot be physically realisable because its mathematical solution lies along a separatrix and
passes through a saddle point in the phase portrait of the flow. We argue that the transonic
solution is owed actually to the dynamics. In studying the dynamic effects, we subject the
stationary flow to a time-dependent radial perturbation, with the equation of the perturbation
containing nonlinearity up to any arbitrary order. 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 Li\'enard system. A dynamical systems
analysis of the Li\'enard 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. We provide numerical support in
favour of this claim.
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