Future destabilisation of Titan as a result of Saturn's tilting

Abstract

Context: As a result of Titan's migration and Saturn's probable capture in secular spin-orbit resonance, recent works show that Saturn's obliquity could be steadily increasing today and may reach large values in the next billions of years. Satellites around high-obliquity planets are known to be unstable near their Laplace radius, but the approximations used so far are invalidated in this regime. Aims: We aim to investigate the behaviour of a planet and its satellite when the satellite crosses its Laplace radius while the planet is locked in secular spin-orbit resonance. Methods: We expand on previous works and revisit the concept of Laplace surface. We use it to build an averaged analytical model that couples the planetary spin-axis and satellite dynamics. Results: We show that the dynamics is organised around a critical point, S1, at which the phase-space structure is singular, located at 90° obliquity and near the Laplace radius. If the spin-axis precession rate of the planet is maintained fixed by a resonance while the satellite migrates outwards or inwards, then S1 acts as an attractor towards which the system is forced to evolve. When it reaches the vicinity of S1, the entire system breaks down, either because the planet is expelled from the resonance or because the satellite is ejected or collides into the planet. Conclusions: Provided that Titan's migration is not halted in the future, Titan and Saturn may reach instability between a few gigayears and several tens of gigayears from now, depending on Titan's migration rate. The evolution would destabilise Titan and drive Saturn towards an obliquity of 90°. Our findings may have important consequences for Uranus. They also provide a straightforward mechanism for producing transiting exoplanets with a face-on massive ring, a configuration that is often put forward to explain some super-puff exoplanets.

Accepted for publication in Astronomy and Astrophysics

References in corpus (16)

• Satellite dynamics on the Laplace surface
• Resonance locking in giant planets indicated by the rapid orbital expansion of Titan
• Obliquity-Driven Sculpting of Exoplanetary Systems
• Exploring Whether Super-Puffs Can Be Explained as Ringed Exoplanets
• Excitation of Planetary Obliquities Through Planet-Disk Interactions
• On the Spin-axis Dynamics of a Moonless Earth
• Can planetary rings explain the extremely low density of HIP 41378f?
• Secular spin-axis dynamics of exoplanets
• Exo-Milankovitch Cycles I: Orbits and Rotation States
• The large obliquity of Saturn explained by the fast migration of Titan
• Planetary Spin and Obliquity from Mergers
• The future large obliquity of Jupiter
• The past and future obliquity of Saturn as Titan migrates
• The Structure and Stability of Extended, Inclined Circumplanetary Disk or Ring Systems
• Primordial giant planet obliquity driven by a circumplanetary disk
• Analytical solution of the Colombo top problem

Cited by in corpus (5)

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• Oblique rings from migrating exomoons: A possible origin for long-period exoplanets with enlarged radii
• Stellar Obliquity Excitation via Disk Dispersal-Driven Resonances in Binaries
• Sculpting of Exoplanetary Systems Driven by a Misaligned Disk and Stellar Oblateness: Origin of Perpendicular Orbits in HD 3167
• The Coupled Tidal Evolution of the Moons and Spins of Warm Exoplanets