Context. Age estimation techniques such as gyrochronology and magnetochronology cannot be applied to stars that have exchanged angular momentum with their close environments. This is especially true for a massive close-in planetary companion (with a period of a few days or less) that could have been strongly impacted by the rotational evolution of the host star, throughout the stellar evolution, through the star-planet tidal interaction.
Aims. In this article, we provide the community with a reliable region in which empirical techniques such as gyrochronology can be used with confidence.
Methods. We combined a stellar angular momentum evolution code with a planetary orbital evolution code to study in detail the impact of star-planet tidal interaction on the evolution of the surface rotation rate of the star.
Results. We show that the interaction of a close-in massive planet with its host star can strongly modify the surface rotation rate of this latter, in most of the cases associated with a planetary engulfment. A modification of the surface rotation period of more than 90% can survive a few hundred Myr after the event and a modification of 10% can last for a few Gyr. In such cases, a gyrochronology analysis of the star would incorrectly make it appear as rejuvenated, thus preventing us from using this method with confidence. To try overcome this issue, we proposed the proof of concept of a new age determination technique that we call the tidal-chronology method, which is based on the observed pair Prot, ⋆–Porb of a given star-planet system, where Prot, ⋆ is the stellar surface rotational period and Porb the planetary orbital period.
Conclusions. The gyrochronology technique can only be applied to isolated stars or star-planet systems outside a specific range of Prot, ⋆–Porb. This region tends to expand for increasing stellar and planetary mass. In that forbidden region, or if any planetary engulfment is suspected, gyrochronology should be used with extreme caution, while tidal-chronology could be considered. This technique does not provide a precise age for the system yet; however, it is already an extension of gyrochronology and could be helpful to determine a more precise range of possible ages for planetary systems composed of a star between 0.3 and 1.2 M⊙ and a planet more massive than 1 Mjup initially located at a few hundredths of au from the host star.
Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length
