Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Distinguishing environmental effects on binary black hole gravitational waveforms

Abstract

Future gravitational wave interferometers such as the Laser Interferometer Space Antenna, Taiji, DECi-hertz Interferometer Gravitational wave Observatory and TianQin will enable precision studies of the environment surrounding black holes. These detectors will probe the millihertz frequency range, as yet unexplored by current gravitational wave detectors. Furthermore, sources will remain in band for durations of up to years, meaning that the inspiral phase of the gravitational wave signal, which can be affected by the environment, will be observable. In this paper, we study intermediate and extreme mass ratio binary black hole inspirals, and consider three possible environments surrounding the primary black hole: accretion disks, dark matter spikes and clouds of ultra-light scalar fields, also known as gravitational atoms. We present a Bayesian analysis of the detectability and measurability of these three environments. Focusing for concreteness on the case of a detection with LISA, we show that the characteristic imprint they leave on the gravitational waveform would allow us to identify the environment that generated the signal and to accurately reconstruct its model parameters.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Density profiles of and energy losses due to environments.
Fig. 2: Parameter estimation using the correct environmental template.
Fig. 3: SNR losses as a function of the environmental parameters.
Fig. 4: Parameter estimation using a vacuum template.

Similar content being viewed by others

Data availability

No raw data were used in the completion of this manuscript.

Code availability

HaloFeedback code can be accessed at ref. 61. pydd code can be accessed at https://github.com/adam-coogan/pydd. For specific adaptations of these codes made for this manuscript, please email p.s.cole@uva.nl.

References

  1. Baker, J. et al. The Laser Interferometer Space Antenna: Unveiling the Millihertz Gravitational Wave Sky. https://doi.org/10.48550/arXiv.1907.06482 (2019).

  2. Luo, Z., Wang, Y., Wu, Y., Hu, W. & Jin, G. The Taiji program: a concise overview. Prog. Theor. Exp. Phys. 2021, 05A108 (2021).

    Article  Google Scholar 

  3. Kawamura, S. et al. Current status of space gravitational wave antenna DECIGO and B-DECIGO. Prog. Theor. Exp. Phys. 2021, 05A105 (2021).

    Article  Google Scholar 

  4. Luo, J. et al. TianQin: a space-borne gravitational wave detector. Class. Quant. Grav. 33, 035010 (2016).

    Article  ADS  Google Scholar 

  5. Aasi, J. et al. Advanced LIGO. Class. Quant. Grav. 32, 074001 (2015).

    Article  ADS  Google Scholar 

  6. Acernese, F. et al. Advanced Virgo: a second-generation interferometric gravitational wave detector. Class. Quant. Grav. 32, 024001 (2015).

    Article  ADS  Google Scholar 

  7. Akutsu, T. et al. Overview of KAGRA: detector design and construction history. Prog. Theor. Exp. Phys. 2021, 05A101 (2021).

    Article  Google Scholar 

  8. Macedo, C. F. B., Pani, P., Cardoso, V. & Crispino, L. C. B. Into the lair: gravitational-wave signatures of dark matter. Astrophys. J. 774, 48 (2013).

    Article  ADS  Google Scholar 

  9. Barausse, E., Cardoso, V. & Pani, P. Can environmental effects spoil precision gravitational-wave astrophysics? Phys. Rev. D 89, 104059 (2014).

    Article  ADS  Google Scholar 

  10. Barausse, E., Cardoso, V. & Pani, P. Environmental effects for gravitational-wave astrophysics. J. Phys. Conf. Ser. 610, 012044 (2015).

    Article  Google Scholar 

  11. Berry, C. et al. The unique potential of extreme mass-ratio inspirals for gravitational-wave astronomy. Bull. Am. Astron. Soc. 51, 42 (2019).

