Magnetostatic structures of the solar corona. III. Normal and inverse quiescent prominences

Analytical solutions describing equilibrium magnetic fields in the solar corona, deformed by prominence-like plasma condensations in the Cartesian plane, are treated in this paper. The equilibrium equations for this class of problems usually take different forms in distinct subdomains, separated by free boundaries to be solved as one of the unknowns, across which solutions on the two sides are matched by suitable jump conditions. By idealizing the plasma condensations as a horizontal, circular cylinder whose weight in a uniform gravitational field is supported by an external magnetic field, we avoid solving free-boundary problems and present a method to directly construct solutions presenting prominence magnetic fields in the so-called normal and inverse configurations. The solutions illustrate the morphologies of plasma and vector magnetic field distributions in the cylindrical condensations in relation to the magnetic fields beneath the condensations. These solutions provide theoretical magnetic field properties that may be relevant to the current renewed interest in observing solar prominence magnetic fields by polarimetric spectroscopy.