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

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.

The Combined Effect of Tidally and Eddy-Driven Diapycnal Mixing on the Large-Scale Ocean Circulation

Several recent studies have shown that ocean western boundaries are the primary regions of eddy energy dissipation. Globally, the eddy energy sinks have been estimated to integrate to about 0.2 TW. This is a sizable fraction of the tidal energy dissipation in the deep oceanic interior, estimated at about 1.0 TW and contributing to diapycnal mixing. The authors conduct sensitivity experiments with an ocean general circulation model assuming that the eddy energy is scattered into high-wavenumber vertical modes, resulting in energy dissipation and locally enhanced diapycnal mixing. When only the tidal energy dissipation maintains diapycnal mixing, the overturning circulation, and stratification in the deep ocean are too weak. With the addition of the eddy dissipation, the deep-ocean thermal structure becomes closer to that observed and the overturning circulation and stratification in the abyss become stronger. Furthermore, the mixing associated with the eddy dissipation can, on its own, drive a relatively strong overturning. The stratification and overturning in the deep ocean are sensitive to the vertical structure of diapycnal mixing. When most of this energy dissipates within 300 m above the bottom, the abyssal overturning and stratification are too weak. Allowing for the dissipation to penetrate higher in the water column, such as suggested by recent observations, results in stronger stratification and meridional circulation. Zonal circulation is also affected. In particular, the Drake Passage transport becomes closer to its observational estimates with the increase in the vertical scale for turbulence above topography. Consistent with some theoretical models, the Drake Passage transport increases with the increase in the mean upper-ocean diffusivity.

Migration and Final Location of Hot Super Earths in the Presence of Gas Giants

Based on the conventional sequential-accretion paradigm, we have proposed that, during the migration of first-born gas giants outside the orbits of planetary embryos, super Earth planets will form inside the 2:1 resonance location by sweeping of mean motion resonances (Zhou et al. 2005). In this paper, we study the subsequent evolution of a super Earth (m1) under the effects of tidal dissipation and perturbation from a first-born gas giant (m2) in an outside orbit. Secular perturbation and mean motion resonances (especially 2 : 1 and 5 : 2 resonances) between m1 and m2 excite the eccentricity of m1, which causes the migration of m1 and results in a hot super Earth. The calculated final location of the hot super Earth is independent of the tidal energy dissipation factor Q′. The study of migration history of a Hot Super Earth is useful to reveal it's Q′ value and to predict its final location in the presence of one or more hot gas giants. When this investigation is applied to the GJ876 system, it correctly reproduces the observed location of GJ876d around 0.02 AU.