Dynamical Evolution Induced by Planet Nine

Abstract

The observational census of trans-Neptunian objects with semimajor 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 the 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 Kuiper Belt objects (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 regulate the orbital confinement and perihelion detachment of distant KBOs. Finally, we demonstrate that the onset of large-amplitude oscillations of the orbital inclinations is accomplished through the capture of low-inclination objects into a high-order secular resonance, and we 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 data set within the broader theoretical framework of the Planet Nine hypothesis.