Stellar hot spots due to star-planet magnetic interactions Power transmission to the chromosphere

Context. Star-planet magnetic interactions (SPMIs) have been proposed as a mechanism for generating stellar hot spots with energy outputs on the order of 1019-21 watts. This interaction is primarily believed to be mediated by Alfven waves, which are produced by the planetary obstacle and propagate towards the star. The stellar atmosphere, as a highly structured region, dictates where and how much of this incoming energy can actually be deposited as heat. Aims. The stellar transition region separating the chromosphere from the corona of cool stars gives rise to a significant variation of the Alfven speed over a short distance. Therefore, a reflection of the Alfven waves at the transition region is naturally expected. We aim to characterize the efficiency of energy transfer due to SPMIs by quantifying a frequency-dependent reflection of the wave energy at the stellar transition region and its transmission to the stellar chromosphere. Methods. We employed magnetohydrodynamic (MHD) simulations to model the frequency-dependent propagation of Alfven waves through a realistic background stellar wind profile. The transmission efficiency as a function of the wave frequency was quantified. Further analyses were conducted to characterize the overall energy transfer efficiency of SPMIs in several candidate systems where chromospheric hot spots have been tentatively detected. Results. Low-frequency waves experience greater reflection compared to high-frequency waves, resulting in reduced energy transfer efficiency for lower frequencies. Conversely, the parametric decay instability of Alfven waves substantially diminishes the energy transfer efficiency at higher frequencies. As a result, there is a specific frequency range where energy transfer is most efficient. A significant fraction of the Alfven wave energy is reflected at the stellar transition region and, in most realistic scenarios, the transmission efficiency to the chromosphere is found to be at a level of approximately 10%.