The Photoeccentric Effect and Proto-Hot-Jupiters I. Measuring photometric eccentricities of individual transiting planets
Exoplanet orbital eccentricities offer valuable clues about the origins and orbital evolution of planetary systems. Eccentric, Jupiter-sized planets are particularly interesting: they may link the "cold" Jupiters beyond the ice line to hot Jupiters at a fraction of an AU, where they are unlikely to have formed in situ. To date, all eccentricities of individual planets come from radial velocity measurements. Kepler has discovered hundreds of transiting Jupiters spanning a range of periods, but the faintness of the host stars precludes radial velocity follow-up of most. Here we demonstrate a Bayesian method of measuring an individual planet's eccentricity solely from its transit light curve using prior knowledge of its host star's density. We show that eccentric Jupiters are readily identified by their short ingress/egress/total transit durations --- the "photoeccentric effect" --- even with long-cadence Kepler photometry and loosely-constrained stellar parameters. A Markov Chain Monte Carlo exploration of parameter posteriors naturally marginalizes over the periapse angle and automatically accounts for the transit probability. As a demonstration, we use four published transit light curves of HD 17156 b to measure an eccentricity of e = 0.72 +0.14/-0.09, in good agreement with the discovery value e = 0.67 +/- 0.08 based on 33 radial-velocity measurements. We present two additional tests using actual Kepler data. In each case the technique proves to be a viable method of measuring exoplanet eccentricities and their confidence intervals. Finally, we argue that this method is the most efficient, effective means of identifying the extremely eccentric, proto-hot-Jupiters predicted by Socrates and collaborators.
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