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

We use 16 quarters of the $\mathit{\text{Kepler}}$ 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 $P=33.648_{-0.005}^{+0.004}$ days) are produced by a non-transiting planet Kepler-46c ($P=57.325_{-0.098}^{+0.116}$ days). The Bayesian inference tool $\mathtt{\text{MultiNest}}$ 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 $M_b=0.885_{-0.343}^{+0.374}$ 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.