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

INAF-Osservatorio Astrofisico di Catania, Via S. Sofia 78, 95123 Catania, Italy
e-mail: antonino.lanza@inaf.it

Received: 2 November 2021
Accepted: 17 January 2022

Abstract

Context. The rotation period of some planet-hosting stars appears to be in close commensurability with the orbital period of their close-by planets. In some cases, starspots rotating with a commensurable period have been detected, while the star displays latitudinal differential rotation.

Aims. 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.

Methods. A magnetic flux tube located in the overshoot layer of the star is assumed in order 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 despite the variations in the magnetic field or tidal frequency, a self-regulating mechanism is proposed.

Results. 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 10² and 10⁴ G. Systems with distant low-mass planets, such as AU Mic and HAT-P-11, cannot be interpreted by the proposed model.

Conclusions. Consequences for the spin–orbit evolution of the systems, including the dynamical tides and gyrochronology of planet-hosting stars, are discussed together with the effects on the chromospheric features produced by star–planet magnetic interactions.