A new non-extensive proxy for the evolution of stellar rotation period in planetary systems

Understanding stellar rotation evolution is crucial for improving stellar dynamics models, especially through tidal interactions. In this work, we investigate the behavior of the non-extensive statistical mechanics index q in star-planet systems where tidal effects are the dominant interaction. Using the solar system as a benchmark, we relate q to the angular momentum transfer process, specifically through the ratio between stellar and orbital angular momentum. Our results reveal that q is highly sensitive to angular momentum exchange. Whereas the inner rocky planets play a minor role in shaping the Sun's rotation, the cold gas giants have a substantial effect on its long-term rotational evolution. This behavior can only be explained by combining tidal interactions and magnetic braking. Conversely, in systems with only rocky planets, magnetic braking alone sufficiently describes the rotation evolution. These results emphasize the pivotal role of gas giants in shaping stellar rotation through tidal coupling.