Heating and cooling in stellar coronae: coronal rain on a young Sun

Recent observations of rapidly-rotating cool dwarfs have revealed H$\alpha$ line asymmetries indicative of clumps of cool, dense plasma in the stars' coronae. These clumps may be either long-lived (persisting for more than one stellar rotation) or dynamic. The fastest dynamic features show velocities greater than the escape speed, suggesting that they may be centrifugally ejected from the star, contributing to the stellar angular momentum loss. Many however show lower velocities, similar to coronal rain observed on the Sun. We present 2.5D magnetohydrodynamic simulations of the formation and dynamics of these condensations in a rapidly rotating ($P_{\rm rot}~=~ 1 \ \mathrm{day}$) young Sun. Formation is triggered by excess surface heating. This pushes the system out of thermal equilibrium and triggers a thermal instability. The resulting condensations fall back towards the surface. They exhibit quasi-periodic behaviour, with periods longer than typical periods for solar coronal rain. We find line-of-sight velocities for these clumps in the range $50 \ \mathrm{km} \ \mathrm{s}^{-1}$ (blue shifted) to $250 \ \mathrm{km} \ \mathrm{s}^{-1}$ (red shifted). These are typical of those inferred from stellar H$\alpha$ line asymmetries, but the inferred clump masses of $3.6\times 10^{14}\ \mathrm{g}$ are significantly smaller. We find that a maximum of $\simeq~3\%$ of the coronal mass is cool clumps. We conclude that coronal rain may be common in solar like stars, but may appear on much larger scales in rapid rotators.