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The large obliquity of Saturn explained by the fast migration of Titan

Abstract

The obliquity of a planet is the tilt between its equator and its orbital plane. Giant planets are expected to form with near-zero obliquities1,2. After the formation of Saturn, some dynamical mechanism must therefore have tilted Saturn up to its current obliquity of 26.7°. This event is traditionally thought to have happened more than 4 Gyr ago during the late planetary migration3,4,5 because of the crossing of a resonance between the spin-axis precession of Saturn and the nodal orbital precession mode of Neptune6. Here, we show that the fast tidal migration of Titan for which the measurement is reported in ref. 7 is incompatible with this scenario, and that it offers a new explanation for Saturn’s current obliquity. A substantial migration of Titan would prevent any early resonance, which would invalidate previous constraints on the late planetary migration that were set by the tilting of Saturn8,9,10. We propose instead that the resonance was encountered more recently, about 1 Gyr ago, and forced Saturn’s obliquity to increase from a small value (possibly less than 3°) to its current state. This scenario suggests that Saturn’s normalized polar moment of inertia lies between 0.224 and 0.237. Our findings bring out a new paradigm for the spin-axis evolution of Saturn, Jupiter11 and possibly giant exoplanets in multiple systems, whereby obliquities are not settled once for all but evolve continuously as a result of the migration of their satellites.

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Fig. 1: Evolution of the effective precession constant α of Saturn due to the tidal migration of Titan.
Fig. 2: Examples of possible obliquity evolution for Saturn.
Fig. 3: Past obliquity of Saturn as a function of its current precession constant α0.
Fig. 4: Past obliquity of Saturn for different migration histories of Titan.

Data availability

Source Data for the figures are provided with this paper. The data supporting other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The parameters and equations of motion are fully described within the paper. All data can be reproduced using any standard implementation. The numerical integration scheme used is fully available from ref. 29.

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Acknowledgements

We thank L. Gomez Casajus for fruitful discussions and S. Renner for his suggestions during the writing of our manuscript. G.L. acknowledges financial support from the Italian Space Agency (ASI) through agreement no. 2017-40-H.0.

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G.B. conceived the original idea. G.L. compiled the data. G.L. and M.S. made the computations. M.S. wrote the article. All authors participated in supervising the whole study.

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Correspondence to Melaine Saillenfest.

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The authors declare no competing interests.

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Peer review information Nature Astronomy thanks David Nesvorny and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Source Data Fig. 2

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Source Data Fig. 3

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Source Data Fig. 4

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Saillenfest, M., Lari, G. & Boué, G. The large obliquity of Saturn explained by the fast migration of Titan. Nat Astron (2021). https://doi.org/10.1038/s41550-020-01284-x

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