Mapping theν_⊙secular resonance for retrograde irregular satellites

Abstract

Constructing dynamical maps from the filtered output of numerical integrations, we analyse the structure of the ν⊙ secular resonance for fictitious irregular satellites in retrograde orbits. This commensurability is associated with the secular angle θ=ϖ−ϖ⊙, where ϖ is the longitude of the pericentre of the satellite and ϖ⊙ corresponds to the (fixed) planetocentric orbit of the Sun. Our study is performed in the restricted three‐body problem, where the satellites are considered as massless particles around a massive planet and perturbed by the Sun. Depending on the initial conditions, the resonance presents a diversity of possible resonant modes, including librations of θ around 0 (as found for Sinope and Pasiphae) or 180° as well as asymmetric librations (e.g. Narvi). Symmetric modes are present in all giant planets, although each regime appears restricted to certain values of the satellite inclination. Asymmetric solutions, on the other hand, seem absent around Neptune due to its almost circular heliocentric orbit. Simulating the effects of a smooth orbital migration on the satellite, we find that the resonance lock is preserved as long as the induced change in the semimajor axis is much slower compared to the period of the resonant angle (adiabatic limit). However, the librational mode may vary during the process, switching between symmetric and asymmetric oscillations. Finally, we present a simple scaling transformation that allows us to estimate the resonant structure around any giant planet from the results calculated around a single primary mass.