Energetics of star–planet magnetic interactions

Context. Star–planet magnetic interactions (SPMIs) occurring in the sub-Alfvénic regime can, in principle, induce stellar chromospheric hotspots. These hotspots could serve as observational markers for inferring key planetary properties, especially the exoplanetary magnetic field, which is otherwise notoriously difficult to constrain. Currently, estimates of the power generated by SPMIs primarily rely on analytical scaling laws that relate stellar and planetary parameters to the interaction energetics. The existing scaling laws published in the literature so far do not agree with each other by at least an order of magnitude. Aims. Our aim was to quantify an absolute upper limit on the power that a planet can channel back to its host star during such interactions, which in turn can lead to the formation of stellar hotspots. Furthermore, we explored how this energy varies with different planetary characteristics and the stellar wind conditions in the vicinity of the planet. Methods. We employed three-dimensional numerical simulations of SPMIs in which the planet orbits within the sub-Alfvénic regime of the stellar wind. By performing a series of simulations with varied parameters known to influence the energetics of SPMIs, we derive a numerically supported scaling law that can be used to reliably estimate the energy channeled from the planet back to the star. Results. Our results suggest that existing analytical scaling laws may not fully capture the power transferred from the planet to the star through SPMI. The scaling law derived from our numerical simulations appears to provide a more comprehensive estimate, reflecting dependences on common stellar and planetary parameters also considered in earlier models. Moreover, our findings indicate that power generation involves not only the planetary obstacle itself but also the extended magnetic structure of the Alfvén wings interacting with the streaming stellar wind. Conclusions. This study suggests that care should be taken when applying analogies directly from Jovian sub-Alfvénic interactions to SPMIs, as the underlying physical conditions (specifically the value of the Alfvénic Mach number) may not be directly comparable. Our numerically derived scaling law offers a potentially improved approach for estimating SPMI power, capturing some of the interaction’s complexities exclusive to SPMIs.