Accurate and Efficient Photoeccentric Transit Modeling

A planet's orbital eccentricity is fundamental to understanding the present dynamical state of a system and is a relic of its formation history. There is high scientific value in measuring the eccentricities of Kepler and Transiting Exoplanet Survey Satellite (TESS) planets given the sheer size of these samples and the diversity of their planetary systems. However, Kepler and TESS light curves typically only permit robust determinations of the planet-to-star radius ratio r, orbital period P, and transit midpoint t0. Three other orbital properties, including the impact parameter b, eccentricity e, and argument of periastron ω, are more challenging to measure because they are all encoded in the light curve through subtle effects on a single observable—the transit duration T14. In Gilbert et al., we showed that a five-parameter transit description {P, t0, r, b, T14} naturally yields unbiased measurements of r and b. Here, we build upon our previous work and introduce an accurate and efficient prescription to measure e and ω. We validate this approach through a suite of injection-and-recovery experiments. Our method agrees with previous approaches that use a seven-parameter transit description {P, t0, r, b, ρ⋆, e, ω}, which explicitly fits the eccentricity vector and mean stellar density. The five-parameter method is simpler than the seven-parameter method and is "future-proof" in that posterior samples can be quickly reweighted (via importance sampling) to accommodate updated priors and updated stellar properties. This method thus circumvents the need for an expensive reanalysis of the raw photometry, offering a streamlined path toward large-scale population analyses of the eccentricity from transit surveys.