The orbit of Planet Nine

TL;DR

This study infers the likely orbital parameters and position of hypothetical Planet Nine based on observed clustering of distant Kuiper belt objects, employing simulations and Bayesian analysis.

Contribution

It introduces a comprehensive method combining observational bias correction, numerical simulations, and Gaussian Process emulation to estimate Planet Nine's orbit and properties.

Findings

Planet Nine likely has a mass of about 6.2 Earth masses.

Orbital parameters are constrained with specific ranges for semimajor axis, inclination, and perihelion.

Predicted on-sky position suggests it is closer and brighter than previously thought.

Abstract

The existence of a giant planet beyond Neptune -- referred to as Planet Nine (P9) -- has been inferred from the clustering of longitude of perihelion and pole position of distant eccentric Kuiper belt objects (KBOs). After updating calculations of observational biases, we find that the clustering remains significant at the 99.6\% confidence level. We thus use these observations to determine orbital elements of P9. A suite of numerical simulations shows that the orbital distribution of the distant KBOs is strongly influenced by the mass and orbital elements of P9 and thus can be used to infer these parameters. Combining the biases with these numerical simulations, we calculate likelihood values for discrete set of P9 parameters, which we then use as input into a Gaussian Process emulator that allows a likelihood computation for arbitrary values of all parameters. We use this emulator in a Markov Chain Monte Carlo analysis to estimate parameters of P9. We find a P9 mass of $6.2^{+2.2}_{-1.3}$ Earth masses, semimajor axis of $380^{+140}_{-80}$ AU, inclination of $16\pm5^\circ$ and perihelion of $300^{+85}_{-60}$ AU. Using samples of the orbital elements and estimates of the radius and albedo of such a planet, we calculate the probability distribution function of the on-sky position of Planet Nine and of its brightness. For many reasonable assumptions, Planet Nine is closer and brighter than initially expected, though the probability distribution includes a long tail to larger distances, and uncertainties in the radius and albedo of Planet Nine could yield fainter objects.