Accurate and efficient photo-eccentric 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 eccentricities of Kepler and TESS planets given the sheer size of these samples and the diversity of their planetary systems. However, Kepler and TESS lightcurves typically only permit robust determinations of planet-to-star radius ratio $r$, orbital period $P$, and transit mid-point $t_0$. Three other orbital properties, including impact parameter $b$, eccentricity $e$, and argument of periastron $\omega$, are more challenging to measure because they are all encoded in the lightcurve through subtle effects on a single observable -- the transit duration $T_{14}$. In Gilbert, MacDougall, & Petigura (2022), we showed that a five-parameter transit description $\{P, t_0, r, b, T_{14}\}$ 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 $\omega$. 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 $\{P, t_0, r, b, \rho_\star, e, \omega\}$ 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 eccentricity from transit surveys.