Elastic Ice Shells of Synchronous Moons

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Scientific paper

A growing number of water-rich, synchronous moons are thought to contain subsurface water oceans below an icy shell, most notably Europa and Titan. Under tidal and rotational stresses, these shells deform and store elastic energy unless the shell yields or viscously deforms on a timescale that is fast compared to the forcing period. Otherwise, the deformed shell experiences a back-torque tending to keep it aligned with the satellite-planet line. The shell will rotate an angle given by the balance between the elastic torque and the spinup torque. For Europa, it has been widely advocated that stresses arising from non-synchronous rotation of the shell are responsible for the large cracks on its surface. The angle giving balance between the tidal and elastic torques is exceedingly small -- of order 10^-6 radians -- and associated stresses are only of the order 1 Pa, well below that needed to crack the shell; this poses a challenge to the prevailing ideas of surface cracking on Europa. Time-dependent gravity anomalies from mantle convection in Europa is a more likely mechanism for producing large surface cracks. On Titan, it has been reported that the surface spin is faster than synchronous, which has been interpreted as resulting from a seasonally varying atmospheric torque on the surface shell. The maximum atmospheric torque could rotate an elastic shell relative to the underlying hydrostatic shape of order 10^-3 radians, implying the shell is effectively coupled to the interior. Therefore, the atmospheric torque forces a libration of the entire figure that is 180 degrees out-of-phase with the forcing and with a smaller amplitude than has been reported.

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