Otor, Oderah Justin, Montet, Benjamin T., Johnson, John Asher, Charbonneau, David, Collier-Cameron, Andrew, Howard, Andrew W., Isaacson, Howard, Latham, David W., López-Morales, Mercedes, Lovis, Christophe, Mayor, Michel, Micela, Giusi, Molinari, Emilio, Pepe, Francesco, Piotto, Giampaolo, Phillips, David F., Queloz, Didier, Rice, Ken, Sasselov, Dimitar, Ségransan, Damien, Sozzetti, Alessandro, Udry, Stéphane, and Watson, Chris. 2016. "The Orbit and Mass of the Third Planet in the Kepler-56 System." The Astronomical Journal, 152 165. https://doi.org/10.3847/0004-6256/152/6/165.
While the vast majority of multiple-planet systems have orbital angular momentum axes that align 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° with respect to the rotation axis of 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 ± 5 days and minimum mass of 5.61 ± 0.38 {M}{Jup}. We also place a 95% upper limit of 0.80 m s-1 yr-1 on long-term trends caused by additional, more distant companions.
