2025ApJ...988..222G

Pulsar timing arrays recently found evidence for a gravitational-wave background (GWB), likely the stochastic overlap of gravitational waves from many supermassive black hole binaries. Anticipating a continuous gravitational-wave (CW) detection from a single binary soon to follow, we examine how well current Bayesian methods can detect CWs and characterize their binary properties by modeling the response of the NANOGrav 15 yr pulsar timing array to simulated binary populations. We run Markov Chain Monte Carlo searches for CWs in these data sets and compare them to quicker detection statistics including the optimal signal-to-noise ratio (S/N), matched filter detection statistic, and reduced log-likelihood ratio between the signal and noise models calculated at the injected parameters. The latter is the best proxy for Bayesian detection fractions, corresponding to a 50% detection fraction (by Bayes factors >10 favoring a CW detection over noise-only model) at an S/N = 4.6. Source confusion between the GWB and a CW, or between multiple CWs, can cause false detections and unexpected dismissals. Fifty-three percent of realistic binary populations consistent with the recently observed GWB have successful CW detections. Additionally, 82% of these CWs are in the fourth or fifth frequency bin of the 16.03 yr data set (6.9 and 10.8 nHz), with 95th percentile regions spanning 4-12 nHz frequencies, 0.7-20 × 10⁹M_⊙ chirp masses, 60 Mpc-8 Gpc luminosity distances, and 18-13,000 deg² 68% confidence localization areas. These successful detections often poorly recover the chirp mass, with only 29% identifying the chirp mass accurately to within 1 dex with a 68% posterior width also narrower than 1 dex.