Fast orbital migration of moons and implications in the solar system

Introduction

Current orbits of moon systems are the result of billion-year evolution, which is mainly driven by tidal forces acting between satellites and their host planet. Past studies of moons' orbital history are based on classic tidal equilibrium models, which assumed constant values of tidal quality factors Q between 10⁴ and 10⁶ for giant planets (Goldreich and Soter 1966). From the resulting secular trend of moons' distance from their host planet, researchers predicted past resonance crossings and captures between moons. Analyzing the dynamical effects of resonances, they tried to explain observed orbital eccentricities and inclinations, and also geophysical features, like past resurfacing events.

However, recent studies and measurements suggest that tidal dissipation within gas giant planets is much higher than previously thought (Fuller et al. 2016, Lainey et al. 2020). As consequence, moons of giant planets could move away from their host planet more rapidly, including outer moons like Callisto and Titan. This new paradigm provides new directions for the reconstruction of the orbital history of natural satellites, and more generally of the co-evolution of moons and planets. More precisely, a fast migration of moons changes their expected orbital expansion, allowing different resonances to have played a fundamental role in shaping the moon systems of Jupiter, Saturn and Uranus. Moreover, as moons' orbital dynamics is coupled with the rotational dynamics of their host planet, a fast migration of moons affects the evolution of planet's obliquity as well.

In this context, we aim at revisiting the history of moon systems in the solar system.

Methods

We investigate orbital evolution of moon systems assuming high tidal dissipation scenarios. More precisely, we assume different values of the planet's quality factor Q for different moons (frequency dependence), considering also values between 1 and 10³, a range outside classic tidal theories (see Downey et al. 2020, Lainey et al. 2020 and Nimmo 2023 for low Q values in the Jupiter, Saturn and Uranus systems, respectively). Since low values of parameters Q cannot be sustained for the whole history, they must start from large values and then decrease during the evolution (Fuller et al. 2016). From the resulting orbital expansion, we can search for crossings of resonances between satellites, focusing on most significant ones and on differences with classic moons' evolution scenarios. Through numerical simulations of specific resonance crossings, we explore the dynamical effects on the orbits and assess whether such evolution is compatible with the current configuration of the moon systems.

Furthermore, for studying the effect of the fast orbital migration on their host planets, we simulate the moons evolution over billion years. From the total orbital expansion of moons, we compute the change of the precession frequency of the host planet's spin axis and we check whether the planet encountered spin-orbit resonances during its evolution. Capture in such resonances makes the obliquity increase, possibly explaining the observed tilt of giant planets in the solar system. Through numerical simulations, we try then to reconstruct the evolution of planets' spin axes.

Results

In the Saturn system, the fast migration of some moons seems confirmed by observations, including Titan (Lainey et al. 2020), and the whole orbital evolution of the system has been recently reviewed in light of new tidal theories (Cuk et al. 2024).

In the Jupiter system, when assuming a fast migration of the moon Callisto, it follows that the outer moon should have encountered the 2:1 resonance with Ganymede, which is already involved in the Laplace resonance with Io and Europa. We show that if Callisto crossed the resonance, all four Galilean satellites could have been temporarily trapped in a four-body resonant chain. This evolution could account for the observed past resurfacing of Ganymede, even in a scenario where the Laplace resonance is primordial (Lari et al. 2023).

In the Uranus system, if we consider a fast migration of Ariel, we show that a past 2:1 resonance crossing between Ariel and Umbriel is almost certain, although past studies tried to avoid it. The capture in this strong resonance would explain past resurfacing of Ariel. However, it is not clear whether it would have been possible for the moons to exit the resonance once captured; the involvement of other satellites of the system could provide a dynamical tool for breaking the resonance.

Finally, when considering the fast and long migration of moons, the tilting history of giant planets greatly change with respect to previously proposed scenarios. Because of moons migration, the planets' spin-axis precession frequencies tend to increase, pushing giant planets into spin-orbit resonances. This way, it is possible to explain the spin axis tilts of Jupiter and Saturn (Saillenfest et al. 2020, 2021) and to bring also key advances into explaining the extreme axis tilt of Uranus (Saillenfest et al. 2022). Evolution through spin-orbit resonances provides a smooth increase of the obliquity, without the need of catastrophic events like giant impacts.

In the end, a fast migration of moons offers a compelling opportunity to explain current configuration of moon systems and address some open questions of the solar system.

 

References

Cuk et al. (2024), Space Science Reviews 220, 20.
Downey et al. (2020), Monthly Notices of the Royal Astronomy Society 499, 40-51.
Fuller et al. (2016), Monthly Notices of the Royal Astronomy Society 458, 3867-3879.
Goldreich and Soter (1966), Icarus 5, 375-389.
Lainey et al. (2020), Nature Astronomy 4, 1053-1058.
Lari et al. (2023), Monthly Notices of the Royal Astronomy 518, 3023-3035.
Nimmo (2023), The Planetary Science Journal 4, 241.
Saillenfest et al. (2020), Astronomy and Astrophysics 640, A11.
Saillenfest et al. (2021), Nature Astronomy 5, 345-349.
Saillenfest et al. (2022), Astronomy and Astrophysics 668, A108.