Modeling multiphase plasma in the corona: prominences and rain

Abstract We review major achievements in our understanding of multiphase coronal plasma, where cool-dense and hot-tenuous matter coexists, brought about by advances in modeling and theory, inspired by observations. We give an overview of models that self-consistently form solar (or stellar) prominences and filaments, or (postflare) coronal rain, and clarify how these different phenomena share a common physical origin, relating radiative losses and coronal heating. While we do not fully understand the coronal heating, multi-dimensional models of solar prominence and rain formation demonstrate how thermal instability triggers condensations, and how their morphology may reveal aspects of the applied heating at play. We emphasize how the many pathways to linear instability due to combined ingredients of heat-loss, gravity, flows, and magnetic topologies are all involved in the resulting nonlinear magnetohydrodynamics. We provide some challenges to future model efforts, especially concerning prominence fine structure, internal dynamics, and their overall lifecycle.