Tidal heating of the Uranian moons during the 2:1 resonance between Ariel and Umbriel

The planet Uranus hosts five regular satellites: Miranda, Ariel, Umbriel, Titania, and Oberon. Unlike the moons of Jupiter and Saturn, these satellites are not involved in any mean motion resonance. However, both current orbital elements and geological features suggest that some of the moons had resonant interactions in the past (Peale 1999). As tidal forces are the main driver of moons' orbital expansion after their formation, the value of the quality factor Q of Uranus dictates the orbital evolution of the satellites and their possible past resonance crossings.

Based on classic tidal models, past works considered values of Uranus' Q larger than 10'000, which set a quite slow migration rate of the moons (e.g. Tittemore and Wisdom 1988, Cuk et al. 2020). With such values, the total variation in semi-major axes for most moons was limited, and consequently only a few low-order resonances were crossed during their orbital migration. In particular, a Q larger than 10'000 allows to avoid the encounter with the 2:1 resonance between Ariel and Umbriel (Tittemore and Wisdom 1990).

However, recent studies and estimations suggest that tidal dissipation within Uranus is much higher than previosuly thought (Nimmo 2023, Jacobson and Park 2025). They proposed a value of Uranus' Q around 1'000, so that the migration rate of the moons would be at least ten times faster than previously assumed. As a consequence, it is almost impossible to avoid the 2:1 resonance between Ariel and Umbriel, and it suffices to go back in time between 200 and 600 Myrs to encounter this resonance, depending on the exact value of Q.

In this context, we investigated the orbital evolution of the Uranus' system through the 2:1 resonance between Ariel and Umbriel, assuming a low value for the Q of the planet (Rossi et al. 2026). Through numerical simulations of the resonance crossing, we found that the two satellites were almost certainly captured into resonance, and their eccentricities were forced to increase. In particular, Ariel's eccentricity could have become as high as 0.02, which is more than ten times its current value. We also showed that eventually the resonance was disrupted through a three-body resonance crossing with Titania (either 4:2:1 or 3:2:1). Though we estimate that the moons left the resonance between 200 and 600 Myrs ago, our research does not allow us to determine when they entered the resonance or for how long they remained locked in.

Nevertheless, the depicted orbital history has a large impact on the geophysical evolution of the moons. The increase in the moons' eccentricities would have enhanced the tidal heating within the satellites, and for some of them the heat flux could have been large enough to induce tectonic activities and even cause partial resurfacing. We estimated the tidal heating within the satellites during the evolution into the 2:1 resonance, and compared it with geophysical estimates obtained from surface data.

The energy dissipation within Ariel due to the eccentric tides during the 2:1 resonance would have amounted to about 200 GWs, which correspond to a heat flux of 50 mW/m^2. This value is within the range obtained from the analysis of the surface of the satellite (28-92 mW/m², Peterson et al. 2015). Therefore, the 2:1 resonance could be responsible for the resurfacing on Ariel. However, a recent study on the Ariel's surface response to tidal stress found that the eccentricity necessary to cause resurfacing should have been at least 0.04 (Strom et al. 2026). In our simulations, we found that with the 2:1 resonance is very difficult for Ariel's eccentricity to reach such a high value.

Although also Umbriel was involved in the resonance, its equilibrium eccentricity was smaller (about 1/4 that of Ariel) and its orbit was farther from the planet. Therefore, the tidal heating within Umbriel resulted to be at least 500 times smaller the one experienced by Ariel. This is coherent with the different geological features observed on the surfaces of the two satellites, as Umbriel does not show signs of significant past tectonic activity.

Finally, even though Miranda was not directly involved in the resonant interaction between the moons, its orbital elements increased significantly during the orbital excitation due to the disruption of the 2:1 resonance. This is due to its small mass compared to the other bodies of the system and its proximity to Ariel. Miranda's eccentricity could have increased up to 0.1, which would have lead to a global tidal heating of tens of GWs, sufficient to explain the formation of the youngest coronae observed on its surface. These geological features are probably younger than 500 Myrs (Beddingfield et al. 2022); such a young age matches the epoch of the disruption of the 2:1 resonance in our scenario.

In the end, a low Q of Uranus changes the classic orbital history that was outlined for the Uranian moons (e.g. Dermott et al. 1988). In particular, the inclusion of the 2:1 resonance between Ariel and Umbriel has a significant impact on the orbital elements of the two moons and provides a natural explanation for the resurfacing of Ariel. Future measurements of the Uranian system, including data from Uranus Orbiter and Probe, will allow to confirm or confute this dynamical scenario.

Acknowledgments:

This research was developed under the ASI/UniBo-CIRI agreement no. 2024-5-HH.0.

 
References:

Beddingfield et al. (2022), Planet. Sci. J., 3, 174.
Cuk et al. (2020), Planet. Sci. J., 1, 22.
Dermott et al. (1988), Icarus, 76, 295-334.
Jacobson and Park (2025), Astron. J. 169, 65.
Nimmo (2023), Planet. Sci. J. 4, 241.
Rossi et al. (2026), Astron. Astrophys. 705, A48.
Peale (1999), Annu. Rev. Astron. Astrophys. 37, 533-602.
Peterson et al. (2015), Icarus, 250, 116-122.
Strom et al. (2026), Icarus 444, 116822.
Tittemore and Wisdom (1988). Icarus 74, 172-230.
Tittemore and Wisdom (1990). Icarus 85, 394-443.