Steady 2D prominence-like solutions of the MHD equations with field-aligned compressible flow

Abstract

An exact two-dimensional solution of the ideal magnetohydrodynamic (MHD) equations with compressible flow in a uniform gravitational field is presented and applied to solar prominences. The solution is constructed via a systematic nonlinear separation of variables method used to calculate several classes of MHD equilibria in Cartesian geometry and uniform gravity. This simple model of steady plasma flow along the dipped field lines of a solar prominence is the first 2D MHD model with a nonisothermal temperature distribution which selfconsistently also examines the required heating. Although the model is 2D, a third magnetic/velocity vector field component is included and the highly sheared fields observed in prominences are reproduced. A description is given of the balance of gas pressure gradient, gravity, Lorentz and inertial forces acting along and across the prominence. It is found that the flow may significantly influence the energy balance as in a similar application of this class of solutions to solar coronal loops.