Transit Light Curves with Finite Integration Time: Fisher Information Analysis

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 at www.its.caltech.edu/~eprice. Subject headings: methods: analytical — occultations — planetary systems — planets and satellites: general — techniques: photometric