My doctoral research at the California Institute of Technology was performed under the enthusiastic direction of my thesis advisor David J. Stevenson.
The first part of my doctoral thesis involved mathematical modeling of the coupled orbital and thermal evolution of Io. The gist of the work is that since tidal heating of Io is strongly dependent on internal temperature, the spectacular volcanic activity of Io becomes episodic, with volcanic episodes lasting perhaps a few million years, followed by longer quiescent periods when the orbital eccentricity builds due to resonant interactions with Europa and Ganymede. This perhaps helps to explain how the present enormous heat output of Io can occur, when theoretical considerations suggest that such high heat flow cannot be representative of the time average. That work resulted in this publication.
(left) The volcano Tvashtar erupting on the Tvashtar Paterae volcanic region on the innermost of Jupiter's Galilean moons, Io, as seen by NASA's New Horizons spacecraft in 2007.
Above are a few figures from the paper accessible by the hyperlink above.
The latter two-thirds of my doctoral work involved detailed analysis of the equilibrium thickness of an ice shell overlying liquid water on Europa. The surprising result was that when such a shell approaches thermal equilibrium, it simultaneously approaches a state of rotation about the intermediate axis of inertia, thus becoming dynamically unstable. Thermal and dynamical equilibrium are thus mutually incompatible, and the shell was predicted to reorient about the Europa-Jupiter axis spontaneously, roughly every 10 million years or so. The resulting stress in the shell may be enormous, thus helping to explain many of the global-scale cracks in Europa's ice. The original papers resulting from this work are here and here. More recently, evidence for such reorientation has been discovered by Dr. Paul Schenk of the Lunar and Planetary Institute. I will include more on this topic as time permits.