On The Applicability of Ring-Moon Cycles to Exoplanets

Abstract: The presence of rings and moons around exoplanets is likely to be one of the next great discoveries in exoplanet research. Using theories developed for the Solar System, we explore the possibility of coupled ring-moon cycles around exoplanets and what these processes mean for the observability of these features. Around Neptune- and Earth-like planets, we find that ring-moon cycles are capable of producing long-lived rings of comparable and greater relative transit depths than Saturn's. In multi-planet systems, secular spin-orbit resonances can provide the necessary planetary obliquity for these rings to contribute noticeably to transit lightcurves. We model the geometry of a ring's cross-section at various angles in comparison to the cross-section of a transiting planet to determine whether the ring may be detectable during the planet's transit. Ringed planets have also been proposed as an alternative to inflated planetary radii seen in transit, leading to abnormally low observed densities. Ring-moon cycles can produce late-forming and sometimes long-lived rings that can have the potential of explaining at least some of these observations. We also discuss some inconsistencies in the calculation of exoplanet oblateness due to rotation that we have come across in the course of this work.

• The paper presents how ring-moon cycles form via satellite disruption under distinct dynamical regimes shaped by tidal and Lindblad torques.
• It applies viscous spreading and tidal decay models to quantify ring lifetimes, optical thickness, and their contributions to transit cross-sections.
• The study offers a viable explanation for super-puff exoplanets by linking anomalous transit radii to ring-induced density reductions.

Applicability of Ring-Moon Cycles to Exoplanets: Dynamical Regimes and Observational Consequences

Introduction

This paper presents a comprehensive analysis of the potential for ring-moon cycles—cyclical processes in which planetary rings accrete into satellites, which may subsequently be disrupted to form new rings—to occur around exoplanets. Building on established Solar System theory, the authors systematically investigate the dynamical regimes that permit such cycles, the lifetimes and observability of resulting rings, and the implications for transit photometry, particularly in the context of anomalously low-density "super-puff" exoplanets.

Dynamical Regimes for Ring-Moon Cycles

The maintenance of ring-moon cycles is governed by the interplay between the Roche limit, synchronous orbit, and Lindblad torques. The paper classifies planets into three regimes:

• Boomerang Regime: The maximum semimajor axis a moon can reach due to Lindblad torques is smaller than the synchronous orbit. Satellites migrate outward but eventually reverse direction and are tidally disrupted, restarting the cycle.
• Torque-Dependent Regime: The synchronous orbit is beyond the Fluid Roche Limit, and the outcome depends on the relative strengths of tidal and Lindblad torques.
• Slingshot Regime: The synchronous orbit is closer to the planet than the Fluid Roche Limit, so satellites always migrate outward and ring-moon cycles do not occur.

The authors focus on non-despun Neptune-like exoplanets (3–5 $R_\oplus$) with orbital periods $>$25 days and despun planets in multi-planet systems. For the former, they calculate despinning timescales using equilibrium tidal theory and select those with $T > 1$ Gyr, ensuring they retain primordial rotation rates. All selected planets fall within the Boomerang regime, supporting the plausibility of ring-moon cycles.

Ring Lifetimes and Equivalent Thickness

The observability of rings depends on their lifetime and optical thickness. Using viscous spreading models and tidal decay timescales, the authors estimate the fraction of time rings are present and their equivalent thickness:

• Non-despun Neptune-like Planets: Rings are present $\sim$20% of the time, with equivalent thicknesses often exceeding that of Saturn's main rings (0.365 m), implying optically thick, potentially observable rings.
• Despun Planets in Multi-Planet Systems: Rings are present for a larger fraction of the time, but equivalent thicknesses are generally lower, especially for high-density super-Earths.

The calculation of equivalent thickness is based on the mass and density of the ring material and the area between the planet and the Fluid Roche Limit. The authors adopt a threshold based on Saturn's rings to identify systems with potentially observable rings.

Secular Spin-Orbit Resonances and Obliquity

In multi-planet systems, secular spin-orbit resonances can induce significant obliquity in tidally despun planets, making rings observable during transits. The authors identify resonances by matching nodal and spin precession rates, using Laplace-Lagrange secular theory and scaling oblateness to Earth or Neptune analogs. They restrict analysis to resonant obliquities $<60^\circ$ due to dynamical stability considerations.

Inclination damping due to obliquity tides is assessed, with all candidate resonant planets exhibiting damping timescales $>$5 Gyr, ensuring that obliquity is maintained over system lifetimes and rings are not forced into edge-on configurations.

Transit Geometry and Observational Signatures

The paper models the geometry of ring cross-sections during planetary transits, considering both cases where the ring fully encompasses the planet and where it partially overlaps. The projected area of the ring is calculated as a function of spin axis orientation, and the contribution to transit depth is quantified.

Key findings include:

• For non-despun Neptune-like planets, a significant fraction of spin axis orientations yield ring contributions $>$10%, $>$20%, and even $>$50% to the total transit cross-section.
• For despun planets in spin-orbit resonances, the fraction is lower but still non-negligible, especially for systems with large Roche limits.

The authors demonstrate that rings can inflate the apparent planetary radius by up to 2.75$\times$ the true value, leading to anomalously low inferred densities. This mechanism is proposed as a plausible explanation for some "super-puff" exoplanets, such as HIP-41378 f, where transit modeling may conflate ring signatures with extended atmospheres.

Implications and Future Directions

The results have several important implications:

• Exoring Detection: Transit photometry is sensitive to ring systems, especially in planets with significant obliquity. Multi-planet systems offer comparative opportunities to break degeneracies with stellar limb darkening.
• Exomoon Formation: The evolutionary link between rings and moons suggests that detection of exorings may precede or accompany the discovery of exomoons.
• Density Anomalies: The ring-moon cycle hypothesis provides a physically motivated alternative to atmospheric inflation for explaining super-puff planets.
• Oblateness Modeling: The paper highlights inconsistencies in the literature regarding the calculation of exoplanet oblateness, advocating for a more rigorous approach based on hydrostatic equilibrium and rotational deformation.

Future work should focus on high-precision transit modeling, leveraging advances in differentiable transit codes and JWST photometry, to distinguish between rings and atmospheric features. Theoretical models of ring-moon cycles should be extended to a broader range of planetary types and system architectures, incorporating more detailed tidal and collisional physics.

Conclusion

This study establishes the dynamical plausibility and observational consequences of ring-moon cycles in exoplanetary systems. By identifying regimes conducive to long-lived, optically thick rings and quantifying their impact on transit photometry, the authors provide a robust framework for interpreting anomalous exoplanet densities and guiding future searches for exorings and exomoons. The work underscores the need for careful modeling of planetary oblateness and ring geometry in the analysis of exoplanet transit data.