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Probing the existence of ultralight bosons with a single gravitational-wave measurement

Nature Astronomy volume 3, pages 447–451 (2019)Cite this article

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Abstract

Light bosons, proposed as a possible solution to various problems in fundamental physics and cosmology1,2,3, include a broad class of candidates for physics beyond the standard model, such as dilatons and moduli4, wave dark matter5 and axion-like particles6. If light bosons exist in nature, they will spontaneously form ‘clouds’ by extracting rotational energy from rotating massive black holes through superradiance, a classical wave amplification process that has been studied for decades7,8. The superradiant growth of the cloud sets the geometry of the final black hole, and the black hole geometry determines the shape of the cloud9,10,11. Hence, both the black hole geometry and the cloud encode information about the light boson. For this reason, measurements of the gravitational field of the black hole/cloud system (as encoded in gravitational waves) are over-determined. We show that a single gravitational-wave measurement can be used to verify the existence of light bosons by model selection, rule out alternative explanations for the signal, and measure the boson mass. Such measurements can be done generically for bosons in the mass range [10−16.5, 10−14] eV using observations of extreme mass-ratio inspirals (EMRIs) by the forthcoming Laser Interferometer Space Antenna (LISA).

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Fig. 1: Three independent posterior distribution measurements of ultralight boson particle masses \(\mu _{\mathrm{s}}^{(1,2,3)}\) from a single gravitational-wave observation with LISA.
Fig. 2: Median error of the measurements \(\mu _{\mathrm{s}}^{(1,2,3)}\) as a function of the SNR, ultralight boson mass μs and mean host black hole mass Mmean.

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Data availability

The data that supports the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. Bertone, G., Hooper, D. & Silk, J. Particle dark matter: evidence, candidates and constraints. Phys. Rep. 405, 279–390 (2005).

    Article  ADS  Google Scholar 

  2. Arvanitaki, A., Dimopoulos, S., Dubovsky, S., Kaloper, N. & March-Russell, J. String axiverse. Phys. Rev. D 81, 123530 (2010).

    Article  ADS  Google Scholar 

  3. Marsh, D. J. E. Axion cosmology. Phys. Rep. 643, 1–79 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  4. Arvanitaki, A., Huang, J. & Van Tilburg, K. Searching for dilaton dark matter with atomic clocks. Phys. Rev. D 91, 015015 (2015).

    Article  ADS  Google Scholar 

  5. Schive, H.-Y., Chiueh, T. & Broadhurst, T. Cosmic structure as the quantum interference of a coherent dark wave. Nat. Phys. 10, 496–499 (2014).

    Article  Google Scholar 

  6. Cardoso, V. et al. Constraining the mass of dark photons and axion-like particles through black-hole superradiance. J. Cosmol. Astropart. Phys. 1803, 043 (2018).

    Article  ADS  Google Scholar 

  7. Zel’Dovich, Y. B. Generation of waves by a rotating body. J. Exp. Theor. Phys. Lett. 14, 180 (1971).

    Google Scholar 

  8. Press, W. H. & Teukolsky, S. A. Floating orbits, superradiant scattering and the black-hole bomb. Nature 238, 211–212 (1972).

    Article  ADS  Google Scholar 

  9. Detweiler, S. L. Klein-Gordon equation and rotating black holes. Phys. Rev. D 22, 2323–2326 (1980).

    Article  ADS  Google Scholar 

  10. Arvanitaki, A. & Dubovsky, S. Exploring the string axiverse with precision black hole physics. Phys. Rev. D 83, 044026 (2011).

    Article  ADS  Google Scholar 

  11. Brito, R., Cardoso, V. & Pani, P. Black holes as particle detectors: evolution of superradiant instabilities. Class. Quant. Grav. 32, 134001 (2015).

    Article  ADS  Google Scholar 

  12. Ferreira, M. C., Macedo, C. F. B. & Cardoso, V. Orbital fingerprints of ultralight scalar fields around black holes. Phys. Rev. D 96, 083017 (2017).

