Extent of the fast Alfvén surface as a function of δ v _⋆. Gray regions mark the minimum value of the fast Alfvén surface. Colored shades show its latitudinal variability for both values of λ _⋆. Horizontal black lines represent the semimajor axis of the first six planets of the TRAPPIST-1 system. For all simulations, at least one planet is within the maximal fast Alfvén radius, and can thus give birth to star–planet interactions. The dashed black line is the semimajor axis of Proxima Cen b in stellar radii.