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 which 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 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 fueling of MBH accretion disks 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 CRTS, while $20$ and $100$ are expected after five years of LSST observations. The brightness variations in most systems are too small to be distinguishable, but almost $1\%$ of AGN at redshifts $z \lesssim 0.6$ could be in massive binaries. We analyze the predicted binary parameters of observable systems and their selection biases, and include an extensive discussion of our model parameters and uncertainties.