The Population of Viscosity- and Gravitational Wave-Driven Supermassive Black Hole Binaries Among Luminous AGN

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 in the stalled "secondary-dominated" regime. SMBHBs spend a non-negligible fraction of 10^7 years at orbital periods t_var between a day and a year. A dedicated optical or X-ray survey could identify coalescing SMBHBs statistically, as a population of periodically variable quasars, whose abundance N_var is proportional to t_var^alpha, in a range of periods t_var around tens of weeks. SMBHBs with M < 10^7 M_sun, with 0.5 < alpha < 1.5, would probe the physics of viscous orbital decay, whereas the detection of a population of higher-mass binaries, with alpha=8/3, would confirm that their decay is driven by GWs. The lowest mass SMBHBs (M < 10^{5-6} M_sun) enter the GW-driven regime at short orbital periods, in the frequency band of the Laser Interferometric Space Antenna (LISA). While viscous processes are strongly sub-dominant in the last few years of coalescence, they could reduce the amplitude of any unresolved background of near-stationary LISA sources. We discuss constraints on the SMBHB population 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.