Tilting Uranus via the migration of an ancient satellite

¹ IMCCE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Université, Université de Lille, 75014 Paris, France
e-mail: melaine.saillenfest@obspm.fr
² Astronomy Department, University of Maryland College Park, MD 20742, USA
³ Department of Mathematics, University of Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
⁴ Université Côte-d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange (UMR7293), Boulevard de l’Observatoire, 06304 Nice cedex 4, France

Received: 4 May 2022
Accepted: 21 September 2022

Abstract

Context. The 98° obliquity of Uranus is commonly attributed to giant impacts that occurred at the end of the planetary formation. This picture, however, is not devoid of weaknesses.

Aims. On a billion-year timescale, the tidal migration of the satellites of Jupiter and Saturn has been shown to strongly affect their spin-axis dynamics. We aim to revisit the scenario of tilting Uranus in light of this mechanism.

Methods. We analyse the precession spectrum of Uranus and identify the candidate secular spin-orbit resonances that could be responsible for the tilting. We determine the properties of the hypothetical ancient satellite required for a capture and explore the dynamics numerically.

Results. If it migrates over 10 Uranus’s radii, a single satellite with minimum mass 4 × 10⁻⁴ Uranus’s mass is able to tilt Uranus from a small obliquity and make it converge towards 90°. In order to achieve the tilting in less than the age of the Solar System, the mean drift rate of the satellite must be comparable to the Moon’s current orbital expansion. Under these conditions, simulations show that Uranus is readily tilted over 80°. Beyond this point, the satellite is strongly destabilised and triggers a phase of chaotic motion for the planet’s spin axis. The chaotic phase ends when the satellite collides into the planet, ultimately freezing the planet’s obliquity in either a prograde or a plainly retrograde state (as Uranus today). Spin states resembling that of Uranus can be obtained with probabilities as large as 80%, but a bigger satellite is favoured, with mass 1.7 × 10⁻³ Uranus’s mass or more. Yet, a smaller ancient satellite is not categorically ruled out, and we discuss several ways to improve this basic scenario in future studies. Interactions among several pre-existing satellites are a promising possibility.

Conclusions. The conditions required for the tilting seem broadly realistic, but it remains to be determined whether Uranus could have hosted a big primordial satellite subject to substantial tidal migration. The efficiency of tidal energy dissipation within Uranus is required to be much higher than traditionally assumed, more in line with that measured for the migration of Titan. Hints about these issues would be given by a measure of the expansion rate of Uranus’s main satellites.