Automatic detection of periodic sources in the K2 data sets

Abstract

We present an automated algorithm for the detection of periodic sources in the K2 data sets. Fast discreet Fourier transformations are used to compute the Fourier spectra of the targets and two different detection algorithms for identifying significant signals are used. The first technique searches through the DFT to identify peaks that are significantly above the background noise level, and which have at least one higher harmonic of the fundamental frequency. We show this approach to be relatively inefficient for detecting weaker sources with narrow features, such as transiting exoplanets. The second algorithm that we apply uses a summation of the DFT harmonics, which relies on the fact that typical planetary transits and binary eclipses have numerous harmonics in their Fourier spectra. In this method we sum the harmonics of the fundamental frequency, which increases the signal-to-noise ratio and substantially increases the detection efficiency of the algorithm. This latter technique yields a smaller number of false positives while having higher detection rates than the first approach. A discussion of the noise level and detection threshold is presented, with a derivation of the threshold for the algorithm based on the noise properties in the K2 data. Furthermore, a discussion of the performance of both algorithms is presented. We then apply this automated search algorithm to the sixth and seventh fields of the K2 mission. In all these fields contained some 45,000 stars that were monitored for nearly three months each. The automated search yielded about 2000 interesting periodic targets. We conclude with a short discussion of the more interesting objects detected in the C7 data release by the K2 team. Finally, we present a catalog of many of the periodic sources that we have detected using these algorithms in the Appendix.