Suppression of the inclination instability in the trans-Neptunian Solar system

Abstract

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.