Magnetostatic atmospheres in a spherical geometry and their application to the solar corona

The formalism for deriving 'two-dimensional' magnetostatic equilibria is extended to spherical coordinates and applied to magnetic fields that are functions of radius and polar angle. A family of analytical solutions is readily found. The basic properties of these solutions are displayed for a dipole magnetic field at the base of the atmosphere and for physical parameters appropriate to the solar corona. Variation of the concentration of plasma at the 'magnetic equator' illustrates the distortion of a simple dipole magnetic field by the electric currents required to maintain force balance in the presence of the imposed pressure gradients in the polar direction. The deviation of the magnetostatic field lines from the simple dipole configuration depends on the parameter (P/sub eq/--P/sub pole/)/(B/sub o/2/8π), where P/sub eq/ and P/sub pole/ are the equatorial and polar plasma pressures and B0 is the dipole field strength at the base of the corona. Reasonable choices of these physical quantities give a value for this parameter of about 1/2, implying deviations in the large-scale coronal magnetic field geometry from the commonly used potential field that are not negligible. These deviations lead to field lines that are more nearly vertical at the base of the corona and to more magnetic flux on open field lines than in potential field models with the same magnetic boundary conditions