Tidal instability in stellar and planetary binary systems

In this paper, we combine theoretical and experimental approaches to study the tidal instability in planetary liquid cores and stars. We demonstrate that numerous complex modes can be excited depending on the relative values of the orbital angular velocity Ωorbit and of the spinning angular velocity Ωspin, except in a stable range characterized by Ωspin/Ωorbit ∈ [−1; 1/3]. Even if the tidal deformation is small, its subsequent instability coming from a resonance process may induce motions with large amplitude, which play a fundamental role at the planetary scale. This general conclusion is illustrated in the case of Jupiter’s moon Io by a coupled model of synchronization, demonstrating the importance of energy dissipation by elliptical instability.