Tilting Saturn without tilting Jupiter: Constraints on giant planet migration

Abstract

The migration and encounter histories of the giant planets in our Solar System can be constrained by the obliquities of Jupiter and Saturn. We have performed secular simulations with imposed migration and N-body simulations with planetesimals to study the expected obliquity distribution of migrating planets with initial conditions resembling those of the smooth migration model, the resonant Nice model and two models with five giant planets initially in resonance (one compact and one loose configuration). For smooth migration, the secular spin-orbit resonance mechanism can tilt Saturn's spin axis to the current obliquity if the product of the migration time scale and the orbital inclinations is sufficiently large (exceeding 30 Myr deg). For the resonant Nice model with imposed migration, it is difficult to reproduce today's obliquity values, because the compactness of the initial system raises the frequency that tilts Saturn above the spin precession frequency of Jupiter, causing a Jupiter spin-orbit resonance crossing. Migration time scales sufficiently long to tilt Saturn generally suffice to tilt Jupiter more than is observed. The full N-body simulations tell a somewhat different story, with Jupiter generally being tilted as often as Saturn, but on average having a higher obliquity. The main obstacle is the final orbital spacing of the giant planets, coupled with the tail of Neptune's migration. The resonant Nice case is barely able to simultaneously reproduce the {orbital and spin} properties of the giant planets, with a probability ~0.15%. The loose five planet model is unable to match all our constraints (probability <0.08%). The compact five planet model has the highest chance of matching the orbital and obliquity constraints simultaneously (probability ~0.3%).

Accepted for publication in the Astronomical Journal

References in corpus (3)

• Statistical Study of the Early Solar System's Instability with 4, 5 and 6 Giant Planets
• Dynamics of the giant planets of the solar system in the gaseous proto-planetary disk and relationship to the current orbital architecture
• Empirical Models of Pressure and Density in Saturn's Interior: Implications for the Helium Concentration, its Depth Dependence, and Saturn's Precession Rate

Cited by in corpus (23)

• Dynamical Evolution of the Early Solar System
• Dynamical evidence for an early giant planet instability
• Onset of giant planet migration before 4480 million years ago
• Impact bombardment chronology of the terrestrial planets from 4.5 Ga to 3.5 Ga
• Solar System Physics for Exoplanet Research
• Excitation of Planetary Obliquities Through Planet-Disk Interactions
• N-body simulations of planet formation via pebble accretion I: First Results
• Formation of Venus, Earth and Mars: Constrained by isotopes
• Born eccentric: constraints on Jupiter and Saturn's pre-instability orbits
• The large obliquity of Saturn explained by the fast migration of Titan
• Atmospheres on Nonsynchronized Eccentric-tilted Exoplanets I: Dynamical Regimes
• The future large obliquity of Jupiter
• Impact bombardment on the regular satellites of Jupiter and Uranus during an episode of giant planet migration
• Oort cloud asteroids: Collisional evolution, the Nice Model, and the Grand Tack
• The past and future obliquity of Saturn as Titan migrates
• A fast-growing tilt instability of detached circumplanetary disks
• Cassini states of a rigid body with a liquid core
• Tilting Styx and Nix but not Uranus with a Spin-Precession-Mean-motion resonance
• Future destabilisation of Titan as a result of Saturn's tilting
• Analytical solution of the Colombo top problem
• Kozai-Lidov oscillations triggered by a tilt instability of detached circumplanetary discs
• Parallelization of the Symplectic Massive Body Algorithm (SyMBA) $N$-body Code
• Planetary Obliquity Excitation Through Pre-Main Sequence Stellar Evolution