Tilting Uranus: Collisions versus Spin--Orbit Resonance

Abstract

In this paper, we investigate whether Uranus's 98$^{\circ}$ obliquity was a by-product of a secular spin-orbit resonance assuming that the planet originated closer to the Sun. In this position, Uranus's spin precession frequency is fast enough to resonate with another planet located beyond Saturn. Using numerical integration, we show that resonance capture is possible in a variety of past solar system configurations, but that the timescale required to tilt the planet to 90$^{\circ}$ is of the order $\sim\!10^{8}$ yr -- a timespan that is uncomfortably long. A resonance kick could tilt the planet to a significant 40$^{\circ}$ in $\sim\!10^{7}$ yr only if conditions were ideal. We also revisit the collisional hypothesis for the origin of Uranus's large obliquity. We consider multiple impacts with a new collisional code that builds up a planet by summing the angular momentum imparted from impactors. Because gas accretion imparts an unknown but likely large part of the planet's spin angular momentum, we compare different collisional models for tilted, untilted, spinning, and nonspinning planets. We find that a 1 $M_{\oplus}$ strike is sufficient to explain the planet's current spin state, but that two $0.5\,M_{\oplus}$ collisions produce better likelihoods. Finally, we investigate hybrid models and show that resonances must produce a tilt of at least $\sim\!40^{\circ}$ for any noticeable improvements to the collision model. Because it is difficult for spin-orbit resonances to drive Uranus's obliquity to 98$^{\circ}$ even under these ideal conditions, giant impacts seem inescapable.