Fig. 1

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Schematic of the geometry considered in this work. Top panel: the central star (orange circle) creates a dipole field (gray arrows and lines) in which the planet (blue open circle symbol) orbits (large blue circle). The x axis corresponds to the star-planet direction at all times, and the y axis the direction of the orbit. The z axis (not shown here) is perpendicular to the orbital plane. Bottom panel: time-varying magnetic field By (in arbitrary unit) seen by the planet along its orbit. The open blue circle corresponds to the orbital phase illustrated in the top panel. This schematic can either represent the case of an inclined orbit with a stellar dipole aligned with the stellar rotation axis, or the case of a star sustaining a dipole inclined by 90° with respect to its rotation axis.
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