Formation of the Supersonic Solar Wind: Parker's Theory Revisited

We examine and propose to fundamentally modify the classical theory of solar wind formation. To form a supersonic solar wind, the classical theory requires that a subsonic flow speed must start at a specific initial speed from the coronal base, called eigenspeed, go along a continuous eigenfunction, and reach the sonic point, which is where the flow speed equals the sonic speed, while the critical condition, which is where the effective driving force is zero, is satisfied. Any mismatch between the sonic point and critical condition distances results in either subsonic winds when the initial speed is below the eigenspeed, or no solar wind when the initial speed is above the eigenspeed. Because the critical condition is determined by the solar wind temperature profile, which depends on ionization process at the top of the chromosphere and the heating process around the coronal base but not by the processes at the sonic point, the required match between the two is generally not met and hence the momentum equation in the conventional theory encounters difficulty when the initial speed is above the eigenspeed. To resolve the difficulty, we propose a discontinuity between the sonic point and the critical condition to reach supersonic solar wind solutions. As a result, supersonic solar winds can be produced when the initial speed in the coronal base is greater than the eigenspeed. The critical solution or eigen function provided by the conventional solar wind model describes the condition that separates the supersonic solar winds from subsonic ones.