Transit Light Curves with Finite Integration Time: Fisher Information Analysis (Fix Title)
Kepler has revolutionized the study of transiting planets with its unprecedented photometric precision on more than 150,000 target stars. Most of the thousands of transiting planet candidates detected by Kepler have been observed as long-cadence targets with 30 minute exposure times, and the upcoming Transiting Exoplanet Survey Satellite (TESS) will record full frame images with a similar integration time. Analytic approximations for the variances and covariances on the transit parameters can be derived from fitting non-binned light curve photometry to a non-binned model. Integrations of 30 minutes affect the transit shape, particularly for small planets and in cases of low signal to noise. We derive light curve models in terms of the transit parameters and exposure time, and we used the Fisher information matrix technique to derive the variances and covariances among the parameters due to fitting these binned models to binned data. We found that binning the light curve can significantly increase the uncertainties and covariances on the inferred parameters. Uncertainties on the transit ingress/egress time can increase by a factor of 34 for Earth-size planets and 3.4 for Jupiter-size planets around Sun-like stars for exposure 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, respectively. On the other hand, uncertainties on the transit depth are largely unaffected by finite exposure times (increasing by a factor of only 1.07 under the influence of 30 minute exposure times). While correlations among the transit depth, ingress duration, and transit duration all increase in magnitude with longer exposure times, the mid-transit time remains uncorrelated with the other parameters. We provide code for predicting the variances and covariances of any set of planet parameters and exposure times at www.its.caltech.edu/~eprice.