One dimensional prominence model

Abstract

Based on reasonable assumptions and mathematical approximations a one dimensional, analytical model for solar quiescent prominences is constructed, which is in both magneto-hydrostatic 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 (rho ). 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 [W0secphi_ {0}]max on the value of W_0sec phi_0 where W0 is the width of the prominence and {phi_ {0}} is the shear angle. For specified values of T_0, T_*, p_0, EH and for W0sec{phi_ {0}} < [W_0secphi_0 ]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 W_0sec phi_0 falls bellow a certain limit defined in the text. Conditions in this solution approach those in a real prominence as W0sec{phi_0 } approaches [W_0secphi_0 ]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 W0sec{phi_0 } approaches [W_0secphi_0 ]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).