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The Stability Boundary of the Distant Scattered Disk

Batygin, Konstantin and Mardling, Rosemary A. and Nesvorný, David (2021) The Stability Boundary of the Distant Scattered Disk. Astrophysical Journal, 920 (2). Art. No. 148. ISSN 0004-637X. doi:10.3847/1538-4357/ac19a4.

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The distant scattered disk is a vast population of trans-Neptunian minor bodies that orbit the Sun on highly elongated, long-period orbits. The orbital stability of scattered-disk objects (SDOs) is primarily controlled by a single parameter—their perihelion distance. While the existence of a perihelion boundary that separates chaotic and regular motion of long-period 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 trans-Neptunian 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 long-period orbits, and demonstrate that rapid dynamical chaos ensues when the perihelion drops below a critical value, given by q_(crit) = a_N(ln((24²/5)(m_N/M⊙)(a/a_N)^(5/2)))^(1/2). This expression constitutes an analytic boundary between the "detached" and actively "scattering" subpopulations of distant trans-Neptunian 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 D_a ∼ (8/(5π))(m_N/M_⊙)√GM_⊙a_N exp [−(q/a_N)²/2]. We confirm our results with direct N-body simulations and highlight the connections between scattered-disk dynamics and the Chirikov Standard Map. Implications of our results for the long-term evolution of minor bodies in the distant solar system are discussed.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Batygin, Konstantin0000-0002-7094-7908
Mardling, Rosemary A.0000-0001-7362-3311
Nesvorný, David0000-0002-4547-4301
Additional Information:© 2021. The American Astronomical Society. Received 2021 June 6; revised 2021 July 23; accepted 2021 July 29; published 2021 October 25. We are indebted to Alessandro Morbidelli, Matt Clement, and Mike Brown for illuminating discussions, as well as to Dan Tamayo for providing a thorough and insightful referee report. We are additionally grateful to Hanno Rein for sharing his expertise in numerical implementation of chaos indicators. K.B. is grateful to Caltech, and the David and Lucile Packard Foundation for their generous support.
Funding AgencyGrant Number
David and Lucile Packard FoundationUNSPECIFIED
Subject Keywords:Orbits; Perturbation methods; Scattered disk objects
Issue or Number:2
Classification Code:Unified Astronomy Thesaurus concepts: Orbits (1184); Perturbation methods (1215); Scattered disk objects (1430)
Record Number:CaltechAUTHORS:20211110-150135307
Persistent URL:
Official Citation:Konstantin Batygin et al 2021 ApJ 920 148
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111814
Deposited By: Tony Diaz
Deposited On:11 Nov 2021 19:26
Last Modified:11 Nov 2021 19:26

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