Detecting stellar flares in photometric data using hidden Markov models

We present a hidden Markov model (HMM) for discovering stellar flares in light curve data of stars. HMMs provide a framework to model time series data that are not stationary; they allow for systems to be in different states at different times and consider the probabilities that describe the switching dynamics between states. In the context of stellar flares discovery, we exploit the HMM framework by allowing the light curve of a star to be in one of three states at any given time step: Quiet, Firing, or Decaying. This three state HMM formulation is designed to enable straightforward identification of stellar flares, their duration, and associated uncertainty. This is crucial for estimating the flare's energy, and is useful for studies of stellar flare energy distributions. We combine our HMM with a celerite model that accounts for quasi periodic stellar oscillations. Through an injection recovery experiment, we demonstrate and evaluate the ability of our method to detect and characterize flares in stellar time series. We also show that the proposed HMM flags fainter and lower energy flares more easily than traditional sigma clipping methods. Lastly, we visually demonstrate that simultaneously conducting detrending and flare detection can mitigate biased estimations arising in multistage modelling approaches. Thus, this method paves a new way to calculating stellar flare energy. We conclude with an example application to one star observed by TESS, showing how the HMM compares with sigma clipping when using real data.