  Supermassive black hole binaries (SMBHBs) are a natural outcome of galaxy
mergers and should form frequently in galactic nuclei. Sub-parsec binaries can
be identified from their bright electromagnetic emission, e.g., Active Galactic
Nuclei (AGN) with Doppler shifted broad emission lines or AGN with periodic
variability, as well as from the emission of strong gravitational radiation.
The most massive binaries (with total mass >10^8 M_sol) emit in the nanohertz
band and are targeted by Pulsar Timing Arrays (PTAs). Here we examine the
synergy between electromagnetic and gravitational wave signatures of SMBHBs. We
connect both signals to the orbital dynamics of the binary and examine the
common link between them, laying the foundation for joint multi-messenger
observations. We find that periodic variability arising from relativistic
Doppler boost is the most promising electromagnetic signature to connect with
GWs. We delineate the parameter space (binary total mass/chirp mass versus
binary period/GW frequency) for which joint observations are feasible.
Currently multi-messenger detections are possible only for the most massive and
nearby galaxies, limited by the sensitivity of PTAs. However, we demonstrate
that as PTAs collect more data in the upcoming years, the overlapping parameter
space is expected to expand significantly.
