One dimensional prominence model

Based on reasonable assumptions and mathematical approximations a one dimensional, analytical model for solar quiescent prominences is constructed, which is in both magnetohydrostatic and thermal equilibrium. Thermal equilibrium here is a balance among thermal conduction, radiation and wave heating. The wave heating (H) is assumed to be equal to a constant (EH ) times the product of pressure (p) and density (ρ). We find the limit on the value of EH for existence of prominence type solution. For given values of EH , temperature at the center of prominence (T0), gas pressure at the center of prominence (p0) and the temperature at the edge of prominence(T∗), we found the following limits on the variables for the existence of the equilibrium: (1) the lower limit on the value of gas pressure at the edge of prominence (p∗), (2) the upper and lower limits on the length of the magnetic field line from the center to the edge of the prominence and (3) the upper limit [W0secφ0]max on the value of W0 secφ0 where W0 is the width of the prominence and φ0 is the shear angle. For specified values of T0, T∗, p0, EH and for W0secφ0 < [W0secφ0]max there exist, in general, two types of solutions. In Type 1 solution, equilibrium is nearly isobaric and the magnetic field is strong and nearly horizontal. This type of solution is physically inadmissible when the value of W0 secφ0 falls bellow a certain limit defined in the text. Conditions in this solution approach those in a real prominence as W0secφ0 approaches [W0secφ0]max. In Type 2 solution, there is a large variation of gas pressure from the center to the edge, and the magnetic field is weak and nearly vertical. Conditions in this solution also approach those in a real prominence as W0secφ0 approaches [W0secφ0]max. The physical characteristics of Type 1 and Type 2 solutions simulate those of ‘normal’ and ‘inverse’ prominences respectively as observed by Bommier et al. (1994).