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Abstract There is a complex inclination structure present in the trans-Neptunian object (TNO) orbital distribution in the main classical-belt region (between orbital semimajor axes of 39 and 48 au). The long-term gravitational effects of the giant planets make TNO orbits precess, but nonresonant objects maintain a nearly constant “free” inclination (Ifree) with respect to a local forced precession pole. Because of the likely cosmogonic importance of the distribution of this quantity, we tabulate free inclinations for all main-belt TNOs, each individually computed using barycentric orbital elements with respect to each object’s local forcing pole. We show that the simplest method, based on the Laplace–Lagrange secular theory, is unable to give correct forcing poles for objects near theν18secular resonance, resulting in poorly conservedIfreevalues in much of the main belt. We thus instead implemented an averaged Hamiltonian to obtain the expected nodal precession for each TNO, yielding significantly more accurate free inclinations for nonresonant objects. For the vast majority (96%) of classical-belt TNOs, theseIfreevalues are conserved to < 1° over 4 Gyr numerical simulations, demonstrating the advantage of using this well-conserved quantity in studies of the TNO population and its primordial inclination profile; our computed distributions only reinforce the idea of a very coplanar surviving “cold” primordial population, overlain by a largeI-width implanted “hot” population.
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Suppression of the inclination instability in the trans-Neptunian Solar system
ABSTRACT The trans-Neptunian scattered disc exhibits unexpected dynamical structure, ranging from an extended dispersion of perihelion distance to a clustered distribution in orbital angles. Self-gravitational modulation of the scattered disc has been suggested in the literature as an alternative mechanism to Planet nine for sculpting the orbital architecture of the trans-Neptunian region. The numerics of this hypothesis have hitherto been limited to N < O(103) superparticle simulations that omit direct gravitational perturbations from the giant planets and instead model them as an orbit-averaged (quadrupolar) potential, through an enhanced J2 moment of the central body. For sufficiently massive discs, such simulations reveal the onset of collective dynamical behaviour – termed the ‘inclination instability’ – wherein orbital circularisation occurs at the expense of coherent excitation of the inclination. Here, we report N = O(104) GPU-accelerated simulations of a self-gravitating scattered disc (across a range of disc masses spanning 5–40 M⊕) that self-consistently account for intraparticle interactions as well as Neptune’s perturbations. Our numerical experiments show that even under the most favourable conditions, the inclination instability never ensues. Instead, due to scattering, the disc depletes. While our calculations show that a transient lopsided structure can emerge within the first few hundreds of Myr, the terminal outcomes of these calculations systematically reveal a scattered disc that is free of any orbital clustering. We conclude thus that the inclination instability mechanism is an inadequate explanation of the observed architecture of the Solar system.
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- Award ID(s):
- 2109276
- PAR ID:
- 10528117
- Publisher / Repository:
- OUP
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 523
- Issue:
- 4
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- 6103 to 6113
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/mnras/stad1687
