Mean Motion Resonances in a Resonance Lock

Abstract

Interactions between tidal migration and the encounter of mean motion resonances (MMRs) have widely been used in attempts to explain unexpectedly young surfaces and high free eccentricities of moons. A driving variable in this process is the planetary quality factor (Q$), which has so far been assumed to be constant throughout the system. However, data showing faster migration rates for moons farther from the primary indicate otherwise. The proposed mechanism behind this phenomenon is resonance locking, which uses steep localised dips in Qp to explain why certain moons migrate faster than expected. These dips evolve along with the primary, and a secondary may reach the same migration rate, "locking" with a frequency mode. This thesis aims to provide a better understanding of the orbital evolution of pairs of moons in MMRs under the influence of the resonance locking mechanism, from the process of capture into a resonance lock, to the possibility of breaking the MMR. In this context, the differences between first- and second-order MMRs are examined. A higher order numerical model has been developed that combines the effects of tidal migration and MMRs with the newly proposed resonance locking mechanism. It is used to examine a variety of scenarios and test the behaviour of a pair of moons when the inner moon is in a resonance lock. Additionally, the stability of the 2:1 and 3:1 e-type resonances when encountering a mode are examined. It was found that the |Im(k2,p)| required to enter the resonance lock can reach values 50% higher than expected from theory, due to oscillations in mean motion caused by the interactions with the second moon. A substantial growth in eccentricity can be experienced, potentially growing indefinitely provided both the resonance lock and MMR are maintained. Finally, while it is unlikely that a resonance lock has caused an MMR to break in the past of our Solar System due to the lower masses, it may occur for heavier exoplanets. It can be concluded that resonance locking mechanism provides an alternative explanation for high free eccentricities and unexpected surface features. However, to better predict whether moons have been or are affected by a mode, for the Galilean moons data from the upcoming JUICE and Europa Clipper missions are needed. Finally, Juno has already helped constrain some of Jupiter's internal properties, and will continue to do so during the remainder of its mission, which may aid characterisation of the mode characteristics.