    Google Scholar 

  12. Tanaka, H., Takeuchi, T. & Ward, W. R. Three-dimensional interaction between a planet and an isothermal gaseous disk. I. Corotation and Lindblad torques and planet migration. Astrophys. J. 565, 1257–1274 (2002).

    Article  ADS  Google Scholar 

  13. Derdzinski, A. M., D’Orazio, D., Duffell, P., Haiman, Z. & MacFadyen, A. Probing gas disc physics with LISA: simulations of an intermediate mass ratio inspiral in an accretion disc. Mon. Not. Roy. Astron. Soc. 486, 2754–2765 (2019). [Erratum: Mon. Not. R. Astron. Soc. 489, 4860–4861 (2019)].

    Article  ADS  Google Scholar 

  14. Duffell, P. C. et al. Circumbinary disks: accretion and torque as a function of mass ratio and disk viscosity. Astrophys. J. 901, 25 (2020).

    Article  ADS  Google Scholar 

  15. Derdzinski, A., D’Orazio, D., Duffell, P., Haiman, Z. & MacFadyen, A. Evolution of gas disc–embedded intermediate mass ratio inspirals in the LISA band. Mon. Not. R. Astron. Soc. 501, 3540–3557 (2020).

    Article  ADS  Google Scholar 

  16. Speri, L. et al. Measuring accretion-disk effects with gravitational waves from extreme mass ratio inspirals. Preprint at https://arxiv.org/abs/2207.10086 (2022).

  17. Yunes, N., Kocsis, B., Loeb, A. & Haiman, Z. Imprint of accretion disk-induced migration on gravitational waves from extreme mass ratio inspirals. Phys. Rev. Lett. 107, 171103 (2011).

    Article  ADS  Google Scholar 

  18. Kocsis, B., Yunes, N. & Loeb, A. Observable signatures of extreme mass-ratio inspiral black hole binaries embedded in thin accretion disks. Phys. Rev. D 84, 024032 (2011).

    Article  ADS  Google Scholar 

  19. Gondolo, P. & Silk, J. Dark matter annihilation at the galactic center. Phys. Rev. Lett. 83, 1719–1722 (1999).

    Article  ADS  Google Scholar 

  20. Bertone, G., Zentner, A. R. & Silk, J. A new signature of dark matter annihilations: gamma-rays from intermediate-mass black holes. Phys. Rev. D 72, 103517 (2005).

    Article  ADS  Google Scholar 

  21. 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 

  22. 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 

  23. Yue, X.-J., Han, W.-B. & Chen, X. Dark matter: an efficient catalyst for intermediate-mass-ratio-inspiral events. Astrophys. J. 874, 34 (2019).

    Article  ADS  Google Scholar 

  24. Kavanagh, B. J., Nichols, D. A., Bertone, G. & Gaggero, D. Detecting dark matter around black holes with gravitational waves: effects of dark-matter dynamics on the gravitational waveform. Phys. Rev. D 102, 083006 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  25. Coogan, A., Bertone, G., Gaggero, D., Kavanagh, B. J. & Nichols, D. A. Measuring the dark matter environments of black hole binaries with gravitational waves. Phys. Rev. D 105, 043009 (2022).

    Article  ADS  Google Scholar 

  26. Dai, N., Gong, Y., Jiang, T. & Liang, D. Intermediate mass-ratio inspirals with dark matter minispikes. Phys. Rev. D 106, 064003 (2022).

    Article  ADS  MathSciNet  Google Scholar 

  27. Hannuksela, O. A., Ng, K. C. Y. & Li, T. G. F. Extreme dark matter tests with extreme mass ratio inspirals. Phys. Rev. D 102, 103022 (2020).

    Article  ADS  Google Scholar 

  28. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. Brito, R., Cardoso, V. & Pani, P. Superradiance. Lect. Notes Phys. 906, 1–237 (2015).

