Stability and solution of the timedependent BondiParker flow
Abstract
Bondi and Parker derived a steadystate solution for Bernoulli's equation in spherical symmetry around a point mass for two cases, respectively, an inward accretion flow and an outward wind. Left unanswered were the stability of the steadystate solution, the solution itself of timedependent flows, whether the timedependent flows would evolve to the steady state, and under what conditions a transonic flow would develop. In a Hamiltonian description, we find that the steadystate solution is equivalent to the Lagrangian implying that timedependent flows evolve to the steady state. We find that the second variation is definite in sign for isothermal and adiabatic flows, implying at least linear stability. We solve the partial differential equation for the timedependent flow as an initialvalue problem and find that a transonic flow develops under a wide range of realistic initial conditions. We present some examples of timedependent solutions.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 April 2020
 DOI:
 10.1093/mnras/staa529
 arXiv:
 arXiv:2002.09004
 Bibcode:
 2020MNRAS.493.2834K
 Keywords:

 hydrodynamics;
 stars: formation;
 stars: massloss;
 stars: winds;
 outflows;
 Physics  Fluid Dynamics;
 Astrophysics  Solar and Stellar Astrophysics
 EPrint:
 To be published in MNRAS