Survey of Kozai Dynamics Beyond Neptune

TL;DR

This paper explores the complex Kozai dynamics affecting transneptunian objects, revealing new stable equilibrium points at a critical inclination and analyzing the influence of Neptune's resonances and diffusion processes on their orbital evolution.

Contribution

It provides the first detailed energy level maps of Kozai dynamics beyond Neptune, identifying a critical inclination and the effects of resonances and diffusion on TNOs' orbits.

Findings

Stable equilibrium points at i ~ 62° for non-resonant TNOs outside Neptune's orbit.

Resonances cause distortions in energy level curves and shift equilibrium points.

Minimum inclination for significant perihelion variation increases with semimajor axis.

Abstract

We study the Kozai dynamics affecting the orbital evolution of transneptunian objects being captured or not in MMR with Neptune. We provide energy level maps of the type ({\omega},q) describing the possible orbital paths from Neptune up to semimajor axis of hundreds of AU. The dynamics for non resonant TNOs with perihelion distances, q, outside Neptune's orbit, a_N, is quite different from the dynamics of TNOs with q < a_N, already studied in previous works. While for the last case there are stable equilibrium points at {\omega} = 0\circ, 90\circ, 180\circ and 270\circ in a wide range of orbital inclinations, for the former case it appears a family of stable equilibrium points only at a specific value of the orbital inclination, i \sim 62\circ, that we call critical inclination. We show this family of equilibrium points is generated by a mechanism analogue to which drives the dynamics of an artificial satellite perturbed by an oblate planet. The planetary system also generates an oscillation in the longitude of the perihelion of the TNOs with i \sim 46\circ, being Eris a paradigmatic case. We discuss how the resonant condition with Neptune modify the energy level curves and the location of equilibrium points. The asymmetric librations of resonances of the type 1:N generate a distortion in the energy level curves and in the resulting location of the equilibrium points in the phase space ({\omega},q). We study the effect on the Kozai dynamics due to the diffusion process in "a" that occurs in the Scattered Disk. We show that a minimum orbital inclination is required to allow substantial variations in perihelion distances once the object is captured in MMR and that minimum inclination is greater for greater semimajor axis.