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).
Subscribe to Journal
Get full journal access for 1 year
only $8.67 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
The data that supports the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
Bertone, G., Hooper, D. & Silk, J. Particle dark matter: evidence, candidates and constraints. Phys. Rep. 405, 279–390 (2005).
Arvanitaki, A., Dimopoulos, S., Dubovsky, S., Kaloper, N. & March-Russell, J. String axiverse. Phys. Rev. D 81, 123530 (2010).
Marsh, D. J. E. Axion cosmology. Phys. Rep. 643, 1–79 (2016).
Arvanitaki, A., Huang, J. & Van Tilburg, K. Searching for dilaton dark matter with atomic clocks. Phys. Rev. D 91, 015015 (2015).
Schive, H.-Y., Chiueh, T. & Broadhurst, T. Cosmic structure as the quantum interference of a coherent dark wave. Nat. Phys. 10, 496–499 (2014).
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).
Zel’Dovich, Y. B. Generation of waves by a rotating body. J. Exp. Theor. Phys. Lett. 14, 180 (1971).
Press, W. H. & Teukolsky, S. A. Floating orbits, superradiant scattering and the black-hole bomb. Nature 238, 211–212 (1972).
Detweiler, S. L. Klein-Gordon equation and rotating black holes. Phys. Rev. D 22, 2323–2326 (1980).
Arvanitaki, A. & Dubovsky, S. Exploring the string axiverse with precision black hole physics. Phys. Rev. D 83, 044026 (2011).
Brito, R., Cardoso, V. & Pani, P. Black holes as particle detectors: evolution of superradiant instabilities. Class. Quant. Grav. 32, 134001 (2015).
Ferreira, M. C., Macedo, C. F. B. & Cardoso, V. Orbital fingerprints of ultralight scalar fields around black holes. Phys. Rev. D 96, 083017 (2017).
Dolan, S. R. Instability of the massive Klein−Gordon field on the Kerr spacetime. Phys. Rev. D 76, 084001 (2007).
Babak, S. et al. Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals. Phys. Rev. D 95, 103012 (2017).
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).
LSC Algorithm Library (accessed 1 January 2018); https://wiki.ligo.org/Computing/DASWG/WebHome.
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).
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).
Gair, J. R. et al. Event rate estimates for LISA extreme mass ratio capture sources. Class. Quant. Grav. 21, S1595–S1606 (2004).
Eda, K., Itoh, Y., Kuroyanagi, S. & Silk, J. Gravitational waves as a probe of dark matter minispikes. Phys. Rev. D 91, 044045 (2015).
Arvanitaki, A., Baryakhtar, M. & Huang, X. Discovering the QCD axion with black holes and gravitational waves. Phys. Rev. D 91, 084011 (2015).
Baumann, D., Chia, H. S. & Porto, R. A. Probing ultralight bosons with binary black holes. Preprint at https://arxiv.org/abs/1804.03208 (2018)..
Amaro-Seoane, P. Relativistic dynamics and extreme mass ratio inspirals. Living Rev. Relativ. 21, 4 (2018).
Nishizawa, A., Berti, E., Klein, A. & Sesana, A. eLISA eccentricity measurements as tracers of binary black hole formation. Phys. Rev. D 94, 064020 (2016).
Herdeiro, C. A. R. & Radu, E. Kerr black holes with scalar hair. Phys. Rev. Lett. 112, 221101 (2014).
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).
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).
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).
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).
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)..
Robson, T., Cornish, N. & Liu, C. The construction and use of LISA sensitivity curves. https://arxiv.org/abs/1803.01944 (2018)..
Mikoczi, B., Vasuth, M. & Gergely, L. A. Self-interaction spin effects in inspiralling compact binaries. Phys. Rev. D 71, 124043 (2005).
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).
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).
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).
Vallisneri, M. Testing general relativity with gravitational waves: a reality check. Phys. Rev. D 86, 082001 (2012).
Maggiore, M. Gravitational Waves: Volume 1: Theory and Experiments (Oxford Univ. Press, Oxford, 2007)..
Gondolo, P. & Silk, J. Dark matter annihilation at the Galactic Center. Phys. Rev. Lett. 83, 1719–1722 (1999).
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’.
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
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
Journal of Cosmology and Astroparticle Physics (2019)
The Astrophysical Journal (2019)
Living Reviews in Relativity (2019)
Monthly Notices of the Royal Astronomical Society (2019)
Physical Review D (2019)