    Article  Google Scholar 

  32. Baumann, D., Chia, H. S., Stout, J. & ter Haar, L. The spectra of gravitational atoms. J. Cosmol. Astropart. Phys. 12, 006 (2019).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Baumann, D., Chia, H. S., Porto, R. A. & Stout, J. Gravitational collider physics. Phys. Rev. D 101, 083019 (2020).

    Article  ADS  Google Scholar 

  34. Baumann, D., Bertone, G., Stout, J. & Tomaselli, G. M. Ionization of gravitational atoms. Phys. Rev. D 105, 115036 (2022).

    Article  ADS  MathSciNet  Google Scholar 

  35. Baumann, D., Bertone, G., Stout, J. & Tomaselli, G. M. Sharp signals of boson clouds in black hole binary inspirals. Phys. Rev. Lett. 128, 221102 (2022).

    Article  ADS  MathSciNet  Google Scholar 

  36. Yoshino, H. & Kodama, H. Gravitational radiation from an axion cloud around a black hole: superradiant phase. Prog. Theor. Exp. Phys. 2014, 043E02 (2014).

    Article  MATH  Google Scholar 

  37. Shakura, N. I. & Sunyaev, R. A. Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337–355 (1973).

    ADS  Google Scholar 

  38. McKernan, B., Ford, K. E. S., Lyra, W. & Perets, H. B. Intermediate mass black holes in AGN discs - I. production and growth. Mon. Not. R. Astron. Soc. 425, 460–469 (2012).

    Article  ADS  Google Scholar 

  39. Becker, N., Sagunski, L., Prinz, L. & Rastgoo, S. Circularization versus eccentrification in intermediate mass ratio inspirals inside dark matter spikes. Phys. Rev. D 105, 063029 (2022).

    Article  ADS  MathSciNet  Google Scholar 

  40. Binney, J. & Tremaine, S. Galactic Dynamics, 2nd edn (Princeton University Press, 2008).

  41. Goldreich, P. & Tremaine, S. The excitation of density waves at the Lindblad and corotation resonances by an external potential. Astrophys. J. 233, 857–871 (1979).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  43. Greene, J. E., Strader, J. & Ho, L. C. Intermediate-mass black holes. Annu. Rev. Astron. Astrophys. 58, 257–312 (2020).

    Article  ADS  Google Scholar 

  44. Hannuksela, O. A., Wong, K. W. K., Brito, R., Berti, E. & Li, T. G. F. Probing the existence of ultralight bosons with a single gravitational-wave measurement. Nat. Astron. 3, 447–451 (2019).

    Article  ADS  Google Scholar 

  45. Jiang, J. et al. High density reflection spectroscopy – II. The density of the inner black hole accretion disc in AGN. Mon. Not. R. Astron. Soc. 489, 3436–3455 (2019).

    Article  ADS  Google Scholar 

  46. Skilling, J. Nested Sampling. In Bayesian Inference and Maximum Entropy Methods in Science and Engineering (eds. Fischer, R., Preuss, R. & von Toussaint, U.) 395–405 (American Institute of Physics, 2004).

  47. Skilling, J. Nested sampling for general Bayesian computation. Bayesian Anal. 1, 833–859 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  48. 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 

  49. Speagle, J. S. DYNESTY: a dynamic nested sampling package for estimating Bayesian posteriors and evidences. Mon. Not. R. Astron. Soc. 493, 3132–3158 (2020).

    Article  ADS  Google Scholar 

  50. Jeffreys, H. The Theory of Probability (Oxford Univ. Press, 1998).

  51. Kass, R. E. & Raftery, A. E. Bayes factors. J. Am. Stat. Assoc. 90, 773–795 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  52. Cardoso, V., Destounis, K., Duque, F., Macedo, R. P. & Maselli, A. Gravitational waves from extreme-mass-ratio systems in astrophysical environments. Phys. Rev. Lett. 129, 241103 (2022).

