Filip Elekes, Joachim Saur, Alexander Grayver

Flares and associated Coronal Mass Ejections (CMEs) are energetic stellar phenomena that shape the space weather around planets. Close-in exoplanets orbiting active cool stars are likely exposed to extreme space weather whose effects on the planets are not understood well enough. The terrestrial Trappist-1 exoplanets are excellent targets to study the impact of CMEs on close-in planets and their atmospheres. We study the role of planetary magnetic fields in shielding the planet from external forcing. We expand on recent studies of CME-induced Joule heating of planetary interiors and atmospheres by including a magnetohydrodynamic (MHD) model of the interaction. We study the interaction of CMEs with Tr-1b & e using MHD simulations. We consider magnetic flux rope and density pulse CMEs. We calculate induction heating in the planetary interior and ionospheric Joule heating for various intrinsic magnetic field strengths and CME energies. Magnetospheric compression is the main driver of magnetic variability. Planetary magnetic fields enhance induction heating in the interior although the effect is weaker with flux rope CMEs. Single event dissipation rates with 1-hour CMEs amount to 20 TW and 1 TW for Trappist-1b and e, respectively. Taking CME occurrence rates into account, annual average heating rates are ~10 TW (b) and ~1 TW (e), which are placed near the lower end of previous estimates. Within the range of studied planetary magnetic field strengths $B_p$, magnetospheric Poynting fluxes scale with $B_p^3$. Thus, stronger magnetic fields increase CME energy absorption. Ionospheric Joule heating rates amount to $10^{3-4}$ TW and decrease for stronger magnetic fields $B_p$. These heating rates exceed the average stellar XUV input by 1-2 orders of magnitude and might severely impact atmospheric erosion. In a steady state stellar wind ionospheric Joule heating amounts to ~$10^2$ TW.