A collisionless scenario for Uranus tilting

Unlike the other planets in the Solar System, Uranus is lying on its orbit : its rotation axis is tilted by 97 degrees from the pole of its orbit. The origin of this high obliquity is still poorly understood. This is indeed one of the most intriguing questions concerning the Solar System.

The mechanism generally invoked to solve this problem is a giant collision with an earth-sized protoplanet at the end of the planet formation. But the presence of regular satellites (Miranda, Ariel, Umbriel, Titania, Oberon) whose orbits are almost in the equatorial plane of Uranus suggests rather that Uranus tilting has occurred gradually, and not through a violent collision.

Following this observation, Gwenaël Boué and Jacques Laskar of the Observatoire de Paris, studied the possibility that Uranus can be tilted without collision. They have found that such a tilt could occur during an early phase of the history of the Solar System when planets have migrated up to the orbits that are observed today. The new mechanism supposes that Uranus has owned a massive satellite in the past and that the orbit of Uranus has experienced a period of large inclination.

In the Solar System, the axes of the planets and the poles of their orbits have a precession motion similar to that of a top, they describe a cone. When a planet is in spin-orbit resonance, ie when its axis and its orbit evolve at the same speed, it can be tilted. Today, Uranus axis precesses very slowly, but researchers have shown that the presence of a satellite one hundred times less massive than Uranus located at 50 planet radii can increase the precession rate by a factor 1000 which then allows resonance.

Of course, now Uranus has no such satellite but the researchers assume that the satellite responsible for Uranus tilting was then ejected in a close encounter with a giant planet at the end of the migration phase.

Figure 1 : Exemple d’évolution de l’axe d’Uranus lors d’un basculement dans un repère tournant à la vitesse de précession de son orbite. Le plan xy est le plan de référence. Le pôle de l’orbite se situe dans le plan xz, du côté des x négatifs. Initialement l’axe d’Uranus est aligné avec l’axe z. Durant les phases de résonance, l’axe effectue une rotation autour de l’axe x, sinon il effectue une rotation autour de l’axe z. Dans cette simulation, il y a deux périodes de résonance (courbe noire, puis verte + rouge) séparées par une évolution non résonante (courbe bleue). A la fin du basculement l’axe est incliné de plus de 80 degrés et sort de la résonance, l’obliquité reste stable (courbe cyan).

To verify this scenario, Gwenaël Boué and Jacques Laskar made 10,000 numerical simulations of the migration of the giant planets, following the model developed by researchers at the Nice Observatory. In these migrations, the order of the planets is sometimes modified, and they have kept only those where the final order of the planets corresponds to the current Solar System. They then selected scenarios in which the orbital inclination of Uranus is large enough to allow the tilt. By setting the threshold to 17 degrees, and after having rejected the simulations leading to systems too unstable, there remained only 17 simulations of the planetary System. Then, for each of these planetary migration scenarios, they simulated the presence of the new satellite. In 2% of cases, this new satellite allows Uranus tilting and is then ejected by a close encounter with one of the other giant planets.

This scenario does not only explain why Uranus is lying on its orbit, but it also solves the problem of the missing satellite raised by recent theories of satellite formation.

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