Stability of Parker's Steady Solar Wind Solution in the Subcritical Region

Abstract

Parker’s steady solar wind solution (PSSWS) is a physically acceptable solution describing a smooth acceleration of the solar wind to supersonic speeds. Parker proposed that PSSWS possesses an intrinsic stability, like a “stable attractor” of this dynamical system. With a view to give a systematic analytical development, we restrict ourselves to the subcritical region inside the Parker critical point (PCP) where the solar wind goes through sonic flow conditions. This enables one to avoid the singularity at PCP plaguing the linear stability problem. Following Parker, we approximate the corona in the subcritical region by a static atmosphere and amend it to include an azimuthal flow and a weak radial flow. These physical simplifications enable us to pose a Sturm–Liouville problem for linearized perturbations about PSSWS. PSSWS is shown to have an intrinsic stability in the subcritical region, while leaving the solar coronal base in a state of (1) rest, (2) corotation with the Sun, and (3) slow radial motion. This result is also shown to hold when a diabatic flow in near-isothermal conditions is included in Parker’s model to explicitly account for the extended coronal heating. The isothermal gas assumption in Parker’s model is then relaxed, and a more realistic barotropic fluid representing variable extended active coronal heating conditions is considered for the gas flow. The stability of PSSWS, as the solar wind flow emerges from a state of rest at the solar surface, is shown to continue to hold.