Feasibility of a resonance-based Planet Nine search

TL;DR

This study investigates the potential of using mean motion resonances to locate Planet Nine by analyzing Kuiper Belt objects, but finds that resonance chaos and high-order resonances limit this method's effectiveness.

Contribution

It characterizes the distribution of resonances in the presence of an eccentric Planet Nine, highlighting challenges in using MMRs for its detection.

Findings

Most objects do not occupy simple resonance ratios with Planet Nine.

High-order resonances are densely spaced, complicating identification.

Chaotic dynamics hinder precise resonance-based constraints.

Abstract

It has been proposed that mean motion resonances (MMRs) between Planet Nine and distant objects of the scattered disk might inform the semimajor axis and instantaneous position of Planet Nine. Within the context of this hypothesis, the specific distribution of occupied MMRs largely determines the available constraints. Here we characterize the behavior of scattered Kuiper Belt objects arising in the presence of an eccentric Planet Nine ($e_9 \in 0.1$, $0.7$), focusing on relative sizes of populations occupying particular commensurabilities. Highlighting the challenge of predicting the exact MMR of a given object, we find that the majority of resonant test particles have period ratios with Planet Nine other than those of the form $P_9/P=N/1$, $N/2$ $(N \in \mathbb{Z}^+)$. Taking into account the updated prior distribution of MMRs outlined in this work, we find that the close spacing of high-order resonances, as well as chaotic transport, preclude resonance-based Planet Nine constraints from current observational data.