The X-ray chirp of a compact black hole binary

The gravitational waves (GWs) from a binary black hole with masses 10^4≲ M≲ 10^7M_⊙ can be detected with the Laser Interferometer Space Antenna (LISA) once their orbital frequency exceeds 10^{-4}-10^{-5} Hz. The binary separation at this stage is a=O(100)Rg (gravitational radius), and the orbital speed is v/c=O(0.1). I argue that at this stage, the binary will be producing bright electromagnetic (EM) radiation via gas bound to the individual BHs. Both BHs will have their own photospheres in X-ray and possibly also in optical bands. Relativistic Doppler modulations and lensing effects will inevitably imprint periodic variability in the EM light-curve, tracking the phase of the orbital motion, and serving as a template for the GW inspiral waveform. Advanced localization of the source by LISA weeks to months prior to merger will enable a measurement of this EM chirp by wide-field X-ray or optical instruments. A comparison of the phases of the GW and EM chirp signals will help break degeneracies between system parameters, and probe a fractional difference difference Δ v in the propagation speed of photons and gravitons as low as Δ v/c ≈ 10^{-17}.