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 \mathrm { days } ) and Kepler-51c ( P _ { c } = 85.3 \mathrm { days } ) , and one transiting planet candidate KOI-620.02 ( P _ { 02 } = 130.2 \mathrm { 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 } ^ { +1.5 } M _ { \oplus } ( Kepler-51b ) , M _ { c } = 4.0 \pm 0.4 M _ { \oplus } ( Kepler-51c ) , and M _ { 02 } = 7.6 \pm 1.1 M _ { \oplus } ( 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 , \rho _ { p } \lesssim 0.05 { g cm ^ { -3 } } .
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 \Delta \Omega = -25.3 _ { -6.8 } ^ { +6.2 } \mathrm { 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 .