The Stability Boundary of the Distant Scattered Disk

Abstract

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 ( ( 24 2 / 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  a ∼ ( 8 / ( 5 π ) ) ( m N / M ⊙ )  M ⊙ 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.

A Low-inclination Neutral Trans-Neptunian Object in an Extreme Orbit

“…Such objects likely originated from the SDO population, but they are now totally disconnected from it because their perihelia have been lifted in the past by external perturbers or other unknown mechanisms. Several scenarios to lift q have been proposed: (1) gravitational influence of nearby stars in the Sun's birth cluster (Brasser et al 2006(Brasser et al , 2012, (2) a passing star (Kenyon & Bromley 2004;Morbidelli & Levison 2004), or (3) undetected planet(s) in the past (Gladman & Chan 2006;Silsbee & Tremaine 2018) or at present (Trujillo & Sheppard 2014;Batygin & Brown 2016;Batygin et al 2021). However, current data are insufficient to identify the dominant mechanism.…”

“…The observational q-gap suggested byOldroyd & Trujillo (2021) is outlined with a red square. The black curve shows the stability limit for distant SDOs as derived byBatygin et al (2021); above this line in the a-q plane, particles are quickly destabilized and ejected from the solar system.…”

Tilting Uranus via Secular Spin-Orbit Resonance with Planet 9

“…No additional forces are imposedthe resulting migration of Planet 9 is fully self-consistent and arises purely from perturbations from the other planets. The shaded region of the plot represents the analytic solution of Batygin et al (2021): in time t the expected scattering is ± √ D a t. For the vast majority of simulations, the numeric results are in good agreement with the analytic prediction. The large excursions from the norm are the cases relevant to our study: these would be the pathways resulting in a Planet 9 which would match present-day parameters.…”

“…Rather, as a typical TNO is scattered outwards its perihelion distance is coupled to Neptune and remains constant, while the semimajor axis grows stochastically. For such a stochastic system, the dynamics of semimajor axis evolution may be described by a conventional diffusion equation, where the relevant physics are encapsulated by the diffusion coefficient (Batygin et al 2021)…”

A New Physical Mechanism for the Onset of Atomic Ionization in an Optical Field with Jolts of Phase

“…An illustrative example of such a process is the Fermi-Ulam mechanism of gain of energy of the charged particles during reflection from magnetic mirrors [7]. This mechanism is evoked to explain stochastic heating of electrons in RF capacitive discharge [8] and instability of the planetary orbits [9].…”