1207.4192 (Yoram Lithwick et al.)

Extracting Planet Mass and Eccentricity From TTV data    [PDF]

Yoram Lithwick, Jiwei Xie, Yanqin Wu

Most planet pairs in the Kepler data that have measured transit time variations (TTV) are near first-order mean-motion resonances. We derive analytical formulae for their TTV signals. We separate planet eccentricity into free and forced parts, where the forced part is purely due to the planets' proximity to resonance. This separation yields simple analytical formulae. The phase of the TTV depends sensitively on the presence of free eccentricity: if the free eccentricity vanishes, the TTV will be in phase with the longitude of conjunctions. This effect is easily detectable in current TTV data. The amplitude of the TTV depends on planet mass and the free eccentricity, and it determines planet mass uniquely only when the free eccentricity is sufficiently small. We proceed to analyze the TTV signals of six short period Kepler pairs. We find three (Kepler-18,24,25) are consistent with having zero TTV phase and are likely devoid of free eccentricities. This result, combined with the observed pile-up of Kepler pairs near mean-motion resonances (explainable by resonant repulsion), suggests that the orbits of at least some low-mass Kepler planets have experienced substantial dissipation. The fact that these pairs likely have zero free eccentricity allows accurate determination of planet masses, subject only to uncertainties in transit parameters. The remaining three systems (Kepler-23,28,32) appear to have free eccentricities of a few percent.

View original: http://arxiv.org/abs/1207.4192