  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.
