Are Thalassa and Despina in Resonance Lock with Neptune's Oscillations?

Abstract: The two innermost moons of Neptune, Naiad and Thalassa, are currently in a 73:69 mean-motion resonance. This resonance relies on the large inclination of Naiad, and we estimate that Naiad requires multiple Gyr to reach its $4.7<sup>{\circ}$ inclination through this resonance. However, we find through direct numerical simulations that the current Naiad-Thalassa resonance is unstable on Myr timescales due to perturbations from the neighboring moon Despina. As this instability is a product of convergent tidal evolution predicted by equilibrium tidal theory, we propose that the innermost moons of Neptune may migrate through resonant-lock tides. If both Despina and Thalassa are locked to two resonant oscillations modes within Neptune, the frequencies of which evolve approximately in parallel, Naiad-Thalassa resonance can be stable for much longer. We find that Lindblad resonances with low-order $l=m=1$, $n=1$ g-modes at Neptune may be suitable candidates for driving the resonant-lock evolution of Thalassa and Despina, and possibly even Galatea.

• The paper reveals that resonance-lock between Neptune's g-modes and the inner moons explains their prolonged orbital stability despite destabilizing interactions.
• Using N-body simulations, the study finds that Despina’s perturbations shorten the Naiad-Thalassa resonance lifetime, challenging classical tidal models.
• The research proposes that resonance-lock tides driven by Neptune’s low-order g-modes synchronize satellite migration, offering new insights into planetary interiors.

Resonance Lock and the Dynamical Evolution of Neptune’s Innermost Moons

Introduction

This paper investigates the dynamical state of Neptune’s innermost moons—Naiad, Thalassa, and Despina—with a focus on the long-term stability of the observed 73:69 mean-motion resonance (MMR) between Naiad and Thalassa. Through analytical analysis and direct $N$-body simulations, it quantifies the stability of the configuration, reveals the destabilizing influence of Despina, and proposes resonance-lock tides with Neptune’s internal oscillations as a mechanism for maintaining co-evolution and resonance stability. The results have significant implications for the tidal evolution theory in giant planets and for understanding satellite formation and migration timescales.

Dynamical Analysis of Naiad-Thalassa Resonance

The Naiad-Thalassa 73:69 MMR is a fourth-order, inclination-type resonance that has been previously identified as responsible for Naiad’s unusually large orbital inclination ($4.7^\circ$), which is anomalous among inner satellites of giant planets. Analytical estimates based on modified equations from the classical theory of orbital resonance yield that producing Naiad’s current inclination via this resonance requires approximately a 20% decrease in semimajor axis over Gyr timescales.

Direct simulations with only Naiad and Thalassa show the resonance to be dynamically stable and consistent with increasing Naiad’s inclination over long times. However, a critical finding is that the strength of this resonance is highly sensitive to inclination: capture into this MMR is not possible at zero inclination because the resonance’s strength scales as $i^4$ (Naiad’s inclination to the fourth power). This supports the hypothesis that Naiad’s inclination must have been excited by past dynamical interactions, possibly with other resonances, before entering the current configuration.

Destabilizing Effects of Despina and Resonance Lifetime

When Despina is included, the stability analysis reveals a contradictory result: the presence of Despina significantly reduces the lifetime of the Naiad-Thalassa resonance to $\lesssim1$ Myr, orders of magnitude shorter than previously estimated timescales for the growth of inclination and inward tidal migration. The simulations show that Despina’s perturbations, especially via near-resonant interactions such as the 29:27 MMR with Thalassa, drive the system into chaos or break the resonance outright.

No stable three-body or higher-order resonances involving Naiad, Thalassa, and Despina are found that could explain the parallel migration or long-term resonance stability; previous analytical and numerical survey of low-order three-body resonances found no viable mechanism to stabilize the system under classical equilibrium tidal theory.

Resonance-Lock Tides with Planetary g-Modes

To resolve this paradox, the authors advocate for a non-equilibrium tidal mechanism: resonance-lock between the moons and resonant oscillation modes in Neptune itself. Unlike the equilibrium tide model, in which the tidal evolution rate is set solely by satellite mass and orbital radius, the resonance-lock paradigm postulates that certain internal modes (such as low-order, $l=m$, $n=1$ g-modes) in Neptune have frequencies that slowly evolve due to the planet’s own structural evolution. Satellites can “lock” onto these frequencies through Lindblad resonances, causing their orbits to evolve in step with the shifting mode, with migration timescales set primarily by the interior evolution of Neptune rather than satellite mass.

An important, specific result is the identification of the locations of predicted g-mode Lindblad resonances (following [ahe22]), showing a striking spatial coincidence with Thalassa and Despina’s orbits. The implication is that Thalassa and Despina may each be resonance-locked to distinct low-order g-mode oscillations of Neptune, migrating in parallel and thereby maintaining relative stability and avoiding disruptive MMR crossings for much longer than possible under equilibrium tides.

This hypothesis is consistent with the constraints from observed rapid outward migration of Saturnian moons, for which resonance-lock tides have become necessary to explain the observed rates. Here, however, the situation is inverted: the inner Neptune satellites (all inside the synchronous radius) migrate inward, and resonance-lock would act to synchronize their evolution and prevent rapid resonance crossings.

Implications and Prospects for Further Research

The theoretical shift from equilibrium tides to resonance-lock with planetary oscillations for satellite migration is substantial. It indicates that satellite system architectures may encode information about the interiors and evolutionary histories of giant planets. For Neptune, confirmation of resonance-lock tides would indicate the dynamical importance of its low-frequency g-modes, provide a probe of planetary $Q$, and potentially explain the survival and configuration of its inner moons.

A speculative yet intriguing extension is the suggestion that Galatea—a more distant inner moon—could also be resonance-locked with another g-mode, given the overlap between its orbit and another mode’s Lindblad resonance.

The efficacy of resonance-locking by low-order modes for such low-mass moons is not fully established. The authors note the need for future numerical and analytical investigation of planet-satellite and mode coupling, quantification of dissipation rates for g-modes, and detailed tracking of the dynamical history of the current satellite system, especially including past disruptive events like Triton’s capture.

Conclusion

This research demonstrates, through $N$-body modeling and resonance theory, that the Naiad-Thalassa resonance is inherently short-lived under equilibrium tidal evolution, an outcome contradicted by both the high inclination of Naiad and the apparent long-term stability of the system. The evidence points toward a regime where resonance-locking between Neptune’s low-order g-modes and Thalassa and Despina governs the satellites’ parallel migration, thereby maintaining resonance stability and avoiding destructive resonance crossings. If validated, this paradigm will have substantial consequences for tidal theory, the interpretation of inner satellite architectures, and constraints on the interiors of giant planets.