On the rotation of co-orbital bodies in eccentric orbits

We investigate the resonant rotation of co-orbital bodies in eccentric and planar orbits. We develop a simple analytical model to study the impact of the eccentricity and orbital perturbations on the spin dynamics. This model is relevant in the entire domain of horseshoe and tadpole orbit, for moderate eccentricities. We show that there are three different families of spin-orbit resonances, one depending on the eccentricity, one depending on the orbital libration frequency, and another depending on the pericenter's dynamics. We can estimate the width and the location of the different resonant islands in the phase space, predicting which are the more likely to capture the spin of the rotating body. In some regions of the phase space the resonant islands may overlap, giving rise to chaotic rotation.

Is the activity level of HD 80606 influenced by its eccentric planet?

Aims: Several studies suggest that the activity level of a planet-host star can be influenced by the presence of a close-by orbiting planet. Moreover, the interaction mechanisms that have been proposed, magnetic interaction and tidal interaction, exhibit a very different dependence on the orbital separation between the star and the planet. A detection of activity enhancement and characterization of its dependence on planetary orbital distance can, in principle, allow us to characterize the physical mechanism behind the activity enhancement. Methods: We used the HARPS-N spectrograph to measure the stellar activity level of HD 80606 during the planetary periastron passage and compared the activity measured to that close to apastron. Being characterized by an eccentricity of 0.93 and an orbital period of 111 days, the system's extreme variation in orbital separation makes it a perfect target to test our hypothesis. Results: We find no evidence for a variation in the activity level of the star as a function of planetary orbital distance, as measured by all activity indicators employed: log(R'HK), Hα, NaI, and HeI. None of the models employed, whether magnetic interaction or tidal interaction, provides a good description of the data. The photometry revealed no variation either, but it was strongly affected by poor weather conditions. Conclusions: We find no evidence for star-planet interaction in HD 80606 at the moment of the periastron passage of its very eccentric planet. The straightforward explanation for the non-detection is the absence of interaction as a result of a low magnetic field strength on either the planet or the star and of the low level of tidal interaction between the two. However, we cannot exclude two scenarios: i) the interaction can be instantaneous and of magnetic origin, being concentrated on the substellar point and its surrounding area; and ii) the interaction can lead to a delayed activity enhancement. In either scenario, a star-planet interaction would not be detectable with the dataset described in this paper.