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Insert Tidal Here: A Planetary Evolution Cookbook

  • Author(s): Walker, Matthew
  • Advisor(s): Mitchell, Jonathan L
  • et al.
Abstract

The observed activity at the surfaces of the Galilean satellites mask subsurface internal dynamics. Tides generated from their primary, the massive planet Jupiter, deform these moons and can generate significant heat. This heat must then escape to space. The heat moving through a satellite has the potential to modify the interior structure, melting regions and causing internal interface boundary migration. We track how tidally generated heat will flow out of Io and Europa, and how this heat will modify the planetary structures. To do this we determine specific forms for the k Love numbers which depend on internal structure and temperature profiles. The Love numbers are used as a linear factor in tidal heating models. Because the Love numbers are very frequency dependent, it is important to consider every frequency term in a tide, as some may be much more significant than others. While some tidal heating models consider the orbital frequency only, we present the full tidal heating spectrum and isolate which terms are significant in which cases. In addition to finding the simple tidal heat forms for use with Io and Europa, we demonstrate with extreme examples, the tidal heating scenarios at Mercury and Venus. In these cases we find systems where the tidal heat delivery comes at frequencies related to sums and differences of mean motion and spin rate. Finally we use the Love numbers for Io and Europa we generated, in the tidal heating models as a term in thermal evolution models. We balance a tidal heat input into the bodies with heat convected upward into an elastic lid. The lid then conducts the once tidal heat into space. We probe the planetary structural and temperature space which leads to equilibrium conditions, where the tidal heat input is balanced by heat escape. For Io, we find no stable equilibrium scenarios for any structure we consider, and the body ultimately melts. This results because the dissipating volume is assumed to extend to the core. This generates much more heat than is able to conduct out through the lid and runaway melting occurs. Reducing the volume of the region, by adding a core or a subsurface fluid silicate layer, may reduce the volume enough for stable conditions to be found. In Europa, we do find stable equilibrium conditions at ice shells of roughly 50 km. For shells thicker than this, the tidal heating is too strong due to increased volume, and so the shell melts some in response until stable equilibrium is achieved. The Europa Clipper mission is slated to measure both shell thickness as well as the k Love number. With the relationships we draw between structural and orbital parameters, these measurements in the system can help constrain our models so that we can use Europa’s current state as a probe for its thermal history and an indicator of its thermal future.

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