Quantifying the coincidence between gravitational waves and fast radio bursts from neutron star-black hole mergers

Fast radio bursts (FRBs) are mysterious astrophysical transients whose origin and mechanism remain unclear. Compact object mergers may be a promising channel to produce some FRBs. Neutron star--black hole (NSBH) mergers could produce FRBs through mechanisms involving neutron star tidal disruption or magnetospheric disturbances. This could present an opportunity for multimessenger gravitational-wave observations, providing new insight into the nature of FRBs and nuclear matter. However, some of the gravitational-wave signals may be marginal detections with signal-to-noise ratios $<8$ or have large sky location and distance uncertainties, making it less straightforward to confidently associate an FRB with the gravitational-wave signal. One must therefore take care to avoid a false positive association. We demonstrate how to do this with simulated data. We calculate the posterior odds---a measurement of our relative belief for a common versus unrelated origin of a coincident NSBH and FRB. We find that a coincident $\mathrm{FRB}+\mathrm{NSBH}$ from a common source can yield a statistically significant posterior odds in a network with at least two observatories, but only if we require a coincidence in time and sky location, rather than time alone. However, we find that, for our model, we require a network signal-to-noise ratio greater than 10 to be confident in the common-source detection, when using a threshold of ln odds $>8$. We suggest that a coincident $\mathrm{NSBH}+\mathrm{FRB}$ detection could help distinguish between FRB engines by discriminating between disrupting and nondisrupting models.