Toward the unambiguous identification of supermassive binary black holes through Bayesian inference.

Supermassive binary black holes at sub-parsec orbital separations have yet to be discovered. In parallel with the global hunt for nanohertz gravitational waves from such binaries using pulsar timing arrays, there has been a growing sample of candidates reported from electromagnetic surveys, particularly searches for periodic variations in optical light curves of quasars. However, the periodicity search is prone to false positives from quasar red noise, especially when the data span is less than a few signal cycles. Here we present a Bayesian method for the detection of quasar periodicity in the presence of red noise. We apply this method to the binary candidate PG1302$-$102, using data from the Catalina Real-Time Transient Survey, the All-Sky Automated Survey for Supernovae (ASAS-SN) and the Lincoln Near-Earth Asteroid Research. We show that a) there is very strong support---with a Bayes factor greater than $10^5$---for periodicity, despite the fact that the inclusion of ASAS-SN data reduces the detection significance, and b) the prevalent damped random walk red-noise model is disfavored with more than 99\% credibility. We discuss practical aspects of a periodicity search in time-series data and implications for the binary black hole nature of PG1302$-$102. Finally, we outline future work that may enable the unambiguous identification of supermassive binary black holes.