Secular resonances between bodies on close orbits: a case study of the Himalia prograde group of jovian irregular satellites

TL;DR

This study investigates secular resonances among the Himalia group of jovian irregular satellites, revealing multiple resonance types, their topological structure, and stability through analytical and extensive numerical simulations.

Contribution

It identifies and characterizes new types of secular resonances in satellite groups, extending understanding of their dynamical behavior and stability.

Findings

Discovered three new secular resonances involving orbital angles.

Confirmed these resonances through N-body simulations.

Found the nodal resonance to be the most stable over 100 Myr.

Abstract

The gravitational interaction between two objects on similar orbits can effect noticeable changes in the orbital evolution even if the ratio of their masses to that of the central body is vanishingly small. Christou (2005) observed an occasional resonant lock in the differential node $\Delta \Omega$ between two members in the Himalia irregular satellite group of Jupiter in the $N$-body simulations (corresponding mass ratio $\sim 10^{-9}$). Using a semianalytical approach, we have reproduced this phenomenon. We also demonstrate the existence of two additional types of resonance, involving angle differences $\Delta\omega$ and $\Delta (\Omega+\varpi)$ between two group members. These resonances cause secular oscillations in eccentricity and/or inclination on timescales $\sim$ 1 Myr. We locate these resonances in $(a,e,i)$ space and analyse their topological structure. In subsequent $N$-body simulations, we confirm these three resonances and find a fourth one involving $\Delta \varpi$. In addition, we study the occurrence rates and the stability of the four resonances from a statistical perspective by integrating 1000 test particles for 100 Myr. We find $\sim 10-30$ librators for each of the resonances. Particularly, the nodal resonance found by Christou is the most stable: 2 particles are observed to stay in libration for the entire integration.