Massive BH binaries as periodically variable AGN

Massive black hole (MBH) binaries, which are expected to form following the merger of their parent galaxies, produce gravitational waves that will be detectable by pulsar timing arrays at nanohertz frequencies (year periods). While no confirmed, compact MBH binary systems have been seen in electromagnetic observations, a large number of candidates have recently been identified in optical surveys of active galactic nucleus (AGN) variability. Using a combination of cosmological, hydrodynamic simulations; comprehensive, semi-analytic binary merger models; and analytic AGN spectra and variability prescriptions; we calculate the expected electromagnetic detection rates of MBH binaries as periodically variable AGN. In particular, we consider two independent variability models: (i) Doppler boosting due to large orbital velocities and (ii) hydrodynamic variability in which the fuelling of MBH accretion discs is periodically modulated by the companion. Our models predict that numerous MBH binaries should be present and distinguishable in the existing data. In particular, our fiducial models produce an expectation value of 0.2 (Doppler) and 5 (hydrodynamic) binaries to be identifiable in the Catalina survey (CRTS), while 20 and 100 are expected after 5 yr of LSST observations. The brightness variations in most systems are too small to be distinguishable, but almost 1 per cent of AGN at redshifts z 0.6 could be in massive binaries. We analyse the predicted binary parameters of observable systems and their selection biases, and include an extensive discussion of our model parameters and uncertainties.