    Article  ADS  Google Scholar 

  13. Dolan, S. R. Instability of the massive Klein−Gordon field on the Kerr spacetime. Phys. Rev. D 76, 084001 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  14. Babak, S. et al. Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals. Phys. Rev. D 95, 103012 (2017).

    Article  ADS  Google Scholar 

  15. Eda, K., Itoh, Y., Kuroyanagi, S. & Silk, J. New probe of dark-matter properties: gravitational waves from an intermediate-mass black hole embedded in a dark-matter minispike. Phys. Rev. Lett. 110, 221101 (2013).

    Article  ADS  Google Scholar 

  16. LSC Algorithm Library (accessed 1 January 2018); https://wiki.ligo.org/Computing/DASWG/WebHome.

  17. Arun, K. G., Buonanno, A., Faye, G. & Ochsner, E. Higher-order spin effects in the amplitude and phase of gravitational waveforms emitted by inspiraling compact binaries: ready-to-use gravitational waveforms. Phys. Rev. D 79, 104023 (2009).

    Article  ADS  Google Scholar 

  18. Bohé, A., Marsat, S. & Blanchet, L. Next-to-next-to-leading order spin–orbit effects in the gravitational wave flux and orbital phasing of compact binaries. Class. Quant. Grav. 30, 135009 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  19. Gair, J. R. et al. Event rate estimates for LISA extreme mass ratio capture sources. Class. Quant. Grav. 21, S1595–S1606 (2004).

    Article  Google Scholar 

  20. Eda, K., Itoh, Y., Kuroyanagi, S. & Silk, J. Gravitational waves as a probe of dark matter minispikes. Phys. Rev. D 91, 044045 (2015).

    Article  ADS  Google Scholar 

  21. Arvanitaki, A., Baryakhtar, M. & Huang, X. Discovering the QCD axion with black holes and gravitational waves. Phys. Rev. D 91, 084011 (2015).

    Article  ADS  Google Scholar 

  22. Baumann, D., Chia, H. S. & Porto, R. A. Probing ultralight bosons with binary black holes. Preprint at https://arxiv.org/abs/1804.03208 (2018)..

  23. Amaro-Seoane, P. Relativistic dynamics and extreme mass ratio inspirals. Living Rev. Relativ. 21, 4 (2018).

    Article  ADS  Google Scholar 

  24. Nishizawa, A., Berti, E., Klein, A. & Sesana, A. eLISA eccentricity measurements as tracers of binary black hole formation. Phys. Rev. D 94, 064020 (2016).

    Article  ADS  Google Scholar 

  25. Herdeiro, C. A. R. & Radu, E. Kerr black holes with scalar hair. Phys. Rev. Lett. 112, 221101 (2014).

    Article  ADS  Google Scholar 

  26. Babak, S., Fang, H., Gair, J. R., Glampedakis, K. & Hughes, S. A. ‘Kludge’ gravitational waveforms for a test-body orbiting a Kerr black hole. Phys. Rev. D 75, 024005 (2007). Erratum: Phys. Rev. D 77, 04990 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  27. Chua, A. J. K., Moore, C. J. & Gair, J. R. Augmented kludge waveforms for detecting extreme-mass-ratio inspirals. Phys. Rev. D 96, 044005 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  28. Feroz, F. & Hobson, M. P. Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis. Mon. Not. R. Astron. Soc. 384, 449 (2008).

    Article  ADS  Google Scholar 

  29. Feroz, F., Hobson, M. P. & Bridges, M. MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics. Mon. Not. R. Astron. Soc. 398, 1601–1614 (2009).

    Article  ADS  Google Scholar 

  30. Feroz, F., Hobson, M. P., Cameron, E. & Pettitt, A. N. Importance nested sampling and the MultiNest algorithm. Preprint at https://arxiv.org/abs/1306.2144 (2013)..

  31. Robson, T., Cornish, N. & Liu, C. The construction and use of LISA sensitivity curves. https://arxiv.org/abs/1803.01944 (2018)..

