Strong tidal energy dissipation in Saturn at Titan’s frequency as an explanation for Iapetus orbit

¹ IMCCE, Observatoire de Paris, PSL Research University, CNRS, UPMC Univ. Paris 06, Univ. Lille, France
e-mail: william.polycarpe@obspm.fr
² Jet Propulsion Laboratory, California Institute of Technology, Pasadena, USA
³ Namur Institute for Complex Systems (naXys), University of Namur, Belgium

Received: 23 July 2018
Accepted: 6 September 2018

Abstract

Context. Natural satellite systems present a large variety of orbital configurations in the solar system. While some are clearly the result of known processes, others still have largely unexplained eccentricity and inclination values. Iapetus, the furthest of Saturn’s main satellites, has a still unexplained 3% orbital eccentricity and its orbital plane is tilted with respect to its local Laplace plane (8° of free inclination). On the other hand, astrometric measurements of saturnian moons have revealed high tidal migration rates, corresponding to a quality factor Q of Saturn of around 1600 for the mid-sized icy moons.

Aims. We show how a past crossing of the 5:1 mean motion resonance between Titan and Iapetus may be a plausible scenario to explain Iapetus’ orbit.

Methods. We have carried out numerical simulations of the resonance crossing using an N-body code as well as using averaged equations of motion. A large span of migration rates were explored for Titan and Iapetus was started on its local Laplace plane (15° with respect to the equatorial plane) with a circular orbit.

Results. The resonance crossing can trigger a chaotic evolution of the eccentricity and the inclination of Iapetus. The outcome of the resonance is highly dependent on the migration rate (or equivalently on Q). For a quality factor Q of over around 2000, the chaotic evolution of Iapetus in the resonance leads in most cases to its ejection, while simulations with a quality factor between 100 and 2000 show a departure from the resonance with post-resonant eccentricities spanning from 0 up to 15%, and free inclinations capable of reaching 11°. Usually high inclinations come with high eccentricities but some simulations (less than 1%) show elements compatible with Iapetus’ current orbit

Conclusions. In the context of high tidal energy dissipation in Saturn, a quality factor between 100 and 2000 at the frequency of Titan would bring Titan and Iapetus into a 5:1 resonance, which would perturb Iapetus’ eccentricity and inclination to values observed today. Such rapid tidal migration would have avoided Iapetus’ ejection around 40–800 million years ago.