Coupled orbital and thermal evolution of Ganymede

Abstract

We explore the hypothesis that passage through an eccentricity-pumping resonance could lead to the resurfacing of Ganymede. To do so, we couple R. Malhotra's (1991, Icarus 94, 399–412) orbital model for the tidal evolution of the Laplace resonance to an internal model of Ganymede. Our model explores the conditions under which Ganymede can undergo global thermal runaway, assuming that the Q/k of Ganymede is strongly dependent on internal temperature. (Here Q is the tidal dissipation function and k is the second-degree Love number.) We allow the system to pass through the ω_1/ω_2≈ 2 or ω_1/ω_2≈ 1/2 resonance, where ω_1≡ 2n_2−n_1, ω_2≡ 2n_3−n_2, and n_1, n_2, and n_3 are the mean motions of Io, Europa, and Ganymede. If Ganymede's initial internal temperature is either “too hot” or “too cold,” no runaway occurs, while for intermediate temperatures (∼200 K in the upper mantle), conditions are “just right,” and runaway occurs. The range of mantle temperatures that allows runaway depends on the model for tidal Q; we use the Maxwell model, which ties Q to the creep viscosity of ice. Runaways can induce up to ∼50–100 K warming and formation of a large internal ocean; they occur over a 10^7 to 10^8-year period. Assuming carbonaceous chondritic abundances of radionuclides in Ganymede's rocky portion, however, we find that the interior cannot cool to the initial temperatures needed to allow large runaways. If our model is correct, large runaways cannot occur, although small runaways are still possible. Different formulations of tidal Q or convective cooling may allow large runaways. Large runaways are also possible if radionuclides are substantially depleted, although this is unlikely. We next consider the consequences of a large runaway, assuming it can occur. Ganymede can undergo 0.5% thermal expansion (by volume) during the largest thermal runaways. Melting of the ice mantle provides up to 2% expansion despite the fact that contraction produced by melting ice I offsets expansion produced by melting high-pressure ice phases. Solid–solid phase transitions cause negligible satellite expansion. Lithospheric stresses caused by expansion of 2% over 10^7 to 10^8 years are ∼10^2 bars at the surface, and drop to a few bars at several kilometers depth. Such stresses could cause cracking to depths of several kilometers. The cracking and near-surface production of warm or partially molten ice make resurfacing a plausible outcome of a large thermal runaway. The tidal heating events proposed here may also be relevant for generation of Ganymede's modern-day magnetic field.