Tides on Europa: The membrane paradigm
Abstract
Jupiter's moon Europa has a thin icy crust which is decoupled from the mantle by a subsurface ocean. The crust thus responds to tidal forcing as a deformed membrane, cold at the top and near melting point at the bottom. In this paper I develop the membrane theory of viscoelastic shells with depthdependent rheology with the dual goal of predicting tidal tectonics and computing tidal dissipation. Two parameters characterize the tidal response of the membrane: the effective Poisson's ratio ν bar and the membrane spring constant Λ, the latter being proportional to the crust thickness and effective shear modulus. I solve membrane theory in terms of tidal Love numbers, for which I derive analytical formulas depending on Λ, ν bar , the oceantobulk density ratio and the number k_{2}^{∘} representing the influence of the deep interior. Membrane formulas predict h_{2} and k_{2} with an accuracy of a few tenths of percent if the crust thickness is less than one hundred kilometers, whereas the error on l_{2} is a few percents. Benchmarking with the thickshell software SatStress leads to the discovery of an error in the original, uncorrected version of the code that changes stress components by up to 40%. Regarding tectonics, I show that different stressfree states account for the conflicting predictions of thin and thick shell models about the magnitude of tensile stresses due to nonsynchronous rotation. Regarding dissipation, I prove that tidal heating in the crust is proportional to Im (Λ) and that it is equal to the global heat flow (proportional to Im (k_{2})) minus the coremantle heat flow (proportional to Im (k_{2}^{∘})). As an illustration, I compute the equilibrium thickness of a convecting crust. More generally, membrane formulas are useful in any application involving tidal Love numbers such as crust thickness estimates, despinning tectonics or true polar wander.
 Publication:

Icarus
 Pub Date:
 March 2015
 DOI:
 10.1016/j.icarus.2014.10.027
 arXiv:
 arXiv:1410.4735
 Bibcode:
 2015Icar..248..109B
 Keywords:

 Europa;
 Tides: solid body;
 Tectonics;
 Planetary dynamics;
 Tides;
 solid body;
 Physics  Geophysics
 EPrint:
 69 pages, 13 figures, 11 tables, accepted for publication in Icarus