Mapping the $\nu_\odot$ Secular Resonance for Retrograde Irregular Satellites

TL;DR

This paper maps the $ u_igodot$ secular resonance for retrograde irregular satellites, revealing diverse resonant modes, their dependence on initial conditions, and the effects of orbital migration, using dynamical maps within the restricted three-body problem.

Contribution

It provides the first detailed dynamical maps of the $ u_igodot$ resonance for irregular satellites, including the effects of orbital migration and a scaling method for different planets.

Findings

Resonance exhibits symmetric and asymmetric libration modes.

Symmetric modes are present across all giant planets, with restrictions based on inclination.

Adiabatic orbital migration preserves resonance lock, but can alter libration modes.

Abstract

Constructing dynamical maps from the filtered output of numerical integrations, we analyze the structure of the $\nu_\odot$ secular resonance for fictitious irregular satellites in retrograde orbits. This commensurability is associated to the secular angle $\theta = \varpi - \varpi_\odot$, where $\varpi$ is the longitude of pericenter of the satellite and $\varpi_\odot$ 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 $\theta$ around zero (as found for Sinope and Pasiphae) or 180 degrees, 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 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 to estimate the resonant structure around any giant planet from the results calculated around a single primary mass.