    Article  ADS  MathSciNet  Google Scholar 

  53. Speeney, N., Antonelli, A., Baibhav, V. & Berti, E. Impact of relativistic corrections on the detectability of dark-matter spikes with gravitational waves. Phys. Rev. D 106, 044027 (2022).

    Article  ADS  MathSciNet  Google Scholar 

  54. Speri, L. & Gair, J. R. Assessing the impact of transient orbital resonances. Phys. Rev. D 103, 124032 (2021).

    Article  ADS  MathSciNet  Google Scholar 

  55. Yue, X.-J. & Cao, Z. Dark matter minispike: a significant enhancement of eccentricity for intermediate-mass-ratio inspirals. Phys. Rev. D 100, 043013 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  56. Fairhurst, S., Green, R., Hannam, M. & Hoy, C. When will we observe binary black holes precessing? Phys. Rev. D 102, 041302 (2020).

    Article  ADS  Google Scholar 

  57. Zhang, X.-H., Mohanty, S. D., Zou, X.-B. & Liu, Y.-X. Resolving galactic binaries in LISA data using particle swarm optimization and cross-validation. Phys. Rev. D 104, 024023 (2021).

    Article  ADS  Google Scholar 

  58. Strub, S. H., Ferraioli, L., Schmelzbach, C., Stähler, S. C. & Giardini, D. Bayesian parameter estimation of galactic binaries in LISA data with Gaussian process regression. Phys. Rev. D 106, 062003 (2022).

    Article  ADS  Google Scholar 

  59. Baghi, Q. et al. Gravitational-wave parameter estimation with gaps in LISA: a Bayesian data augmentation method. Phys. Rev. D 100, 022003 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  60. Dey, K. et al. Effect of data gaps on the detectability and parameter estimation of massive black hole binaries with lisa. Phys. Rev. D 104, 044035 (2021).

    Article  ADS  Google Scholar 

  61. Kavanagh, B. J. HaloFeedback code version 0.9. GitHub https://github.com/bradkav/HaloFeedback (2020).

Download references

Acknowledgements

We thank P. Pani and S. Witte for helpful discussions. P.S.C. acknowledges support from the Institute of Physics at the University of Amsterdam. A.C. received funding from the Schmidt Futures Foundation. D.G. was supported by Spanish MINECO through the Ramon y Cajal programme RYC2020-029184-I between September 2022 and November 2022 and is currently supported from the project ‘Theoretical Astroparticle Physics (TAsP)’ funded by the National Institute for Nuclear Physics (INFN). B.J.K. thanks the Spanish Agencia Estatal de Investigación (AEI, Ministerio de Ciencia, Innovación y Universidades) for the support to the Unidad de Excelencia María de Maeztu Instituto de Física de Cantabria (ref. MDM-2017-0765). T.F.M.S. is supported by VILLUM FONDEN (grant no. 37766), the Danish Research Foundation and the European Union’s H2020 ERC Advanced Grant ‘Black holes: gravitational engines of discovery’ (grant agreement no. Gravitas-101052587).

Author information

Authors and Affiliations

Authors

Contributions

P.S.C. conducted the main analysis in this manuscript and produced all of the figures. G.B. initiated the project idea and coordinated the members of the group. A.C. provided the dark dress code for the analysis that was extended for use in this broader context. D.G. consulted on issues to do with DF and gas torques. T.K. wrote the surrogate model and did the analysis for the dark dress that appears in the Supplementary Information. B.J.K. provided code for calculating feedback processes. T.F.M.S. and G.M.T. provided code for calculating the energy losses for the gravitational atom. All authors contributed to writing and editing the manuscript.

Corresponding author

Correspondence to Philippa S. Cole.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Astronomy thanks the anonymous reviewers for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–5, discussion and related references.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cole, P.S., Bertone, G., Coogan, A. et al. Distinguishing environmental effects on binary black hole gravitational waveforms. Nat Astron 7, 943–950 (2023). https://doi.org/10.1038/s41550-023-01990-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41550-023-01990-2

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing