A Bayesian Method to Determine the Distribution of Transiting Exoplanets in Binary, Multiplanet Kepler Systems

Abstract

To date, almost 5000 confirmed or candidate planets have been found in the Kepler Space Telescope data. We expect a significant number of these planets to exist in binary, multi-planet systems. Because the derived planetary properties of planets in these systems depend strongly on the host star, it is important for our understanding of exoplanetary properties that we correctly model the system and each planet’s host star. Using the MultiNest algorithm we use a Bayesian argument to probabilistically determine each planet’s host star. Each ‘distribution’ of planets is the set containing the given host star of each planet. We studied the 5-planet Kepler-296 (KOI-1422) system, previously studied in Barclay et al. (2015) as a test of our method, and compared our results with Barclay’s. We found good agreement between the analyses of the planets’ likely host star and the derived planetary properties – we estimate that there is a 96.77% chance the planets all orbit the primary star. We also studied the 3-planet Kepler-192 system. We find that the planets are very likely to all orbit the primary component, with that distribution containing 99.5% of the total probability mass. This is an expected result due to the large difference in brightness between the two stars in the system, and serves as another test of our method. Lastly, we studied the 3-planet Kepler-336 system, the most likely candidate to be a split-multi in our selection of systems. Although the distribution where all planets orbit the primary is the most likely, the distribution where the planet 1916.01 orbits the secondary and the other two planets orbit the primary has a higher evidence. This is due to the penalty of 1/40 assessed against split-multi systems, based on arguments given in Barclay et al. (2015). This suggests that further study is needed to accurately identify the penalty factor against split-multi systems and also suggests that systems studied with purely statistical methods under the assumption that all the planets must orbit the same star should be reevaluated with a better understanding of this penalty factor.