Extracting Periodic Transit Signals from Noisy Light Curves using Fourier Series

We present a simple and powerful method for extracting transit signals associated with a known transiting planet from noisy light curves. Assuming the orbital period of the planet is known and the signal is periodic, we illustrate that systematic noise can be removed in Fourier space at all frequencies, by only using data within a fixed time frame with a width equal to an integer number of orbital periods. This results in a reconstruction of the full transit signal which on average is unbiased, despite that no prior knowledge of either the noise or the transit signal itself is used in the analysis. The method has therefore clear advantages over standard phase folding, which normally requires external input such as nearby stars or noise models for removing systematic components. In addition, we can extract the full orbital transit signal ($360$ degrees) simultaneously, and \emph{Kepler} like data can be analyzed in just a few seconds. We illustrate the performance of our method by applying it to a dataset composed of light curves from \emph{Kepler} with a fake injected signal emulating a planet with rings. For extracting periodic transit signals, our presented method is in general the optimal and least biased estimator and could therefore lead the way toward the first detections of, e.g., planet rings and exo-trojan asteroids.