Joint dynamical-geophysical evidence for a limit cycle in the Galilean moons
Io, Europa, and Ganymede orbit in the Laplace mean-motion resonance, where their orbital and thermochemical evolution are strongly coupled [1-5]. Forced eccentricities sustain tidal dissipation, powering Io's volcanism and maintaining Europa's subsurface ocean [6-8]. Tidal heating depends on the moons' eccentricities, semimajor axes, and interior properties. Orbital evolution depends on how satellite dissipation affects the resonant dynamics [4, 8]. This coupled evolution has not been treated in a self-consistent framework constrained by modern observations. Here, we combine modern astrometric and geophysical measurements of migration rates, surface heat fluxes, tidal response, and moment of inertia [9-13] with an orbital-thermochemical evolution model to constrain the long-term evolution and present state of the moons. We show that the joint observations select an ongoing late-time limit cycle, likely established $\sim$0.8-2.0 Gyr ago through feedback between thermal and orbital evolution. The present-day state recurs within this oscillatory branch, whose cycles repeat every $\sim$95-150 Myr. Io presently experiences high dissipation and migrates inward, whereas Europa and Ganymede continue to migrate outward. Europa is predicted to undergo episodes of inward migration during the cycle. During the cycles, Io's mean melt fraction varies substantially ($\sim$10-30%), while Europa's ice-shell thickness varies by $\sim$3-15 km. The predicted structures of Europa and Io will be assessed by future missions including Europa Clipper, JUICE, and IVO [14-17].