Orbital evolution of Saturn’s mid-sized moons and the tidal heating of Enceladus
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
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 . We adopt and . 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 . 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,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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