Chaos and the Effects of Planetary Migration on the Orbit of S/2000 S5 Kiviuq

Abstract

Among the many new irregular satellites that have been discovered in the last 5 years, five or more are in the so-called Kozai resonance. Because of solar perturbations, the argument of pericenter ω of a satellite usually precesses from 0° to 360°. However, at inclinations higher than ≃39°.3 and lower than ≃140°.7, a new kind of behavior occurs for which the argument of pericenter oscillates around ±90°. In this work we concentrate on the orbital history of the Saturnian satellite S/2000 S5 Kiviuq, one of the satellites currently known to be in such resonance. Kiviuq's orbit is very close to the separatrix of the Kozai resonance. Because of perturbations from the other Jovian planets, it is expected that orbits near the Kozai separatrix may show significant chaotic behavior. This is important because chaotic diffusion may transfer orbits from libration to circulation, and vice versa. To identify chaotic orbits, we used two well-known methods: the frequency analysis method of Laskar and the maximum Lyapunov exponents method of Benettin and coworkers. Our results show that the Kozai resonance is crossed by a web of secondary resonances, whose arguments involve combinations of the argument of pericenter, the argument of the Great Inequality (GI) (2λJ - 5λS), the longitude of the node Ω, and other terms related to the secular frequencies g5, g6, and s6. Many test orbits whose precession period are close to the period of the GI (883 yr), or some of its harmonics, are trapped by these secondary resonances and show significant chaotic behavior. Because the GI's period is connected to the semimajor axes of Jupiter and Saturn and because the positions of the Jovian planets have likely changed since their formation, the phase-space location of these secondary resonances should have been different in the past. By simulating the effect of planetary migration, we show that a mechanism of sweeping secondary resonances, similar to the one studied by Ferraz-Mello and coworkers. for the asteroids in the 2:1 mean motion resonance with Jupiter, could significantly deplete a primordial population of Kozai resonators and push several circulators near the Kozai separatrix. This mechanism is not limited to Kiviuq's region and could have worked to destabilize any initial population of satellites in the Kozai resonance around Saturn and Jupiter.