Searching for quasi-periodic oscillations in astrophysical transients using Gaussian processes

Analyses of quasi-periodic oscillations (QPOs) are important to understanding the dynamic behaviour in many astrophysical objects during transient events like gamma-ray bursts, solar flares, magnetar flares and fast radio bursts. Astrophysicists often search for QPOs with frequency-domain methods such as (Lomb-Scargle) periodograms, which generally assume power-law models plus some excess around the QPO frequency. Time-series data can alternatively be investigated directly in the time domain using Gaussian Process (GP) regression. While GP regression is computationally expensive in the general case, the properties of astrophysical data and models allow fast likelihood strategies. Heteroscedasticity and non-stationarity in data have been shown to cause bias in periodogram-based analyses. Gaussian processes can take account of these properties. Using GPs, we model QPOs as a stochastic process on top of a deterministic flare shape. Using Bayesian inference, we demonstrate how to infer GP hyperparameters and assign them physical meaning, such as the QPO frequency. We also perform model selection between QPOs and alternative models such as red noise and show that this can be used to reliably find QPOs. This method is easily applicable to a variety of different astrophysical data sets. We demonstrate the use of this method on a range of short transients: a gamma-ray burst, a magnetar flare, a magnetar giant flare, and simulated solar flare data.