Context. Late-type stars interact with their close-in planets through their coronal magnetic fields. Aims. We introduce a theory for the interaction between the stellar and planetary fields focussing on the processes that release magnetic energy in the stellar coronae. Methods. We consider the energy dissipated by the reconnection between the stellar and planetary magnetic fields as well as that made available by the modulation of the magnetic helicity of the coronal field produced by the orbital motion of the planet. We estimate the powers released by both processes in the case of axisymmetric and non-axisymmetric, linear and non-linear force-free coronal fields finding that they scale as B04/3 Bp02/3 Rp2 vrel, where?B0 is the mean stellar surface field, Bp0 the planetary field at the poles, Rp the radius of the planet, and?vrel the relative velocity between the stellar and the planetary fields. Results. A chromospheric hot spot or a flaring activity phased to the orbital motion of the planet are found only when the stellar field is axisymmetric. In the case of a non-axisymmetric field, the time modulation of the energy release is multiperiodic and can be easily confused with the intrinsic stellar variability. We apply our theory to the systems with some reported evidence of star-planet magnetic interaction finding a dissipated power at least one order of magnitude smaller than that emitted by the chromospheric hot spots. The phase lags between the planets and the hot spots are reproduced by our models in all the cases except for υ?And. Conclusions. The chromospheric hot spots rotating in phase with the planets cannot be explained by the energy dissipation produced by the interaction between stellar and planetary fields as considered by our models and require a different mechanism.
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