# The electromagnetic chirp of a compact binary black hole: a phase template for the gravitational wave inspiral

## TL;DR

This paper proposes that electromagnetic signals from gas around binary black holes can serve as phase templates for gravitational wave signals, enabling improved parameter estimation and tests of fundamental physics with LISA.

## Contribution

It introduces the concept of an electromagnetic chirp as a phase template for GW inspiral signals from supermassive binary black holes.

## Key findings

- Electromagnetic signals can track the orbital phase of binary black holes.
- Phase comparison can measure differences in photon and graviton speeds as low as 10^-17.
- Electromagnetic observations can improve localization and parameter estimation of GW sources.

## Abstract

The gravitational waves (GWs) from a binary black hole (BBH) with masses between 10^4 and 10^7 Msun 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 approximately a=100 R_g (gravitational radius), and the orbital speed is of order v/c=0.1. We 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 Delta v in the propagation speed of photons and gravitons as low as Delta v/c = O(10^-17).