Fast and Robust Noise Background Modeling and Quasiperiodic Oscillation Detection for Astronomical Time Series

Abstract Spectrum with confidence levels is a commonly used method for quasiperiodic oscillation (QPO) detection, but it is prone to yield false positives for two reasons: poor choice and/or biased modeling of the null hypothesis (or noise background). Motivated by this, we propose a new time-domain maximum-likelihood estimation method, which can quickly and accurately estimate the noise background free from background trends, spectra peaks, and even QPOs. Our method provides a wide range of candidate stochastic models (e.g., conventional first-order autoregressive, power law, generalized Gauss–Markov, Matérn, and damped random walk), some of which have not been considered previously. Some pitfalls (e.g., detrending) in previous QPO detections are also correctly processed to minimize the false detections. Along with the multitaper method and wavelet, we revisit QPO detection in the X-ray emission from the active galaxies RE J10341+396 and 1H 0707-495, and point out why the significance levels of the QPO at ∼2.6 × 10 −4 Hz would be different in previous detections and reduced if the whole observation duration is considered. Our algorithm can be easily extended to other branches of astrophysics and beyond.