Non-resonant secular dynamics of trans-Neptunian objects perturbed by a distant super-Earth

TL;DR

This paper models the non-resonant secular dynamics of trans-Neptunian objects influenced by a distant super-Earth, revealing how perturbations affect orbital stability and lead to chaotic behaviors at large distances.

Contribution

It introduces a secular model incorporating both inner giant planets and an outer super-Earth, analyzing the transition from regular to chaotic dynamics at various semi-major axes.

Findings

Integrable dynamics valid below 70 AU

Chaotic behavior and orbital flips at >150 AU

Resonance relations linked to apsidal alignments

Abstract

We use a secular model to describe the non-resonant dynamics of trans-Neptunian objects in the presence of an external ten-earth-mass perturber. The secular dynamics is analogous to an "eccentric Kozai mechanism" but with both an inner component (the four giant planets) and an outer one (the eccentric distant perturber). By the means of Poincar\'e sections, the cases of a non-inclined or inclined outer planet are successively studied, making the connection with previous works. In the inclined case, the problem is reduced to two degrees of freedom by assuming a non-precessing argument of perihelion for the perturbing body. The size of the perturbation is typically ruled by the semi-major axis of the small body: we show that the classic integrable picture is still valid below about 70 AU, but it is progressively destroyed when we get closer to the external perturber. In particular, for a>150 AU, large-amplitude orbital flips become possible, and for a>200 AU, the Kozai libration islands are totally submerged by the chaotic sea. Numerous resonance relations are highlighted. The most large and persistent ones are associated to apsidal alignments or anti-alignments with the orbit of the distant perturber.