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The X-ray Chirp of a Compact Black Hole Binary

A Phase Template for the Gravitational Wave Inspiral

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Abstract

The gravitational waves (GWs) from a binary black hole with masses \(10^4\lesssim M\lesssim 10^7\mathrm{M_\odot }\) 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 \(a=O(100)R_{\mathrm{g}}\) (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 \(\Delta v\) in the propagation speed of photons and gravitons as low as \(\Delta v/c \approx 10^{-17}\).

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Notes

  1. Ref. [34] considered a similar Doppler modulation that would arise following the tidal disruption of a star by a massive BBH at somewhat larger separations, but did not consider simultaneous direct measurement of GWs.

  2. For a circular orbit; non-sinusoidal modulations from eccentric orbits are easily incorporated into the analysis.

  3. See www.lsst.org.

  4. See www.cosmos.esa.int/web/athena.

  5. See wwwastro.msfc.nasa.gov/lynx.

  6. D.J. D’Orazio and R. Di Stefano, in preparation.

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Acknowledgements

I thank the organizers for putting together a very stimulating meeting. I also thank Alessandra Buonanno, Csaba Csáki, Daniel Chung, Kohei Inayoshi, Feryal Ozel, Lorenzo Sironi, and Luigi Stella for useful discussions, and Daniel D’Orazio, Bence Kocsis and Geoffrey Ryan for useful comments on a draft of this manuscript. I also gratefully acknowledge support by a Simons Fellowship in Theoretical Physics (ZH) and by NASA Grant NNX15AB19G.

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  1. Department of Astronomy, Columbia University, 550 W120th St., New York, NY, 10027, USA

    Zoltán Haiman

  2. Department of Physics, New York University, New York, NY, 10003, USA

    Zoltán Haiman

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Haiman, Z. The X-ray Chirp of a Compact Black Hole Binary. Found Phys 48, 1430–1445 (2018). https://doi.org/10.1007/s10701-018-0201-0

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