The Stability Boundary of the Distant Scattered Disk
Abstract
The distant scattered disk is a vast population of transNeptunian minor bodies that orbit the Sun on highly elongated, longperiod orbits. The orbital stability of scattereddisk objects (SDOs) is primarily controlled by a single parametertheir perihelion distance. While the existence of a perihelion boundary that separates chaotic and regular motion of longperiod orbits is well established through numerical experiments, its theoretical basis as well as its semimajor axis dependence remain poorly understood. In this work, we outline an analytical model for the dynamics of distant transNeptunian objects and show that the orbital architecture of the scattered disk is shaped by an infinite chain of exterior 2:j resonances with Neptune. The widths of these resonances increase as the perihelion distance approaches Neptune's semimajor axis, and their overlap drives chaotic motion. Within the context of this theoretical picture, we derive an analytic criterion for instability of longperiod orbits, and demonstrate that rapid dynamical chaos ensues when the perihelion drops below a critical value, given by ${q}_{\mathrm{crit}}={a}_{{\rm{N}}}{\left(\mathrm{ln}(({24}^{2}/5)({m}_{{\rm{N}}}/{M}_{\odot }){\left(a/{a}_{{\rm{N}}}\right)}^{5/2})\right)}^{1/2}$ . This expression constitutes an analytic boundary between the "detached" and actively "scattering" subpopulations of distant transNeptunian minor bodies. Additionally, we find that within the stochastic layer, the Lyapunov time of SDOs approaches the orbital period, and show that the semimajor axis diffusion coefficient is approximated by ${{ \mathcal D }}_{a}\,\sim (8/(5\pi ))({m}_{{\rm{N}}}/{M}_{\odot })\sqrt{{ \mathcal G }{M}_{\odot }{a}_{{\rm{N}}}}\,\exp \left[{\left(q/{a}_{{\rm{N}}}\right)}^{2}/2\right]$ . We confirm our results with direct Nbody simulations and highlight the connections between scattereddisk dynamics and the Chirikov Standard Map. Implications of our results for the longterm evolution of minor bodies in the distant solar system are discussed.
 Publication:

The Astrophysical Journal
 Pub Date:
 October 2021
 DOI:
 10.3847/15384357/ac19a4
 arXiv:
 arXiv:2111.00305
 Bibcode:
 2021ApJ...920..148B
 Keywords:

 Orbits;
 Perturbation methods;
 Scattered disk objects;
 1184;
 1215;
 1430;
 Astrophysics  Earth and Planetary Astrophysics;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 14 pages, 3 figures, published in ApJ