Multi-messenger Approaches to Supermassive Black Hole Binary Detection and Parameter Estimation: Implications for Nanohertz Gravitational Wave Searches with Pulsar Timing Arrays

Pulsar timing array (PTA) experiments are becoming increasingly sensitive to gravitational waves (GWs) in the nanohertz frequency range, where the main astrophysical sources are supermassive black hole binaries (SMBHBs), which are expected to form following galaxy mergers. Some of these individual SMBHBs may power active galactic nuclei, and thus their binary parameters could be obtained electromagnetically, which makes it possible to apply electromagnetic (EM) information to aid the search for a GW signal in PTA data. In this work, we investigate the effects of such an EM-informed search on binary detection and parameter estimation by performing mock data analyses on simulated PTA datasets. We find that by applying EM priors, the Bayes factor of some injected signals with originally marginal or sub-threshold detectability (i.e., Bayes factor $\sim 1$) can increase by a factor of a few to an order of magnitude, and thus an EM-informed targeted search is able to find hints of a signal when an uninformed search fails to find any. Additionally, by combining EM and GW data, one can achieve an overall improvement in parameter estimation, regardless of the source's sky location or GW frequency. We discuss the implications for the multi-messenger studies of SMBHBs with PTAs.