Dynamical Evolution Induced by Planet Nine

TL;DR

This paper investigates the dynamical effects of Planet Nine on distant Kuiper belt objects, revealing that mean-motion resonances and secular dynamics within these resonances explain observed orbital clustering, perihelion detachment, and inclination oscillations.

Contribution

It provides a semi-analytic framework showing how resonances and secular dynamics driven by Planet Nine account for observed orbital structures, advancing theoretical understanding.

Findings

Resonance-driven dynamics enable long-term stability of distant objects.

Secular resonances explain orbital confinement and perihelion detachment.

Inclination oscillations result from capture into high-order secular resonances.

Abstract

The observational census of trans-Neptunian objects with semi-major axes greater than ~250 AU exhibits unexpected orbital structure that is most readily attributed to gravitational perturbations induced by a yet-undetected, massive planet. Although the capacity of this planet to (i) reproduce the observed clustering of distant orbits in physical space, (ii) facilitate dynamical detachment of their perihelia from Neptune, and (iii) excite a population of long-period centaurs to extreme inclinations is well established through numerical experiments, a coherent theoretical description of the dynamical mechanisms responsible for these effects remains elusive. In this work, we characterize the dynamical processes at play, from semi-analytic grounds. We begin by considering a purely secular model of orbital evolution induced by Planet Nine, and show that it is at odds with the ensuing stability of distant objects. Instead, the long-term survival of the clustered population of long-period KBOs is enabled by a web of mean-motion resonances driven by Planet Nine. Then, by taking a compact-form approach to perturbation theory, we show that it is the secular dynamics embedded within these resonances that regulates the orbital confinement and perihelion detachment of distant Kuiper belt objects. Finally, we demonstrate that the onset of large-amplitude oscillations of orbital inclinations is accomplished through capture of low-inclination objects into a high-order secular resonance and identify the specific harmonic that drives the evolution. In light of the developed qualitative understanding of the governing dynamics, we offer an updated interpretation of the current observational dataset within the broader theoretical framework of the Planet Nine hypothesis.