A model for spin-orbit commensurability and synchronous starspot activity in stars with close-by planets

The rotation period of some planet-hosting stars appears to be in close commensurability with the orbital period of their close-by planets. A model is proposed to interpret such a phenomenon based on the excitation of resonant oscillations in the interior magnetic field of the star by a component of the tidal potential with a very low frequency in the reference frame rotating with the star. A magnetic flux tube located in the overshoot layer of the star is assumed to study the excitation of the resonant oscillations in the magnetostrophic regime. The model considers a planet on a circular oblique orbit and the growth timescale of the oscillations is estimated. To keep the system in resonance with the exciting potential, in spite of the variations in the magnetic field or tidal frequency, a self-regulating mechanism is proposed. The model is applied to ten systems and proves capable of accounting for the observed close commensurability in eight of them by assuming a magnetic field between $10^{2}$ and $10^{4}$ G. Systems with low-mass distant planets, such as AU Mic and HAT-P-11, cannot be interpreted by the proposed model. Consequences for the spin-orbit evolution of the systems, including dynamical tides and gyrochronology of planet-hosting stars, are discussed together with the effects on the chromospheric features produced by star-planet magnetic interactions.