Detecting Stellar Flares in Photometric Data Using Hidden Markov Models

Abstract

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 nonstationary; 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 the discovery of stellar flares, 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 quasiperiodic 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 modeling approaches. Thus, this method paves a new way to calculate 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.

Keywords

• Stellar flares
• Bayesian statistics
• Astrostatistics tools
• Time series analysis
• M dwarf stars
• Stellar activity