Bayesian Analysis of Quasi-periodic Pulsations in Stellar Flares

Quasi-periodic pulsations (QPPs) are routinely observed in a range of wavelengths during flares, but in most cases the mechanism responsible is unknown. We present a method to detect and characterize QPPs in time series such as light curves for solar or stellar flares based on forward modeling and Bayesian analysis. We include models for QPPs as oscillations with finite lifetimes and nonmonotonic amplitude modulation, such as wave trains formed by dispersive evolution in structured plasmas. By quantitatively comparing different models using Bayes factors, we characterize the QPPs according to five properties: sinusoidal or nonsinusoidal, finite or indefinite duration, symmetric or asymmetric perturbations, monotonic or nonmonotonic amplitude modulation, and constant or varying period of oscillation. We demonstrate our method and show examples of these five characteristics by analyzing QPPs in white-light stellar flares observed by the Kepler space telescope. Different combinations of properties may be able to identify particular physical mechanisms and so improve our understanding of QPPs and allow their use as seismological diagnostics. We propose that three observational classes of QPPs can be distinguished: decaying harmonic oscillations, finite wave trains, and nonsinusoidal pulsations