Tidal heating in multilayer planets: Application to the TRAPPIST-1 system

TRAPPIST-1 (Gillon et al. 2017) is an extremely compact planetary system: seven earth-sized planets orbit at distances lower than 0.07 AU around one of the smallest M-dwarf known in the close neighborhood of the Sun (with a mass of less than 0.09 $M_\odot$). With 3 planets within the classical habitable zone, this system represents an interesting observational target for future instruments such as the JWST (e.g. Barstow & Irwin 2016). As the planets are close-in, tidal interactions play a crucial role in the evolution of the system by controlling both orbital configurations and rotational states of the planets. For the closest planets, the associated tidal dissipation could have an influence on their internal evolution and potentially on their climate and habitability Turbet et al. (2018). Following (Tobie et al. 2005), we build multilayer models of the internal structure of the TRAPPIST-1 planets accounting for the mass and radius of Grimm et al. (2018), then we compute the tidal response and estimate the tidal heat flux of each planet as well as the profile of tidal heating with depth. Finally, we compare our results to the homogeneous model of Efroimsky (2012) and assess the impact heating rate on the thermal state of each layer of the planet.