Detection of periodic signals in AGN red noise light curves: empirical tests on the Auto-Correlation Function and Phase Dispersion Minimization

Active galactic nucleus (AGN) emission is dominated by stochastic, aperiodic variability which overwhelms any periodic/quasi-periodic signal (QPO) if one is present. The Auto Correlation Function (ACF) and Phase Dispersion Minimization (PDM) techniques have been used previously to claim detections of QPOs in AGN light curves. In this paper we perform Monte Carlo simulations to empirically test QPO detection feasibility in the presence of red noise. Given the community's access to large databases of monitoring light curves via large-area monitoring programmes, our goal is to provide guidance to those searching for QPOs via data trawls. We simulate evenly-sampled pure red noise light curves to estimate false alarm probabilities; false positives in both tools tend to occur towards timescales longer than (very roughly) one-third of the light curve duration. We simulate QPOs mixed with pure red noise and determine the true-positive detection sensitivity; in both tools, it depends strongly on the relative strength of the QPO against the red noise and on the steepness of the red noise PSD slope. We find that extremely large values of peak QPO power relative to red noise (typically $\sim 10^{4-5}$) are needed for a 99.7 per cent true-positive detection rate. Given that the true-positive detections using the ACF or PDM are generally rare to obtain, we conclude that period searches based on the ACF or PDM must be treated with extreme caution when the data quality is not good. We consider the feasibility of QPO detection in the context of highly-inclined, periodically self-lensing supermassive black hole binaries.