Stability of Parker's Solar Wind Solution Near the Solar Surface

Stability of Parker's steady solar wind solution near the solar surface is systematically investigated by posing a Sturm-Liouville problem for this solution. Parker's solar wind solution, whether it turns into a breeze or a supersonic wind depending on the pressure in the interstellar medium, is shown to describe the solar wind to start in a stable way as it leaves the solar surface from a state of: rest, co-rotation with the Sun, slow motion. The isothermal gas flow assumption in Parker's solar wind model is then relaxed, and more realistic barotropic fluid and diabatic models are used for the gas flow. The stability of the solar wind flow, as it starts from a state of rest at the solar surface, is shown to continue to hold. Parker's solar wind solution therefore appears to be a stable attractor of this dynamical system.