Magnetic interactions between close-in planets and their host star can play an important role in the secular orbital evolution of the planets, as well as the rotational evolution of their host. As long as the planet orbits inside the Alfven surface of the stellar wind, the magnetic interaction between the star and the planet can modify the wind properties and also lead to direct angular momentum transfers between the two. We model these star-planet interactions using compressible magneto-hydrodynamic (MHD) simulations, and quantify the angular momentum transfers between the star, the planet, and the stellar wind. We study the cases of magnetized and non-magnetized planets and vary the orbital radius inside the Alfven surface of the stellar wind. Based on a grid of numerical simulations, we propose general scaling laws for the modification of the stellar wind torque, for the torque between the star and the planet, and for the planet migration associated with the star-planet magnetic interactions. We show that when the coronal magnetic field is large enough and the star is rotating sufficiently slowly, the effect of the magnetic star-planet interaction is comparable to tidal effects and can lead to a rapid orbital decay.
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