The structure of solar filaments. Prominences in the corona free from external magnetic field

The new approach to the modeling of quiescent solar prominences is proposed. We solve the inverse magnetohydrostatic problem, when the pressure, density and temperature of plasma in the filament are calculated from the equilibrium equations using the given magnetic structure (magnetic flux function is proposed to be known). The new exact nonlinear solutions for dense (n ≈ (2?3) × 10¹¹ cm^?3) and cold (T ≈ (5?10) × 10³ K) filaments, embedded in the plan, vertically stratified atmosphere (hot solar corona) free of magnetic field, are derived. The filaments are stretched along the horizontal axisy(the translational symmetry is assumed: ?/?y = 0) and located parallel to and above a photospheric, magnetic polarity reversal line. The magnetic field lines have a structure of magnetic flux rope with helical field lines in three-dimensional space; the strength of magnetic field falls rapidly with distance from a rope axis. No external longitudinal magnetic field is needed to equilibrate the prominence. The net electric current along the filament is equal to zero. The model of magnetic arcade with the deflection (sag) on the top, proposed by Pikelner (1971) as a basic form of normal prominence, is calculated also using the method proposed. It is shown that such magnetic arcade, having the magnetic field strength of few gauss only, can effectively maintain the equilibrium of cool dense filament at the heights about 50–60 Mm.