The migration of Mimas and the implications for the resonant motion of small Saturnian moons

Abstract

Mimas is currently evolving in resonant motion with three tiny Saturnian moons, namely, Aegaeon, Methone and Anthe. The process of resonant capture in systems of natural satellites is usually linked to the orbital migration due to tides. The tidal interaction with Saturn results in the orbital expansion of Mimas on timescales which depend on physical properties of both the satellite and its host planet. In this work we investigate the dynamical environment of the resonant moons during the Mimas’ tidal orbital expansion. Through the construction of dynamical maps, varying the initial Mimas’ semi-major axis and eccentricity, we show that Aegaeon, Methone and Anthe may have experienced multiple crossings of first-order mean motion resonances with Mimas, revealing a complex dynamical history. Nonetheless, several strong resonances may be avoided depending on the strength of the Mimas’s migration, which in turns depends on physical parameters associated with the tidal evolution. For critical values of the viscosity of the Saturnian core’s, we show that Mimas cannot trap Aegaeon, Methone and Anthe in their current corotation resonances. Our results impose constraints on the values of the Saturnian core’s viscosity, which plays a fundamental role in the tidal migration of Mimas.