Tidal heating and orbital evolution of the Galilean satellites: a coupled modelling approach

Tidal heating sustained by the Laplace resonance between Io, Europa, and Ganymede shapes the interiors of these moons and is thought to play an important role in the thermo-chemical evolution of their interiors, thereby conditioning the long-term habitability potential of the subsurface oceans of Jupiter’s icy Galilean moons. The joint history of the moons' orbits and interiors, intricately linked through dissipation processes, is therefore a central scientific question and a core objective of the upcoming JUICE and Europa Clipper missions.

Beyond present-day astrometric constraints on the resonance evolution (Lainey et al., 2009), the longer-term history of the system remains poorly constrained. Geological evidence observed on the moons' surfaces suggest that the moons experienced past changes in their orbital configuration (Greenberg, 2010), likely involving eccentricity excursions and associated episodes of enhanced tidal dissipation. Such variations in tidal forcing are expected to strongly affect the thermal state, structure, and rheology of the moons’ interiors. They may drive transitions between thinning/thickening of icy shells, expansion/crystallisation of subsurface oceans, and episodes of melting within the silicate mantles (Běhounková et al., 2021), with feedback on the efficiency of tidal dissipation. The frequency and intensity of these intense tidal activity periods are tightly linked to the resonance history. Existing studies have largely treated orbital and interior evolutions in isolation, with only limited attempts at consistent coupling (Showman et al., 1997; Hussmann and Spohn, 2004; Bland et al., 2009).

As a first step towards addressing this, we combine a N-body integrator with interior structure and dissipation models, exploiting the large separation in characteristic timescales between orbit evolution and interior evolution. As tidal heating is most significant in Io and Europa, we focus on the interiors of the innermost Galilean satellites, keeping dissipation in Ganymede and Callisto constant in this first implementation. The dynamical model integrates the full equations of motion of the Jovian system, accounting for Jupiter's oblateness, mutual gravitational interactions between the moons, third-body perturbation from the Sun, and tidal forces. Tidal dissipation within each moon is parametrised through the imaginary part of the Love number, Im(k2). The interior model is evolved on a much coarser time step than the orbital integration: it uses the eccentricity history produced by the dynamics to update the tidal heating budget, compute the temperature and dissipation profiles within each moon, and subsequently evolve the melt distribution in the silicate mantles of Io and Europa (total volume and depth) together with the thickness of Europa's ice shell. A new Im(k₂), reflecting the evolving internal structure and rheology, is then derived and fed back into the dynamical model. This approach allows us to capture potential transient episodes of enhanced dissipation associated with partial melting in the mantle of Io, and to a lesser extent Europa, and to quantify its impact on orbital evolution.

We apply this framework to the last few hundred million years of the Galilean system, with particular attention to eccentricity variations and associated tidal heating episodes. The objective is twofold: to place quantitative constraints on the intensity and duration of past dissipation episodes consistent with present-day observations, and to identify families of plausible evolution scenarios. The resulting picture is intended as an interpretive framework for the detailed characterisation of the present-day system to be returned by JUICE and Europa Clipper.

References

Lainey, V., et al. "Strong tidal dissipation in Io and Jupiter from astrometric observations." Nature 459.7249 (2009): 957-959.

Greenberg, R. "The icy Jovian satellites after the Galileo mission." Reports on Progress in Physics 73.3 (2010): 036801.

Běhounková, M., et al. "Tidally induced magmatic pulses on the oceanic floor of Jupiter's moon Europa." Geophysical Research Letters 48.3 (2021): e2020GL090077

Showman, A. P., and Malhotra, R. "Tidal evolution into the Laplace resonance and the resurfacing of Ganymede." Icarus 127.1 (1997): 93-111.

Hussmann, H., and Spohn, T.. "Thermal-orbital evolution of Io and Europa." Icarus 171.2 (2004): 391-410.

Bland, M. T., Showman, A. P., and Tobie, G. "The production of Ganymede's magnetic field." Icarus 198.2 (2008): 384-399.