2014ApJ...783...53M

We present an analysis of the transit timing variations (TTVs) in the multi-transiting planetary system around Kepler-51 (KOI-620). This system consists of two confirmed transiting planets, Kepler-51b (P_b= 45.2 days) and Kepler-51c (P_c= 85.3 days), and one transiting planet candidate KOI-620.02 (P₀₂= 130.2 days), which lie close to a 1: 2: 3 resonance chain. Our analysis shows that their TTVs are consistently explained by the three-planet model, and constrains their masses as M_b = 2.1_–0.8^+1.5M_⊕ (Kepler-51b), M_c= 4.0±0.4 M_⊕(Kepler-51c), and M₀₂= 7.6±1.1 M_⊕(KOI-620.02), thus confirming KOI-620.02 as a planet in this system. The masses inferred from the TTVs are rather small compared to the planetary radii based on the stellar density and planet-to-star radius ratios determined from the transit light curves. Combining these estimates, we find that all three planets in this system have densities among the lowest determined, ρ_p ≲ 0.05 g/cm3. With this feature, the Kepler-51 system serves as another example of low-density compact multi-transiting planetary systems. We also identify a curious feature in the archived Kepler light curve during the double transit of Kepler-51b and KOI-620.02, which could be explained by their overlapping on the stellar disk (a planet-planet eclipse). If this is really the case, the sky-plane inclination of KOI-620.02's orbit relative to that of Kepler-51b is given by ΔΩ = -25.3_–6.8^+6.2 deg, implying significant misalignment of their orbital planes. This interpretation, however, seems unlikely because such an event that is consistent with all of the observations is found to be exceedingly rare.