THE POPULATION OF VISCOSITY- AND GRAVITATIONAL WAVE-DRIVEN SUPERMASSIVE BLACK HOLE BINARIES AMONG LUMINOUS ACTIVE GALACTIC NUCLEI

Abstract

ABSTRACT 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 10 7 yr at orbital periods between days ≲ t orb ≲ 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 N var ∝ t α var within a range of periods around t var ∼ tens of weeks. SMBHBs with M ≲ 10 7 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 ≲ 10 5–6 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.