A Simplified Photodynamical Model for Planetary Mass Determination in Low-eccentricity Multitransiting Systems

Inferring planetary parameters from transit timing variations (TTVs) is challenging for small exoplanets because their transits may be so weak that determination of individual transit timing is difficult or impossible. We implement a useful combination of tools that together provide a numerically fast global photodynamical model. This is used to fit the TTV-bearing light curve, in order to constrain the masses of transiting exoplanets in low-eccentricity, multiplanet systems—and small planets in particular. We present inferred dynamical masses and orbital eccentricities in four multi-planet systems from Kepler's complete long-cadence data set. We test our model against Kepler-36/KOI-277, a system with some of the most precisely determined planetary masses through TTV inversion methods, and find masses of 5.56^+0.41_-0.45 and 9.76^+0.79_-0.89 ${m}_{\oplus }$ for Kepler-36 b and c, respectively—consistent with literature in both value and error. We then improve the mass determination of the four planets in Kepler-79/KOI-152, where literature values were physically problematic to 12.5^+4.5_-3.6, 9.5^+2.3_-2.1, 11.3^+2.2_-2.2 and 6.3^+1.0_-1.0 ${m}_{\oplus }$ for Kepler-79 b, c, d, and e, respectively. We provide new mass constraints where none existed before for two systems. These are 12.5^+3.2_-2.6 ${m}_{\oplus }$ for Kepler-450 c, and 3.3^+1.7_-1.0 and 17.4^+7.1_-3.8 ${m}_{\oplus }$ for Kepler-595 c (previously KOI-547.03) and b, respectively. The photodynamical code used here, called PyDynamicaLC, is made publicly available.