2D MHD modelling of compressible and heated coronal loops obtained via nonlinear separation of variables and compared to TRACE and SoHO observations

Abstract

An analytical MHD model of coronal loops with compressible flows and including heating is compared to obser- vational data. The model is constructed via a systematic nonlinear separation of the variables method used to calculate several classes of exact MHD equilibria in Cartesian geometry and uniform gravity. By choosing a particularly versatile solution class with a large parameter space we are able to calculate models whose loop length, shape, plasma density, temperature and ve- locity profiles are fitted to loops observed with TRACE, SoHO/CDS and SoHO/SUMER. Synthetic emission profiles are also calculated and fitted to the observed emission patterns. An analytical discussion is given of the two-dimenional balance of the Lorentz force and the gas pressure gradient, gravity and inertial forces acting along and across the loop. These models are the first to include a fully consistent description of the magnetic field, 2D geometry, plasma density and temperature, flow velocity and thermodynamics of loops. The consistently calculated heating profiles which are largely dominated by radiative losses and concentrated at the footpoints are influenced by the flow and are asymmetric, being biased towards the upflow footpoint.