Secular resonance between Iapetus and the giant planets

Abstract

Using numerical integrations, we find that the orbital eccentricity of Saturn's moon Iapetus undergoes prominent multi-Myr oscillations. We identify the responsible resonant argument to be ω -ωg5 + Ω -Ωeq, with the terms being the longitudes of pericentre of Iapetus and planetary secular mode g5, Iapetus's longitude of the node and Saturn's equinox. We find that this argument currently (on a 107 yr time-scale) appears to librate with a very large amplitude. On longer time-scales, the behaviour of this resonant angle is strongly dependent on the resonant interaction between Saturn's spin axis and the planetary mode f8, with long-term secular resonance being possible if Saturn's equinox is librating relative to the node of the f8 eigenmode. We present analytical estimates of the dependence of the resonant argument on the orbital elements of Iapetus. We find that this Iapetus-g5 secular resonance could have been established only after the passage of Iapetus through the 5:1 mean-motion resonance with Titan, possibly in the last Gyr. Using numerical simulations, we show that the capture into the secular resonance appears to be a low-probability event. While the Iapetus-g5 secular resonance can potentially help us put new constraints on the past dynamics of the Saturnian system, uncertainties in both the spin axis dynamics of Saturn and the tidal evolution rate of Titan make it impossible to make any firm conclusions about the resonance's longevity and origin.