Introducing an unknown companion in the Kepler-56 system (via radial velocity observations and dynamical analysis)

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 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 radial velocity data to update the orbital parameters of the two transiting planets and infer the physical properties of the third, nontransiting planet. We employ a Markov Chain Monte Carlo sampler to calculate the best-fitting orbital parameters and the uncertainties, calculating posterior distributions on the physical parameters of each planet.We find a maximally likely scenario in which the additional RV signal beyond the two transiting planets come from only one planet with a period of 1000 days and minimum mass of 6 Jupiter masses. Given this minimum mass, the perturber could be a giant planet or brown dwarf, either of which would have implications on the formation of the Kepler-56 system. To further refine the allowed parameters of Kepler-56d, we use REBOUND to test the gravitational stability of simulated Kepler-56 systems to determine which of our RV-allowed systems are dynamically stable over the lifetime of this planetary system.