Distinguishing environmental effects on binary black hole gravitational waveforms

Nature Astronomy (2023)Cite this article

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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.

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

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 [email protected].

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

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

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

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

Article ADS Google Scholar

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

Article ADS Google Scholar

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

Article ADS Google Scholar

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

Article Google Scholar

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

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

Article ADS Google Scholar

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

Article Google Scholar

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

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

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

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

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

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).

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

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

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

Article ADS Google Scholar

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

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

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

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

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

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

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

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

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

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

Article ADS Google Scholar

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

Article ADS Google Scholar

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

Article Google Scholar

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

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

Article ADS Google Scholar

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

Article ADS MathSciNet Google Scholar

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

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

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

ADS Google Scholar

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

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

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

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

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

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

Article ADS Google Scholar

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

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

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).

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

Article MathSciNet MATH Google Scholar

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

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

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

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

Article MathSciNet MATH Google Scholar

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

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

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

Article ADS MathSciNet Google Scholar

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

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

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

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

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

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

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

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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).

Gravitation Astroparticle Physics Amsterdam (GRAPPA), Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical Physics, University of Amsterdam, Amsterdam, the Netherlands

Philippa S. Cole, Gianfranco Bertone, Theophanes Karydas, Thomas F. M. Spieksma & Giovanni Maria Tomaselli

Ciela – Computation and Astrophysical Data Analysis Institute, Montreal, Quebec, Canada

Adam Coogan

Département de Physique, Université de Montréal, Montreal, Quebec, Canada

Adam Coogan

Mila – Quebec AI Institute, Montreal, Quebec, Canada

Adam Coogan

INFN Sezione di Pisa, Polo Fibonacci, Pisa, Italy

Daniele Gaggero

Instituto de Física Corpuscular, Universidad de Valencia and CSIC, Paterna, Spain

Daniele Gaggero

Instituto de Física de Cantabria, UC-CSIC, Santander, Spain

Bradley J. Kavanagh

Niels Bohr International Academy, Niels Bohr Institute, Copenhagen, Denmark

Thomas F. M. Spieksma

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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.

Correspondence to Philippa S. Cole.

The authors declare no competing interests.

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

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

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Received: 10 November 2022

Accepted: 03 May 2023

Published: 05 June 2023

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

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Distinguishing environmental effects on binary black hole gravitational waveforms