Fifth-year graduate student at the Center for Astrophysics | Harvard & Smithsonian.
It is well-known that the light curve of a transiting planet contains information about the planet's orbital period and size relative to the host star. More recently, it has been demonstrated that a tight constraint on an individual planet's eccentricity can sometimes be derived from the light curve via the "photoeccentric effect," the effect of a planet's eccentricity on the shape and duration of its light curve. This has only been studied for large planets and high signal-to-noise scenarios, raising the question of how well it can be measured for smaller planets or low signal-to-noise cases. We explore the limits of the photoeccentric effect over a wide range of planet parameters. The method hinges upon measuring g directly from the light curve, where g is the ratio of the planet's speed (projected on the plane of the sky) during transit to the speed expected for a circular orbit. We find that when the signal-to-noise in the measurement of g is < 10, the ability to measure eccentricity with the photoeccentric effect decreases. We develop a "rule of thumb" that for per-point relative photometric uncertainties σ = {1e-3, 1e-4, 1e-5}, the critical values of planet-star radius ratio are Rp/R⋆ ≈ {0.1, 0.05, 0.03} for Kepler-like 30-minute integration times. We demonstrate how to predict the best-case uncertainty in eccentricity that can be found with the photoeccentric effect for any light curve. This clears the path to study eccentricities of individual planets of various sizes in the Kepler sample and future transit surveys.
Kepler has revolutionized the study of transiting planets with its unprecedented photometric precision on more than 150,000 target stars. Most of the transiting planet candidates detected by Kepler have been observed as long-cadence targets with 30 minute integration times, and the upcoming Transiting Exoplanet Survey Satellite (TESS) will record full frame images with a similar integration time. Integrations of 30 minutes affect the transit shape, particularly for small planets and in cases of low signal-to-noise. Using the Fisher information matrix technique, we derive analytic approximations for the variances and covariances on the transit parameters obtained from fitting light curve photometry collected with a finite integration time. We find that binning the light curve can significantly increase the uncertainties and covariances on the inferred parameters when comparing scenarios with constant total signal-to-noise (constant total integration time in the absence of read noise). Uncertainties on the transit ingress/egress time increase by a factor of 34 for Earth-size planets and 3.4 for Jupiter-size planets around Sun-like stars for integration times of 30 minutes compared to instantaneously-sampled light curves. Similarly, uncertainties on the mid-transit time for Earth and Jupiter-size planets increase by factors of 3.9 and 1.4. Uncertainties on the transit depth are largely unaffected by finite integration times. While correlations among the transit depth, ingress duration, and transit duration all increase in magnitude with longer integration times, the mid-transit time remains uncorrelated with the other parameters. We provide code in Python and Mathematica for predicting the variances and covariances on this website.