Thermal stability of magnetohydrodynamic modes in homogeneous plasmas

Abstract

Context. Thermal instabilities give rise to condensations in the solar corona, and are the most probable scenario for coronal rain and prominence formation. We revisit the original theoretical treatment done by Field (1965, ApJ, 142, 531) in a homogeneous plasma with heat-loss effects and combine this with state-of-the-art numerical simulations to verify growth-rate predictions and address the long-term non-linear regime. We especially investigate interaction between multiple magnetohydrodynamic (MHD) wave modes and how they in turn trigger thermal mode development. Aims. We assess how well the numerical MHD simulations retrieve the analytically predicted growth rates. We complete the original theory with quantifications of the eigenfunctions, calculated to consistently excite each wave mode. Thermal growth rates are fitted also in the non-linear regime of multiple wave–wave interaction setups, at the onset of thermal instability formation. Methods. We performed 2D numerical MHD simulations, including an additional (radiative) heat-loss term and a constant heating term to the energy equation. We mainly focus on the thermal (i.e. entropy) and slow MHD wave modes and use the wave amplitude as a function of time to make a comparison to predicted growth rates. Results. It is shown that the numerical MHD simulations retrieve analytically predicted growth rates for all modes, of thermal and slow or fast MHD type. In typical coronal conditions, the latter are damped due to radiative losses, but their interaction can cause slowly changing equilibrium conditions which ultimately trigger thermal mode development. Even in these non-linear wave-wave interaction setups, the growth rate of the thermal instability agrees with the exponential profile predicted by linear theory. The non-linear evolutions show systematic field-guided motions of condensations with fairly complex morphologies, resulting from thermal modes excited through damped slow MHD waves. These results are of direct interest to the study of solar coronal rain and prominence fine structure. Our wave–wave interaction setups are relevant for coronal loop sections which are known to host slow wave modes, and hence provide a new route to explain the sudden onset of coronal condensation.