Three‐dimensional steady compressible perturbations in the magnetohydrodynamic solar wind

Abstract

We present a steady three‐dimensional magnetohydrodynamic (MHD) perturbation formulation for inhomogeneous solar wind stream structures. We derive analytical solutions for asymptotic behaviors of three‐dimensional compressible MHD perturbations at a large radial distance r in a background radial wind of spherical symmetry. There are three independent perturbation solutions at large r. In contrast with a three‐dimensional propagation of Alfvénic perturbations in the same kind of background wind, the magnetic field perturbation associated with a steady compressible MHD perturbation does not dominate the background radial magnetic field at large r. Since the three independent compressible MHD perturbation solutions are related by the two regularity conditions at the MHD slow and fast critical points, the leading asymptotic radial scalings of the relevant compressible MHD perturbation variables are the same as those of the background variables at large r. In other words, while the radial variations of compressible MHD perturbations gradually merge into the background MHD wind at large r, the distinct angular variations of the perturbations persist throughout the wind. To complement these analytical analyses, we obtain complete numerical solutions in the entire radial range, which smoothly pass through the MHD slow and fast critical points. We provide numerical examples in which the perturbation increase (or decrease) of the radial wind speed can be as large as ∼ 100 km s−1 due to the perturbation increase (or decrease) of the temperature above the coronal base while the solar wind mass flux variation remains sufficiently small. This is possible because of our three‐dimensional approach and because of the regulation mechanism of the magnetic field in the wind. We also present an axisymmetric model for steady MHD solar wind structures in the presence of solar differential rotation.