  Magnetic interactions between a star and a close-in planet are postulated to
be a source of enhanced emissions and to play a role in the secular evolution
of the orbital system. Close-in planets generally orbit in the sub-alfv\'enic
region of the stellar wind, which leads to efficient transfers of energy and
angular momentum between the star and the planet. We model the magnetic
interactions occurring in close-in star-planet systems with three-dimensional,
global, compressible magneto-hydrodynamic numerical simulations of a planet
orbiting in a self-consistent stellar wind. We focus on the cases of magnetized
planets and explore three representative magnetic configurations. The Poynting
flux originating from the magnetic interactions is an energy source for
enhanced emissions in star-planet systems. Our results suggest a simple
geometrical explanation for ubiquitous on/off enhanced emissions associated
with close-in planets, and confirm that the Poynting fluxes can reach powers of
the order of $10^{19}$ W. Close-in planets are also showed to migrate due to
magnetic torques for sufficiently strong stellar wind magnetic fields. The
topology of the interaction significantly modifies the shape of the magnetic
obstacle that leads to magnetic torques. As a consequence, the torques can vary
by at least an order of magnitude as the magnetic topology of the interaction
varies.
