False periodicities in quasar time-domain surveys

There have recently been several reports of apparently periodic variations in the light curves of quasars, e.g. PG 1302−102 by Graham et al. Any quasar showing periodic oscillations in brightness would be a strong candidate to be a close binary supermassive black hole and, in turn, a candidate for gravitational wave studies. However, normal quasars – powered by accretion on to a single, supermassive black hole – usually show stochastic variability over a wide range of time-scales. It is therefore important to carefully assess the methods for identifying periodic candidates from among a population dominated by stochastic variability. Using a Bayesian analysis of the light curve of PG 1302−102, we find that a simple stochastic process is preferred over a sinusoidal variation. We then discuss some of the problems one encounters when searching for rare, strictly periodic signals among a large number of irregularly sampled, stochastic time series, and use simulations of quasar light curves to illustrate these points. From a few thousand simulations of steep spectrum (‘red noise’) stochastic processes, we find many simulations that display few-cycle periodicity like that seen in PG 1302−102. We emphasize the importance of calibrating the false positive rate when the number of targets in a search is very large.