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With the discovery of TRAPPIST-1 and its seven planets within 0.06 au, thecorrect treatment of tidal interactions is becoming necessary. Theeccentricity, rotation, and obliquity of the planets of TRAPPIST-1 are indeedthe result of tidal evolution over the lifetime of the system. Tidalinteractions can also lead to tidal heating in the interior of the planets,which can then be responsible for volcanism and/or surface deformation. In themajority of studies to estimate the rotation of close-in planets or their tidalheating, the planets are considered as homogeneous bodies and their rheology isoften taken to be a Maxwell rheology.  We investigate here the impact of considering a multi-layer structure and anAndrade rheology on the way planets dissipate tidal energy as a function of theexcitation frequency. We use an internal structure model, which provides theradial profile of structural and rheological quantities to compute the tidalresponse of multi-layer bodies. We then compare the outcome to the dissipationof a homogeneous planet.  We find that for purely rocky bodies, it is possible to approximate theresponse of a multi-layer planet by that of a homogeneous planet. However,using average profiles of shear modulus and viscosity to compute thehomogeneous planet response leads to an overestimation of the averageddissipation. We provide fitted values of shear modulus and viscosity to be ableto reproduce the response of various types of rocky planets. However, we findthat if the planet has an icy layer, its tidal response can no longer beapproximated by a homogeneous body because of the very different properties ofthe icy layers, which lead to a second dissipation peak at higher frequencies.We also compute the tidal heating profiles for the outer TRAPPIST-1 planets (eto h).

astronomy and astrophysics

Solid tidal friction in multi-layer planets: Application to Earth,  Venus, a Super Earth and the TRAPPIST-1 planets. Can a multi-layer planet be  approximated as a homogeneous planet?