  32. Mikoczi, B., Vasuth, M. & Gergely, L. A. Self-interaction spin effects in inspiralling compact binaries. Phys. Rev. D 71, 124043 (2005).

    Article  ADS  Google Scholar 

  33. Jaranowski, P., Krolak, A. & Schutz, B. F. Data analysis of gravitational-wave signals from spinning neutron stars. 1. The signal and its detection. Phys. Rev. D 58, 063001 (1998).

    Article  ADS  Google Scholar 

  34. Allen, B., Anderson, W. G., Brady, P. R., Brown, D. A. & Creighton, J. D. E. FINDCHIRP: an algorithm for detection of gravitational waves from inspiraling compact binaries. Phys. Rev. D 85, 122006 (2012).

    Article  ADS  Google Scholar 

  35. Berti, E., Buonanno, A. & Will, C. M. Estimating spinning binary parameters and testing alternative theories of gravity with LISA. Phys. Rev. D 71, 084025 (2005).

    Article  ADS  Google Scholar 

  36. Vallisneri, M. Testing general relativity with gravitational waves: a reality check. Phys. Rev. D 86, 082001 (2012).

    Article  ADS  Google Scholar 

  37. Maggiore, M. Gravitational Waves: Volume 1: Theory and Experiments (Oxford Univ. Press, Oxford, 2007)..

  38. Gondolo, P. & Silk, J. Dark matter annihilation at the Galactic Center. Phys. Rev. Lett. 83, 1719–1722 (1999).

    Article  ADS  Google Scholar 

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Acknowledgements

We thank C. Macedo, J. L. Rosa and G. Raposo for discussions on cloud depletion. O.A.H. is supported by the Hong Kong PhD Fellowship Scheme (HKPFS) issued by the Research Grants Council (RGC) of Hong Kong. E.B. and K.W.K.W. are supported by NSF grant no. PHY-1841464, NSF grant no. AST-1841358, NSF-XSEDE grant no. PHY-090003 and NASA ATP grant no. 17-ATP17-0225. R.B. acknowledges financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 792862. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Skłodowska-Curie grant agreement No. 690904. T.G.F.L. was partially supported by grants from the Research Grants Council of Hong Kong (project no. CUHK14310816 and CUHK24304317) and the Direct Grant for Research from the Research Committee of the Chinese University of Hong Kong. The authors acknowledge networking support by the GWverse COST Action CA16104, ‘Black holes, gravitational waves and fundamental physics’.

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Authors and Affiliations

  1. Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong

    Otto A. Hannuksela & Tjonnie G. F. Li

  2. Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, USA

    Kaze W. K. Wong & Emanuele Berti

  3. Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Potsdam-Golm, Germany

    Richard Brito

  4. Dipartimento di Fisica, ‘Sapienza’ Universitá di Roma and Sezione INFN Roma, Rome, Italy

    Richard Brito

  5. Department of Physics and Astronomy, The University of Mississippi, University, MS, USA

    Emanuele Berti

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Contributions

O.A.H. conceived the idea of probing the existence of ultralight bosons, performed the full analysis, led the project and wrote the initial manuscript. K.W.K.W. surveyed the full LISA parameter space for the measurement and performed key analysis for the second figure. T.G.F.L. closely supervised all parts of the project, including its implementation and writing of the manuscript, and played an instrumental role in the development of the idea. E.B. made major revisions and contributions to the manuscript and provided theoretical input on superradiance and the overall study. R.B. provided detailed theoretical insight on superradiance and its coupling to gravitational waves, pointed out an error in the initial study that contributed to the final results and contributed significantly to the manuscript. All authors commented on the manuscript and wrote parts of it.

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Correspondence to Otto A. Hannuksela.

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Hannuksela, O.A., Wong, K.W.K., Brito, R. et al. Probing the existence of ultralight bosons with a single gravitational-wave measurement. Nat Astron 3, 447–451 (2019). https://doi.org/10.1038/s41550-019-0712-4

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