The Tilts and Spins of Planets and Moons

Abstract

The planets' spin states, specifically their tilts and spins, can provide useful constraints to planetary formation as they evolve and interact with their surroundings. In this thesis, we explore the spin dynamics required to reproduce Uranus's and Neptune's spin states through collisions, gas accretion, and secular spin-orbit resonances, and discuss the role these processes play in the greater context of solar system formation. Gas accretion is the likely source for their similar spin periods, yet a simple 2D accretion model with gas flowing to the planet's equator yields planets spinning at near break-up speeds. We confirm this using numerical simulations, further supporting the idea that a combination of magnetic effects and polar accretion are responsible for the gas planets' slower spin periods. Gas accretion should also drive obliquities to 0°, but both Uranus and Neptune are tilted to 98° and 30° respectively. The leading hypothesis for their large obliquities is giant collisions, where for Uranus an Earth mass impactor struck the planet's North pole, while Neptune was struck by an impactor closer to the mass of Mars. Generating two nearly identically sized planets with widely different tilts yet very similar spins is, however, a low probability event, as the planets would likely remain near their initial spin states. We compare different collisional models for tilted, untilted, spinning, and non-spinning planets, and find that two 0.5 M_{\oplus} impacts produce better likelihoods than a single M_{\oplus} strike. We can noticeably improve these statistics if the planet was already tilted beyond 40° by a spin-orbit resonance, and an initial tilt of 70° can increase the likelihood by an order of magnitude, compared to a pure collision scenario, while also halving the mass of the required subsequent impactor.

Tilting a planet without altering its spin period or inner satellite system is possible with a secular spin-orbit resonance, a coupling between spin and orbit precession frequencies, yet neither Uranus's nor Neptune's spin axes are precessing fast enough to match any present-day orbital precession rates. Here, we seek conditions in the past that could have augmented the ice giant's spin precession rates enough to excite their obliquities. First, we explore the possibility of Uranus forming closer to the Sun, as solar tides near 7 au can increase spin precession rates enough to match another planet's orbital precession rate located beyond Saturn. We show using numerical simulations that Uranus can be tilted to 90° on 100 Myr timescales, but leaving Uranus between Jupiter and Saturn for that long is unstable. While resonance kicks can tilt the planet to ~ 40° on 10 Myr timescales, conditions need to be ideal. Another way to increase the ice giants' spin precession rates is if they harbored circumplanetary disks 3-10 times the mass of their satellite systems. We find that the presence of a massive disk moves the Laplace radius significantly outwards from its classical value, resulting in more of the disk contributing to the planet's pole precession. In this case, the planets would resonate with their own orbits during the lifetime of the disk (~1 Myr), and Uranus can potentially be tilted to as high as 70°. Neptune, by contrast, can be tilted all the way to 30°, eliminating the need for collisions altogether.

Lastly, in the spirit of collisions and spin dynamics, we explore a collisional origin to the spin rates of the irregular satellites around Saturn, and show the conditions required to also vary the satellites' orbits. Irregular satellites are located far away from the planet on highly eccentric and inclined orbits, and recently reported Cassini observations show that the satellites that orbit retrograde spin on average faster than satellites that orbit prograde to Saturn's spin. Generating the spin rates of both prograde and retrograde populations, sans Phoebe, through collisions requires an initial population of 10^4 - 10^5 particles more massive than 10^9 kg, and have more than half of them orbit in the retrograde direction. Spinning up Phoebe to its current spin rate requires imparting about 10% of its mass with giant collisions, which is enough to significantly alter its orbital parameters. As such, Phoebe may have scattered the inner prograde irregular satellites to more eccentric orbits, but this signature may also be a result of observation bias.