Towards robust gravitational wave detections from individual supermassive black hole binaries

The recent discovery of the stochastic gravitational-wave background via pulsar timing arrays will likely be followed by the detection of individual black hole binaries that stand out above the background. However, to confidently claim the detection of an individual binary, we need not only more and better data, but also more sophisticated analysis techniques. In this paper, we develop two new approaches that can help us more robustly ascertain if a candidate found by a search algorithm is indeed an individual supermassive black hole binary. One of these is a coherence test that directly compares the full signal model to an incoherent version of that. The other is a model scrambling approach that builds null distributions of our detection statistic and compares that with the measured value to quantify our confidence in signal coherence. Both of these rely on finding the coherence between pulsars characteristic to gravitational waves from a binary system. We test these methods on simple simulated datasets and find that they work well in correctly identifying both true gravitational waves and false positives. However, as expected for such a flexible and simple signal model, confidently identifying signal coherence is significantly harder than simply finding a candidate in most scenarios. Our analyses also indicate that the confidence with which we can identify a true signal depends not only on the signal-to-noise ratio, but also on the number of contributing pulsars and the amount of frequency evolution shown by the signal.