Volume 644, December 2020
|Number of page(s)||15|
|Section||Planets and planetary systems|
|Published online||16 December 2020|
Solid tidal friction in multi-layer planets: Application to Earth, Venus, a Super Earth and the TRAPPIST-1 planets
Potential approximation of a multi-layer planet as a homogeneous body
Observatoire de Genève, Université de Genève,
51 Chemin des Maillettes,
2 AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, 91191 Gif- sur-Yvette, France
3 Laboratoire de Planétologie et Géodynamique, UMR-CNRS 6112, Université de Nantes, 44322 Nantes cedex 03, France
Accepted: 7 October 2020
With the discovery of TRAPPIST-1 and its seven planets residing within 0.06 au, it is becoming increasingly necessary to carry out correct treatments of tidal interactions. The eccentricity, rotation, and obliquity of the planets of TRAPPIST-1 do indeed result from the tidal evolution over the lifetime of the system. Tidal interactions can also lead to tidal heating in the interior of the planets (as for Io), which may then be responsible for volcanism or surface deformation. In the majority of studies aimed at estimating the rotation of close-in planets or their tidal heating, the planets are considered as homogeneous bodies and their rheology is often taken to be a Maxwell rheology. Here, we investigate the impact of taking into account a multi-layer structure and an Andrade rheology in the way planets dissipate tidal energy as a function of the excitation frequency. We use an internal structure model, which provides the radial profile of structural and rheological quantities (such as density, shear modulus, and viscosity) to compute the tidal response of multi-layered bodies. We then compare the outcome to the dissipation of a homogeneous planet (which only take a uniform value for shear modulus and viscosity). We find that for purely rocky bodies, it is possible to approximate the response of a multi-layer planet by that of a homogeneous planet. However, using average profiles of shear modulus and viscosity to compute the homogeneous planet response leads to an overestimation of the averaged dissipation. We provide fitted values of shear modulus and viscosity that are capable of reproducing the response of various types of rocky planets. However, we find that if the planet has an icy layer, its tidal response can no longer be approximated by a homogeneous body because of the very different properties of the icy layers (in particular, their viscosity), which leads to a second dissipation peak at higher frequencies. We also compute the tidal heating profiles for the outer TRAPPIST-1 planets (e to h).
Key words: planet-star interactions / planets and satellites: terrestrial planets / planets and satellites: interiors / planets and satellites: individual: TRAPPIST-1
© ESO 2020
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