Ganymede’s tidal response to moon-moon tides: A 3D time-domain approach

Although Ganymede's tidal response is primarily governed by the eccentricity tides, it is also affected by additional forcing from its neighbouring moons. The compact Galilean system, locked in 4:2:1 orbital resonance, results in complex gravitational interactions between Io, Europa, and Ganymede. Consequently, Ganymede experiences additional tidal forces at frequencies different from its orbital frequency. This forcing is particularly important for a moon with a subsurface ocean, as prior studies have shown that moon-moon tides may excite oceanic flows that could be visible in the gravity field^1,2. These studies on moon-moon tides relied on 2D models based on the Laplace tidal equations (LTE), which are typically solved in the frequency domain^3,4.   

Building on the work of Hay et al. (2022), we present an approach to simulate Ganymede’s tidal response by solving the 3D equations of motion in the time domain⁵. The 3D method enables us to avoid biases associated with 2D approximations, while the time domain captures variations in gravity over a tidal cycle. We explore a range of internal structures with ocean thicknesses between 1 and 300 km, corresponding to ice shell thicknesses from 152 to 10 km. For each internal structure, we solve the system forced by both eccentricity and moon-moon tides and obtain the tidal response in terms of time-dependent degree-2 potential Love numbers.  

In the case of only eccentricity tides, the Love numbers remain constant over a tidal cycle, while the addition of moon-moon tides results in significant variations of the Love numbers over a full tidal cycle. Due to these variations, we separate the Love numbers into time-averaged and oscillatory components. Our results show that the oscillatory part of the Love numbers exhibits variations from the time-averaged Love number of approximately 1% for thick oceans (>6 km) and up to 10% for thin oceans. The thin oceans strongly alter the gravity signal and can be readily constrained by Juice. For the thick oceans, although the variations are small, they remain detectable by Juice⁶. For all the ocean thicknesses, the time-averaged Love numbers are similar to one from the eccentricity tides, and the tidal response is dominated by tides due to Jupiter. The small variations can provide additional constraints for the thickness and composition of the ocean. Finally, in addition to tides due to Io and Europa, we aim to include the eccentricity modulations of Ganymede expected during Juice's lifetime. 

Acknowledgments 

This project is supported by the Czech Science Foundation (project No. 25-16801S), by the Agence Nationale de Recherche (France; project COLOSSe, ANR-2020-CE49-0010), the Czech-French exchange Barrande programme, and by CNES for the preparation of the ESA Juice mission. 

References 

[1] Hay et al., 2022, J. Geophys. Res.: Planets 127, e2021JE007064 

[2] De Marchi et al. 2022, Icarus 386, 115150 

[3] Matsuyama et al. 2018, Icarus 312, 208–230 

[4] Buthe et al. 2016, Icarus 280, 278–299 

[5] Aygün & Čadek, 2023, J. Geophys. Res.: Planets 128, e2023JE007907 

[6] Cappuccio et al. 2020, Plane. & Spa. Sci. 187, 104902