Tides on Membrane Worlds: Europa, Titan and Co.

Abstract:

Once seen as exotic, global subsurface oceans are now considered to be a likely feature of many large icy satellites, with Europa and Titan as prime candidates. Under tidal forcing, the icy crust deforms as a viscoelastic membrane decoupled from the deep interior by the ocean layer. Regarding tidal effects, these satellites thus deserve more to be called `membrane worlds' rather than `ocean worlds'. I describe here the viscoelastic membrane approach, a new powerful tool to compute all tidal effects in a laterally uniform crust with depth-dependent rheology. This approach leads to simple analytical formulas for viscoelastic tidal Love numbers, with an accuracy better than one percent for h₂ and k₂, and a few percents for l₂. This accuracy is sufficient for most applications. Membrane formulas clearly show how Love numbers depend on the interior structure (primarily the crust rigidity, crust thickness, ocean density and mean density). This method also yields simple analytical formulas for viscoelastic tidal stresses and tidal dissipation in the crust. All in all, the viscoelastic membrane approach is a good alternative to software encoding the full theory of viscoelastic-gravitational deformations.