Gravitational Radiation Driven Supermassive Black Hole Binary Inspirals as Periodically Variable Electromagnetic Sources

Supermassive black hole binaries (SMBHBs) produced in galaxy mergers are thought to complete their coalescence, at separations r ∼ < rGW ≈ 10 (MBH/10M⊙) pc, as their orbit decays due to the emission of gravitational waves (GWs). Here we propose that it may be possible to identify such GW–driven inspirals statistically in a deep electromagnetic (EM) survey for variable sources, before the Laser Interferometric Space Antenna (LISA) detects the GWs directly. A purely GW–driven binary spends a characteristic time TGW at each orbital separation rorb < rGW that scales with the corresponding orbital time torb as TGW ∝ t orb . If the coalescing binary perturbs the ambient gas and produces variations in the EM emission on this timescale, then it could be identified as a variable source with a characteristic period tvar ≈ torb. The incidence rate of sources that have similar inferred BH masses, and show near–periodic variability on the time-scale tvar, would then be ∝ t var . Luminosity variations corresponding to a fraction fEdd ∼ < 0.01 of the Eddington luminosity would have not been found in existing variability surveys. However, under the assumption that the binary inspirals are associated with quasar activity, we show that a dedicated survey, possibly with existing instruments, could detect the population of SMBHBs with a range of periods around tens of weeks. The discovery of a population of periodic sources whose abundance obeys Nvar ∝ t var would confirm (i) that the orbital decay is indeed driven by GWs, and (ii) also that circumbinary gas is present at small orbital radii and is being perturbed by the BHs. Deviations from the t var power–law, on the other hand, could constrain the structure of the circumbinary gas disk and viscosity–driven orbital decay. We discuss some constraints already available from existing data, and quantify the sensitivity and sky coverage that could yield a positive detection in future surveys. Subject headings: black hole physics – galaxies: nuclei – gravitational waves