Masses of Kepler-46b, c from Transit Timing Variations

We use 16 quarters of the \textit{Kepler} mission data to analyze the transit timing variations (TTVs) of the extrasolar planet Kepler-46b (KOI-872). Our dynamical fits confirm that the TTVs of this planet (period $P=33.648^{+0.004}_{-0.005}$ days) are produced by a non-transiting planet Kepler-46c ($P=57.325^{+0.116}_{-0.098}$ days). The Bayesian inference tool \texttt{MultiNest} is used to infer the dynamical parameters of Kepler-46b and Kepler-46c. We find that the two planets have nearly coplanar and circular orbits, with eccentricities $\simeq 0.03$ somewhat higher than previously estimated. The masses of the two planets are found to be $M_{b}=0.885^{+0.374}_{-0.343}$ and $M_{c}=0.362^{+0.016}_{-0.016}$ Jupiter masses, with $M_{b}$ being determined here from TTVs for the first time. Due to the precession of its orbital plane, Kepler-46c should start transiting its host star in a few decades from now.