Drifts of the substellar points of the TRAPPIST-1 planets

Accurate modeling of tidal interactions is crucial for interpreting recent JWST observations of the thermal emissions of TRAPPIST-1 b and c and for characterizing the surface conditions and potential habitability of the other planets in the system. Indeed, the rotation state of the planets, driven by tidal forces, significantly influences the heat redistribution regime. Due to their proximity to their host star and the estimated age of the system, the TRAPPIST-1 planets are commonly assumed to be in a synchronization state. In this work, we present the recent implementation of the co-planar tidal torque and forces equations within the formalism of Kaula in the N-body code Posidonius. This enables us to explore the hypothesis of synchronization using a tidal model well suited to rocky planets. We studied the rotational state of each planet by taking into account their multi-layer internal structure computed with the code Burnman. Our simulations show that the TRAPPIST-1 planets are not perfectly synchronized but oscillate around the synchronization state. Planet-planet interactions lead to strong variations on the mean motion and tides fail to keep the spin synchronized with respect to the mean motion. As a result, the substellar point of each planet experiences short oscillations and long-timescale drifts that lead the planets to achieve a synodic day with periods varying from 55 years to 290 years depending on the planet.