The Orbit and Mass of the Third Planet in the Kepler-56 System

TL;DR

This paper determines the orbit and mass of a third, non-transiting planet in the Kepler-56 system, explaining the observed stellar and planetary misalignment through detailed modeling of transit and radial velocity data.

Contribution

It provides updated orbital parameters and mass estimates for the third planet, revealing its role in the system's unique orbital architecture.

Findings

Outer planet has a period of 1002 days

Minimum mass of the outer planet is 5.61 Jupiter masses

No significant long-term trend detected in radial velocities

Abstract

While the vast majority of multiple-planet systems have their orbital angular momentum axes aligned with the spin axis of their host star, Kepler-56 is an exception: its two transiting planets are coplanar yet misaligned by at least 40 degrees with respect to their host star. Additional follow-up observations of Kepler-56 suggest the presence of a massive, non-transiting companion that may help explain this misalignment. We model the transit data along with Keck/HIRES and HARPS-N radial velocity data to update the masses of the two transiting planets and infer the physical properties of the third, non-transiting planet. We employ a Markov Chain Monte Carlo sampler to calculate the best-fitting orbital parameters and their uncertainties for each planet. We find the outer planet has a period of 1002 $\pm$ 5 days and minimum mass of 5.61 $\pm$ 0.38 Jupiter masses. We also place a 95% upper limit of 0.80 m/s/yr on long-term trends caused by additional, more distant companions.