The Orbit of Planet Nine

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(-1.3)(+2.2) Earth masses, semimajor axis of 380(-80)(+140)au, inclination of 16 +/- 5 degrees and perihelion of 300(-60)(+85) 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.

Automated summary

The study infers the existence of Planet Nine (P9) based on the clustering of KBOs and calculates its orbital elements. Numerical simulations show a significant influence of P9's mass and orbital elements on the orbital distribution of distant KBOs. Using likelihood values, the parameters of Planet Nine are estimated through a Markov chain Monte Carlo analysis.