Three‐dimensional nonsteady compressible magnetohydrodynamic fluctuations in the solar wind

Abstract

We investigate some basic properties of three‐dimensional nonsteady compressible magnetohydrodynamic (MHD) perturbations in a polytropic radial MHD wind with spherical symmetry. At a large radial distance r, we derive analytical solutions for MHD slow‐ and fast‐type perturbations for several rational values of the polytropic index γ. The propagation characteristics of MHD slow‐type perturbations, which are more magnetic at large r, are very similar to those of Alfvénic perturbations; namely, there exists the same characteristic frequency fnof;c for both types of perturbations, and the transverse magnetic field perturbation associated with MHD slow‐type perturbations also tends to dominate the background radial magnetic field at large r except in the zero frequency limit. The propagation characteristics of MHD fast‐type perturbations, which are more acoustic at large r, depend upon the value of γ because the sound speed CS in the wind scales as ∼r−(γ‐1) at large r. For the typical case of γ < 2, MHD fast‐type perturbations always propagate relative to the wind. For the atypical case of γ > 2, acoustic perturbations actually become MHD slow perturbations at large r because CS is now slower than the Alfvén speed CA, which scales as ∼r−1 at large r, and these acoustic perturbations do not propagate relative to the wind, yet the wind advects them radially outward. For the special case of γ = 2, there exists another characteristic frequency fnof;a. For perturbation frequency fnof; > fnof;a, acoustic perturbations propagate relative to the wind, whereas for fnof; < fa, they appear standing relative to the wind. We discuss the relevance of these results, both MHD fast‐ and slow‐type perturbations with γ < 2, to interplanetary fluctuations in the inner solar wind. In particular, we interpret the increasing trends with r of the relative density and magnetic field fluctuations observed in high‐speed solar winds within 0.3 to 1 AU as manifestation of MHD fast‐ and slow‐type perturbations.