The Generation of the Distant Kuiper Belt by Planet Nine from an Initially Broad Perihelion Distribution

TL;DR

This study explores how initial conditions of the Kuiper Belt influence the orbital distribution of distant objects under the Planet Nine hypothesis, revealing a bimodal perihelion distribution linked to stable aligned and anti-aligned orbits.

Contribution

It demonstrates that the primordial perihelion distribution extending beyond 36 AU is crucial for reproducing the observed bimodal structure in Kuiper Belt objects within the Planet Nine model.

Findings

Final perihelion distribution depends on initial conditions.

Bimodal structure arises only with extended initial perihelion distribution.

Stable objects are associated with specific phase space regions.

Abstract

The observation that the orbits of long-period Kuiper Belt objects are anomalously clustered in physical space has recently prompted the Planet Nine hypothesis - the proposed existence of a distant and eccentric planetary member of our solar system. Within the framework of this model, a Neptune-like perturber sculpts the orbital distribution of distant Kuiper Belt objects through a complex interplay of resonant and secular effects, such that in addition to perihelion-circulating objects, the surviving orbits get organized into apsidally aligned and anti-aligned configurations with respect to Planet Nine's orbit. In this work, we investigate the role of Kuiper Belt initial conditions on the evolution of the outer solar system using numerical simulations. Intriguingly, we find that the final perihelion distance distribution depends strongly on the primordial state of the system, and demonstrate that a bimodal structure corresponding to the existence of both aligned and anti-aligned clusters is only reproduced if the initial perihelion distribution is assumed to extend well beyond $\sim 36$ AU. The bimodality in the final perihelion distance distribution is due to the existence of permanently stable objects, with the lower perihelion peak corresponding to the anti-aligned orbits and the higher perihelion peak corresponding to the aligned orbits. We identify the mechanisms which enable the persistent stability of these objects and locate the regions of phase space in which they reside. The obtained results contextualize the Planet Nine hypothesis within the broader narrative of solar system formation, and offer further insight into the observational search for Planet Nine.