Survey of Kozai dynamics beyond Neptune

We study the Kozai dynamics affecting the orbital evolution of trans-neptunian objects being captured or not in MMR with Neptune. We provide energy level maps of the type (ω, 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, aN, is quite different from the dynamics of TNOs with q < aN, already studied in previous works. While for the last case there are stable equilibrium points at ω = 0°, 90°,180° and 270° 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 ∼ 62°, 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 ∼ 46°, 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 (ω, 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.

► The secular dynamics at a > 50 AU is analogue to the dynamics generated by an oblate planet.
► There is a Kozai resonance associated with orbital inclination of about 62°.
► TNOs with inclination of about 46° have their longitude of the perihelion oscillating, like Eris.
► Exterior MMRs of the type 1:N have asymmetric energy level curves and equilibrium points.
► Larger semimajor axis need larger inclinations to generate large variations in perihelion distances.