Origin of Hyperion and Saturn's Rings in A Two-Stage Saturnian System Instability

TL;DR

The paper argues for a recent, dynamical history in which Titan's rapid orbital expansion drives Saturn's spin-orbit resonance breaking via loss of an exterior moon, triggering an outer-system instability that forms Hyperion from collision debris. This outer event excites Titan and Iapetus, leading to an inner-system instability that re-accretes the rings and inner moons, while Titan's eccentricity evolves to enable a Titan–Iapetus resonant interaction. A subsequent Titan–Iapetus 5:1 resonance crossing helps shape Iapetus's high inclination and current orbit. The model accounts for the youth of Saturn's rings and inner moons and suggests specific observational tests, including Saturn's obliquity history and Titan's tidal properties, to validate the proposed sequence.

Abstract

The age of the rings and some of the moons of Saturn is an open question, and multiple lines of evidence point to a recent (few hundred Myr ago) cataclysm involving disruption of past moons. The main driver of the evolution of the Saturnian system is the relatively rapid tidal expansion of its largest moon, Titan, which is likely driven by resonant tides within Saturn. The obliquity of Saturn and the orbit of the small moon Hyperion both serve as a record of the past orbital evolution of Titan. Saturn's obliquity was likely generated by a secular spin-orbit resonance with the planets, while Hyperion is caught in a mean-motion resonance with Titan, with both phenomena driven by Titan's orbital expansion. We propose that the breaking of Saturn's spin resonance was also the event in which Hyperion formed, when an outer mid-sized satellite (``Proto-Hyperion'') was destabilized and collided with Titan, with some of the debris accreting into Hyperion. During the instability Proto-Hyperion's perturbations produced the observed orbital inclination of Iapetus. The same event also excited the eccentricity of Titan, which then, through Titan's resonant interaction with the inner moons, led to destabilization, collisional disruption and re-accretion of the inner moon system, including the rings. We present numerical integrations that show that this chain of events has a relatively high probability, and discuss how it fits within our knowledge of the Saturnian system.

Figures (16)

• Figure 1: Simulations of Titan and Hyperion encountering and evolving through their mutual 4:3 mean-motion resonance, replotted from cuk13. The top panel plots Titan's semimajor axis (green) and the location of the 4:3 MMR with Hyperion (purple; calculated as $a_H (3/4)^{2/3}$), and the middle panel plots their eccentricities. The resonant argument plotted in the bottom panel is $4 \lambda_H - 3 \lambda_T - \varpi_H$, where $\lambda$ is the mean longitude and $\varpi$ the longitude of pericenter. The current proper eccentricity of Hyperion (comparable to the one plotted in this figure) is $e_H=0.1$. Titan was put on a low-eccentricity orbit for more direct comparison with analytical calculations.
• Figure 2: The numerical experiment using ssimpl in which Titan was made to migrate inward at the same rate it is found to migrate outward by lai20. The top panel plots the obliquity of Saturn, while the bottom one shows Titan's semimajor axis (green) and the location of the 4:3 MMR with Hyperion (purple; calculated as $a_H (3/4)^{2/3}$). While not a reverse-time simulation, this run shows approximate past points in Titan's evolution when the spin-orbit resonance was crossed (indicated by a large jump in Saturn's obliquity) and Titan-Hyperion resonance was established (consistent with the forward-time simulation shown in Fig. \ref{['hyp_plot']}).
• Figure 3: Distance vs. mass of hypothetical additional satellite needed to put Saturn in the spin-orbit resonance with secular mode $s_8$ in the past.
• Figure 4: A (successful) example of the evolution of the system in our simulations that place "Proto-Hyperion" in the outer 2:1 resonance with Titan. The top panel plots Titan's semimajor axis (purple) and the location of the 2:1 MMR with Proto-Hyperion (green; calculated as $a_{P-H} (1/2)^{2/3}$) and 5:1 with Iapetus (orange; calculated as $a_I (1/5)^{2/3}$). The middle and bottom panels plot the eccentricities and inclinations to Saturn's equator of the three moons using the same color scheme.
• Figure 5: Final eccentricities and inclinations of Titan and Iapetus in the 42 runs that resulted in a collision between Titan and Proto-Hyperion. The red circle indicates the simulation plotted in Fig. \ref{['p-h4.4b57']}, and the green "X" plots the current orbital elements.