The Hydromagnetic Interior of a Solar Quiescent Prominence. I. Coupling between Force-balance and Steady Energy-transport

TL;DR

This paper models the static equilibrium of solar prominences, revealing that most states require a cold mass sheet or resistive effects, and suggests prominence threads may be falling across magnetic fields with implications for observations.

Contribution

It provides analytical solutions for prominence equilibrium, introduces a resistive extension resolving mass-sheet singularities, and offers new insights into prominence dynamics and magnetic field interactions.

Findings

Most equilibrium states involve a cold mass sheet or resistive effects.

Resistive extension models prominence threads as falling dense fluid.

Implications for prominence observations and magnetic field measurements.

Abstract

This series of papers investigates the dynamic interior of a quiescent prominence revealed by recent {\it Hinode} and {\it SDO/AIA} high-resolution observations. This first paper is a study of the static equilibrium of the Kippenhahn-Schl\"{u}ter 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-Schl\"{u}ter 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 $H_{\alpha}$ 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 (i) the recent {\it SDO/AIA} observations of quiescent prominences that are massive and yet draining mass everywhere in their interiors, (ii) the canonical range of $5-60 G$ determined from spectral-polarimetric observations of prominence magnetic fields over the years and (iii) the need for a more realistic multi-fluid treatment.