Elsevier

Icarus

Volume 317, 1 January 2019, Pages 570-582
Icarus

Orbital evolution of Saturn’s mid-sized moons and the tidal heating of Enceladus

https://doi.org/10.1016/j.icarus.2018.08.030Get rights and content

Highlights

  • How Saturnian mid-sized moons avoid resonant capture during orbital evolution?

  • The tidal orbital evolution of these moons was investigated by N-body simulations.

  • The ring torque is a key to reproduce the current orbits of the mid-sized moons.

  • The stored heat in Enceladus during the evolution may explain the current heat flow.

Abstract

The formation and orbital evolution of Saturn’s inner mid-sized moons – Rhea, Dione, Tethys, Enceladus, and Mimas – are still debated. The most puzzling aspects are 1) how the Tethys–Dione pair and the Mimas–Enceladus pair passed through their strong 3:2 mean-motion resonances during the tidal orbital evolution, and 2) the current strong heat flow from Enceladus, which is a few orders of magnitude higher than the tidal energy dissipation caused by the present orbital eccentricity of Enceladus. Here we perform N-body simulations of the moons’ orbital evolution from various initial conditions – assuming that the moons were formed from Saturn’s hypothetical massive ring – and investigate possible paths to solve the above difficulties. If the moons remain on nearly circular orbits and the influence of the rings is neglected, we find that the Tethys–Dione pair cannot avoid becoming trapped in the 2:1 and 3:2 mean-motion resonances as they recede from Saturn, and that the Tethys–Enceladus pair cannot avoid collisions after the resonance trapping, in case Saturn’s quality factor is smaller than 15,000. These findings are inconsistent with the current orbital configuration. However, taking into account both the eccentricity excitation and the orbital expansion caused by the ring torque, we find that these resonance captures are avoided. With the relatively high eccentricity pumped up by the torque, Enceladus passes through all the mean-motion resonances with Tethys, and the Dione–Tethys pair passes through their 2:1 resonance and possibly the 3:2 resonance as well. After Enceladus resides beyond the 2:1 resonance with the outer ring edge, the eccentricity can be tidally damped. While this is a promising path of evolution, in most runs, Enceladus collides with Tethys by the excited eccentricity. There is a hint that a ring mass decrease (possibly due to Mimas formation) could avoid the collision between Enceladus and Tethys. The parameter survey taking into account detailed ring evolution and Mimas is left for future study. The heat that was tidally dissipated due to the eccentricity excitation by the ring torque in the past is stored in the moons and slowly radiated away through conductive transfer. The stored heat in Enceladus may account for the current anomalously high heat flow.

Section snippets

Introduction and tidal evolution

The evolution and origin of Saturn’s mid-sized moons – Mimas, Enceladus, Tethys, Dione, and Rhea – remain an enigma. Located closer than Saturn’s massive moon Titan, but farther away than Saturn’s famous ring system and a collection of much smaller moons, the classical mid-sized moons form a rich dynamical system both now and in the past.

The masses and orbital elements of these moons are listed in Table 1. When ignoring mutual gravitational interactions and orbital eccentricities, the relative

Numerical model

We simulate the orbital evolution of the system – which mainly consists of Saturn, Enceladus, Tethys, and Dione – to investigate the detailed orbital evolution of strongly interacting moons starting from many different initial conditions; in some runs we also added Rhea. Dynamically, Rhea is almost decoupled from other moons. Mimas has the smallest mass and could not affect other moons’ motions significantly.

Fig. 1 suggests that the Enceladus–Tethys pair undergoes orbital crossing if Qp<15,000

SET1: Enceladus forms no later than Tethys

Fig. 3 shows a typical result of orbital evolution of SET1A. In this case, the ring torque is not taken into account (Mring=0). We adopt Qp=1700 and C=104. Because interactions of Enceladus, Tethys and Dione are essential for the orbital evolution in SET1A, we omit Mimas.

We start simulations when Tethys is formed at aT,0aF=1. Enceladus was already formed and has migrated to aE, 0 ∼ 1.5aF in agreement with Fig. 1. Because Tethys is 5.7 times more massive (Table 1), it catches up with Enceladus (

Heat flux

As we have shown, the moons would have undergone a high eccentricity phase in the past during orbital evolution. As we show below, the heat generated during the high eccentricity phase can be stored in the interior and the current high heat flux can reflect the stored heat (the current heat generation is not balanced with the surface heat flux). From the numerical simulations, here we calculate the stored heat energy for each moon,EHdt,where H is given by Eq. (2).

Although Enceladus would have

Conclusion and discussion

Through N-body simulations, we have numerically investigated the orbital evolution of Saturn’s mid-sized moons (mainly Dione, Tethys and Enceladus), under the influence of Saturn’s tidal force, tidal dissipation in the moons, and the torque exerted by its ring. Our work was based on the model of the mid-sized moons having formed relatively recently from the spreading out of a massive ring, a theory that was proposed by Charnoz et al. (2011). We have performed 80 runs in total with various

Acknowledgments

We thank anonymous referees for their helpful and very detailed comments. This work was supported by JSPS Kakenhi grant 15H02065 and 17K05635. We thank Daigo Shoji for helpful comments.

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