Dynamical Evolution Within Neptune’s Remote n:1 Resonances: Implications for the Planet Nine Hypothesis

Powerful mean motion resonances with Neptune largely govern the dynamics of Trans-Neptunian Objects (TNOs) in the scattered disk. Since the large eccentricities of these bodies were acquired through past gravitational encounters, understanding the constituencies of Neptune’s resonances provides a useful window into the solar system’s history. As a product of a number of deep ecliptic surveys over the past decade that were specifically tuned to detect such objects, the historically theoretical realm of bodies with 50 < a < 200 au that are thought to cluster near Neptune’s successive n:1 resonances (e.g., 3:1, 4:1, 5:1, etc.) is beginning to be constrained observationally. In spite of spending most of their lives at exceedingly large heliocentric by virtue of their characteristically large eccentricities, TNO dynamics largely couple to Neptune's. Indeed, the majority of detected scattered disk objects possess perihelia within around 40 au. However, a small number of extreme TNOs with a > 250 au and detached perihelia contradict this general trend as their orbits are essentially free from Neptune’s influence while still being too close for external forces such as passing stars and the galactic tide to appreciably affect their trajectories. Recent theoretical modeling work proposed that an apparent clustering of this small collection of orbits in physical space evidences the existence of a distant ~5-10 Earth-mass planet.

We present a suite of new numerical simulations specifically designed to investigate the effects of the hypothetical Planet Nine on the dynamical stability of objects in Neptune’s remote n:1 resonances. Our work demonstrates that both resonant and non-resonant objects beyond the 12:1 resonance (a≈157 au) are removed rather efficiently via secular interactions with the hypothetical distant planet. In many cases, TNOs remain locked in resonant configurations with Neptune while Planet Nine lifts their perihelia in excess of 60-80 au before finally detaching them from the influence of the known planets. Thus, if the Planet Nine hypothesis is correct, it would imply that the more distant n:1 resonances (i.e.: 13:1, 14:1, etc.) are more sparsely populated than the closer ones. While this region of trans-Neptunian space is still not sufficiently constrained to make a meaningful statistical prediction in this manner, to first order, there does not appear to be a dip in the semi-major axis distribution of TNOs between 100-200 au. Additionally, our simulations produce an alluring collection of low-inclination objects with a > 100 au and 40 < q < 45 au, that experience transient periods of resonance with both Neptune and Planet Nine. Finally, we follow the dynamical evolution of 64 observed TNOs with a > 100 au. Through this process, we distinguish several previously unidentified TNOs that are likely locked in n:1 resonances with Neptune. Notably, these include the most distant known resonant candidates, 2014 JW₈₀ in the 10:1 and 2014 OS₃₉₄ in the 11:1. We argue that the detection of additional objects in the vicinity of Neptune’s far reaching resonances will provide meaningful constraints on the formation and evolution of the very distant solar system.