Magnetohydrodynamic standing oscillations in a spherical dipole field

Abstract

The coupled toroidal and poloidal modes forming a standing oscillation along the line of force and propagating azimuthally in a spherical dipole magnetic field are investigated under the magnetohydrodynamic (MHD) approximation with infinite conductivity, including the pressure effect but neglecting compressibility. We obtain a linearized coupled differential equation. When the azimuthal wavenumber becomes zero in the coupled equation, the axisymmetric toroidal wave equation is obtained with no pressure effect. For a large azimuthal wavenumber, on the other hand, a differential equation of the poloidal wave associated with a compressional magnetic component, which is different from the equation hitherto obtained under the zero pressure term, is derived from the coupled equation. It is found that the fluid pressure perturbation acts on the poloidal wave like the spring for the stretched string model and then contributes to the enhancement of the eigenvalues of the standing oscillations, especially for the first few. In this case, the magnetic pressure perturbation is in antiphase to that of the fluid pressure.