Improving tidal interaction for compact N-body planetary system.

Recent JWST observations of rocky planets, such as TRAPPIST-1, and the increasing number of rocky planets discovered orbiting close to their host star, strongly motivates the improvement of tidal modeling.
Beside, recent JWST observations of the thermal emission from TRAPPIST-1 b and c have provided constraints on their atmospheres (Greene et al. 2023; Ih et al. 2023; Zieba et al. 2023; Lincowski et al. 2023). 
In this context, It is crucial to use a coherent tidal model that encapsulates the complex response of rocky planets to stress, to understand the evolution of exoplanets and interpret new data.

Our presentation will focus on recent developments on the implementation of the formalism of Kaula (1964) in the N-body code Posidonius (Blanco-Cuaresma & Bolmont 2017; Bolmont et al. 2020).
This formalism consists in using a decomposition of the tidal potential into Fourier harmonic modes, which allows to account for the frequency dependence of the tidal response of rocky bodies.
It makes it general enough to take into account for any type of internal structure, as well as the presence of ice or surface liquid water.
We will present our results on the rotational state of TRAPPIST-1 planets, revisiting the assumption of the perfect synchronization state resulting from tidal evolution. 
Given that the rotational state influences the heat redistribution regime, precise estimation of their rotational state is critical.
Various internal structures were explored with the Burnman code (Cottaar et al. 2014; Myhill et al. 2021)., considering compositions and core sizes compatible with mass and radius estimations from Agol et al. (2021).

Our simulations showed that planet-planet interactions induce rapid variations in the mean motions of the planets. 
These variations occur too quickly for tides to maintain synchronized rotation states with the mean motion. 
This results in sub-stellar point drifts, causing planets to complete full solar days with periods ranging from 42 to 103 years depending on the planet. 
The competition between mean motion variations and tidal damping, and thus sub-stellar drifts, is contingent on the internal structure of the planet under consideration. 
As a result, remnant rotation is expected to facilitate the redistribution of heat on the planet's surface, modifying habitability conditions by mitigating the cold-trap effect on the night side (Turbet et al. 2016) and redistributing cloud formation on the day side (Turbet et al. 2021).
Additionally, we will present preliminary results on the coupling between the spin and the orbital evolution of planets in compact mean motion resonances (MMRs), in particular with the presence of obliquity spin-orbit resonances (SOR), on time transit variations (TTV) and on the mean motion resonances for the TRAPPIST-1 system and the potential observability of such effects.