The population of viscosity- and gravitational wave-driven supermassive black hole binaries among luminous active galactic nuclei

Supermassive black hole binaries (SMBHBs) in galactic nuclei are thought to be a common by-product of major galaxy mergers. We use simple disk models for the circumbinary gas and for the binary–disk interaction to follow the orbital decay of SMBHBs with a range of total masses (M) and mass ratios (q), through physically distinct regions of the disk, until gravitational waves (GWs) take over their evolution. Prior to the GW-driven phase, the viscous decay is generically in the stalled "secondary-dominated" regime. SMBHBs spend a non-negligible fraction of a fiducial time of 107 yr at orbital periods between days ≲torb≲ yr, and we argue that they may be sufficiently common to be detectable, provided they are luminous during these stages. A dedicated optical or X-ray survey could identify coalescing SMBHBs statistically, as a population of periodically variable quasars, whose abundance obeys the scaling Nvar ∝ tαvar within a range of periods around tvar∼ tens of weeks. SMBHBs with M ≲ 107 M☉, with 0.5 ≲ α ≲ 1.5, would probe the physics of viscous orbital decay, whereas the detection of a population of higher-mass binaries, with α = 8/3, would confirm that their decay is driven by GWs. The lowest-mass SMBHBs (M ≲ 105–6 M☉) enter the GW-driven regime at short orbital periods, when they are already in the frequency band of the Laser Interferometric Space Antenna (LISA). While viscous processes are negligible in the last few years of coalescence, they could reduce the amplitude of any unresolved background due to near-stationary LISA sources. We discuss modest constraints on the SMBHB population already available from existing data, and the sensitivity and sky coverage requirements for a detection in future surveys. SMBHBs may also be identified from velocity shifts in their spectra; we discuss the expected abundance of SMBHBs as a function of their orbital velocity.