Dynamical Instabilities in High-Obliquity Systems

TL;DR

This paper investigates how high-obliquity planetary systems experience dynamical instabilities due to Kozai oscillations, modified by planetary oblateness and radiation pressure, affecting orbit stability and particle dynamics.

Contribution

It provides a clearer analysis of orbital stability thresholds in high-obliquity systems, incorporating effects of planetary oblateness and radiation pressure on orbit dynamics.

Findings

Orbits become unstable at obliquities > 68.875 degrees in the local Laplace plane.

Inclined orbits are unstable over broader radial ranges, even below the threshold obliquity.

Radiation pressure shifts the unstable range and can prevent instability for small retrograde particles.

Abstract

High-inclination circumplanetary orbits that are gravitationally perturbed by the central star can undergo Kozai oscillations---large-amplitude, coupled variations in the orbital eccentricity and inclination. We first study how this effect is modified by incorporating perturbations from the planetary oblateness. Tremaine et al. (2009) found that, for planets with obliquities > 68.875 degrees, orbits in the equilibrium local Laplace plane are unstable to eccentricity perturbations over a finite radial range, and execute large-amplitude chaotic oscillations in eccentricity and inclination. In the hope of making that treatment more easily understandable, we analyze the problem using orbital elements, confirming this threshold obliquity. Furthermore, we find that orbits inclined to the Laplace plane will be unstable over a broader radial range, and that such orbits can go unstable for obliquities less than 68.875 degrees. Finally, we analyze the added effects of radiation pressure, which are important for dust grains and provide a natural mechanism for particle semimajor axes to sweep via Poynting-Robertson drag through any unstable range. We find that generally the effect persists; however, the unstable radial range is shifted and small retrograde particles can avoid the instability altogether. We argue that this is occurs because radiation pressure modifies the equilibrium Laplace plane.