The hydromagnetic interior of a solar quiescent prominence. I. coupling between force balance and steady energy transport

This series of papers investigates the dynamic interiors of quiescent prominences revealed by recent Hinode and SDO/AIA high-resolution observations. This first paper is a study of the static equilibrium of the Kippenhahn-Schlüter diffuse plasma slab, suspended vertically in a bowed magnetic field, under the frozen-in condition and subject to a theoretical thermal balance among an optically thin radiation, heating, and field-aligned thermal conduction. The everywhere-analytical solutions to this nonlinear problem are an extremely restricted subset of the physically admissible states of the system. For most values of the total mass frozen into a given bowed field, force balance and steady energy transport cannot both be met without a finite fraction of the total mass having collapsed into a cold sheet of zero thickness, within which the frozen-in condition must break down. An exact, resistive hydromagnetic extension of the Kippenhahn-Schlüter slab is also presented, resolving the mass-sheet singularity into a finite-thickness layer of steadily falling dense fluid. Our hydromagnetic result suggests that the narrow, vertical prominence H_α threads may be falling across magnetic fields, with optically thick cores much denser and ionized to much lower degrees than conventionally considered. This implication is discussed in relation to (1) the recent SDO/AIA observations of quiescent prominences that are massive and yet draining mass everywhere in their interiors, (2) the canonical range of 5-60G determined from spectral polarimetric observations of prominence magnetic fields over the years, and (3) the need for a more realistic multi-fluid treatment.