The Five Planets in the Kepler-296 Binary System All Orbit the Primary: A Statistical and Analytical Analysis

Kepler-296 is a binary star system with two M-dwarf components separated by 0.2 arcsec. Five transiting planets have been confirmed to be associated with the Kepler-296 system; given the evidence to date, however, the planets could in principle orbit either star. This ambiguity has made it difficult to constrain both the orbital and physical properties of the planets. Using both statistical and analytical arguments, this paper shows that all five planets are highly likely to orbit the primary star in this system. We performed a Markov-Chain Monte Carlo simulation using a five transiting planet model, leaving the stellar density and dilution with uniform priors. Using importance sampling, we compared the model probabilities under the priors of the planets orbiting either the brighter or the fainter component of the binary. A model where the planets orbit the brighter component, Kepler-296A, is strongly preferred by the data. Combined with our assertion that all five planets orbit the same star, the two outer planets in the system, Kepler-296 Ae and Kepler-296 Af, have radii of 1.53 +/- 0.26 and 1.80 +/- 0.31 R_earth, respectively, and receive incident stellar fluxes of 1.40 +/- 0.23 and 0.62 +/- 0.10 times the incident flux the Earth receives from the Sun. This level of irradiation places both planets within or close to the circumstellar habitable zone of their parent star.