How noise thresholds affect the information content of stellar flare sequences

Systems that exhibit discrete dynamics can be well described and reconstructed by considering the set of time intervals between the discrete events of the system. The Kepler satellite has cataloged light curves for many Sun-like stars, and these light curves show strong bursts in intensity that are associated with stellar flares. The waiting time between these flares describes the fundamental dynamics of the stars and is driven by physical processes, such as flux emergence. While it is rather straightforward to identify large flares, the identification of weaker flares can be challenging because of the presence of noise. A common practice is to limit flare identification to events stronger than a threshold value that significantly exceeds the noise level (k sigma), where sigma is the standard deviation of the fluctuations about the detrended light curve. However, the selection of the k-value is normally made based on an empirical rule (typically k = 3), which can lead to a biased threshold level. This study examines the information content in the waiting time sequence of enhancements in the light curve of a solar-type star (KIC 7985370) as a function of threshold. Information content is quantified by the mutual information between successive flare waiting times. It is found that the information content increases as the threshold is reduced from k = 3 to k = 1.56, in contrast with the notion that low amplitude enhancements are simply random noise. However, below k = 1.56 the information content dramatically decreases, consistent with shot noise. The information that is detected at k = 1.56 and above is similar to that of solar flares and indicates a significant relationship between the low amplitude enhancements, suggesting that many of those events are likely flares. We suggest that mutual information could be used to identify a threshold that maximizes the information content of the flare sequence, making it possible to extract more flare information from stellar light curves.