Three-dimensional solutions of the magnetohydrostatic equations: Rigidly rotating magnetized coronae in spherical geometry

摘要

Context. Magnetohydrostatic (MHS) equilibria are often usedto model astrophysical plasmas, for example, planetary magnetospheresor coronae of magnetized stars. However, finding realisticthree-dimensional solutions to the MHS equations is difficult, withonly a few known analytical solutions and even finding numericalsolution is far from easy. Aims. We extend the results of a previous paper onthree-dimensional solutions of the MHS equations around rigidlyrotating massive cylinders to the much more realistic case of rigidlyrotating massive spheres. An obvious application is to model the closedfield line regions of the coronae of rapidly rotating stars. Methods. We used a number of simplifying assumptions to reducethe MHS equations to a single elliptic partial differential equationfor a pseudo-potential U, from which all physical quantities,such as the magnetic field, the plasma pressure, and the density, canbe derived by differentiation. The most important assumptions made arestationarity in the co-rotating frame of reference, a particular formfor the current density, and neglect of outflows. Results. In this paper we demonstrate that standard methods canbe used to find numerical solutions to the fundamental equation of thetheory. We present three simple different cases of magnetic fieldboundary conditions on the surface of the central sphere, correspondingto an aligned dipole field, a non-aligned dipole field, and a displaceddipole field. Our results show that it should be possible in the futureto use this method without dramatically increasing the demands oncomputational resources to improve upon potential field models ofrotating magnetospheres and coronae. Key words: magnetic fields - magnetohydrodynamics (MHD) - stars: magnetic field - stars: coronae - stars: activity