An Electromagnetic Signature of Galactic Black Hole Binaries That Enter Their Gravitational-Wave Induced Inspiral

Mergers of gas-rich galaxies lead to black hole binaries that coalesce as a result of dynamical friction on the ambient gas. Once the binary tightens to <10^3 Schwarzschild radii, its merger is driven by the emission of gravitational waves (GWs). We show that this transition occurs generically at orbital periods of ~1-10 years and an orbital velocity V of a few thousand km/s, with a very weak dependence on the supply rate of gas (V proportional to Mdot^{1/8}). Therefore, as binaries enter their GW-dominated inspiral, they inevitably induce large periodic shifts in the broad emission lines of any associated quasar(s). The probability of finding a binary in tighter configurations scales as V^{-8} owing to their much shorter lifetimes. Systematic monitoring of the broad emission lines of quasars on timescales of months to decades can set a lower limit on the expected rate of GW sources for LISA.