Complex stellar magnetism and realistic star-planet magnetic interactions

A large population of close-in exoplanets has been discovered around cool stars over the past decades. Due to their proximity with their host star, these planets can act as external perturbations of the stellar environment. Through magnetically coupling with the stellar wind, they can channel magnetic energy toward the stellar atmosphere via Alfvén waves. Star-planet magnetic interactions (SPMI) therefore offer a unique window to study the coupled magnetism of cool stars and their close-in planets. In existing analytical model (Saur et al. 2013, Lanza et al. 2013, Paul & Strugarek 2025) the SPMI efficiency is primarly controlled by the topology, strength, and temporal variability of the stellar magnetic field. However, all these models have considered so far that the planet was interacting with a homogenous medium along its orbit. This assumption fails for complex stellar magnetic fields, such as during solar maximum, and motivates the need for more realistic modelling. I will present a 3D non-axisymmetric MHD model of a cool star’s stellar wind, explicitly including for the first time the orbital motion of its exoplanet. The planet’s hypothetical magnetosphere is also modelled and I will show that its size induces significant variations in the topology of the Alfvén surface. Our ab-initio modelling also demonstrates how variations in the orbital phase affect the excitation and transport of Alfvén waves triggered by the planet, leading to drastic changes in the propagation of Alfvén wings over the two-day orbital timescale. As a result, the magnetic interaction between the planet and its environment is found to vary signifcantly along the orbit and to depend sensitively on the assumed size of the exoplanet magnetosphere. Such strong spatio-temporal variability in magnetic energy transport is expected to directly impact the dissipation of electromagnetic energy in the planetary ionosphere. We demonstrate that such modelling is now needed to go beyond order-of-magnitude estimates and toward a precise characterisation of SPMI in the magnetically structured environments of cool stars. By explicitly accounting for stellar magnetic topology and variability, these models enable robust constraints on exoplanetary magnetospheric properties through SPMI. Despite playing a crucial role in assessing dynamo theories and atmospheric retention, exoplanetary magnetic fields still remain a largely unexplored parameter.