Published November 12, 2025 | Version Published
Journal Article Open

Efficient waveforms for asymmetric-mass eccentric equatorial inspirals into rapidly spinning black holes

  • 1. ROR icon University of Birmingham
  • 2. ROR icon University of Glasgow
  • 3. ROR icon European Space Agency
  • 4. ROR icon University of Southampton
  • 5. ROR icon Laboratoire des 2 Infinis Toulouse
  • 6. ROR icon Marshall Space Flight Center
  • 7. ROR icon Max Planck Institute for Gravitational Physics
  • 8. ROR icon National University of Singapore
  • 9. ROR icon Perimeter Institute
  • 10. ROR icon University of Guelph
  • 11. ROR icon California Institute of Technology
  • 12. ROR icon Massachusetts Institute of Technology
  • 13. ROR icon University College Dublin

Abstract

Observations of gravitational-wave signals emitted by compact binary inspirals provide unique insights into their properties, but their analysis requires accurate and efficient waveform models. Intermediate- and extreme-mass-ratio inspirals (I/EMRIs), with mass ratios 𝑞 ≳102, are promising sources for future detectors such as the Laser Interferometer Space Antenna (LISA). Modeling waveforms for these asymmetric-mass binaries is challenging, entailing the tracking of many harmonic modes over thousands to millions of cycles. The FastEMRIWaveforms (few) modeling framework addresses this need, leveraging precomputation of mode data and interpolation to rapidly compute adiabatic waveforms for eccentric inspirals into zero-spin black holes. In this work, we extend few to model eccentric equatorial inspirals into black holes with spin magnitudes |𝑎| ≤0.999. Our model supports eccentricities 𝑒 ≤0.9 and semilatus recta 𝑝 ≤200, enabling the generation of long-duration IMRI waveforms, and produces waveforms in ∼100  ms with hardware acceleration. Characterizing systematic errors, we estimate that our model attains mismatches of ∼10 (for LISA sensitivity) with respect to error-free adiabatic waveforms over the majority of the parameter space. We find that kludge models can introduce errors in signal-to-noise ratios (SNRs) as great as +^(+60%)_(−40%) and induce marginal biases of up to ∼1⁢𝜎 in parameter estimation. We show that LISA’s horizon redshift for I/EMRI signals varies significantly with 𝑎, reaching a redshift of 3 (15) for EMRIs (IMRIs) with only minor ( ∼10%) dependence on 𝑒 for an SNR threshold of 20. For signals with SNR ∼50, spin and eccentricity at plunge are measured with uncertainties of 𝛿⁢𝑎 ∼10 and 𝛿⁢𝑒f ∼10. This work advances the state of the art in waveform generation for asymmetric-mass binaries, providing open-source tools for the investigation of I/EMRI astrophysics and data analysis.

Copyright and License

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Acknowledgement

We are also indebted to BHPC (in particular Ryuichi Fujita, Hiroyuki Nakano, Norichika Sago, and Masaru Shibata) for providing us with independent analytical and numerical data for the forcing functions and mode amplitudes used in Sec. IV and Appendix E 2 for the validation, upon request. C. E. A. C.-B. acknowledges support from UKSA Grant No. UKRI971. L. S. would like to acknowledge the support of the European Space Agency through ESA’s postdoctoral Research Fellowship programme. Z. N. acknowledges support from the ERC Consolidator/UKRI Frontier Research Grant GWModels (selected by the ERC and funded by UKRI [Grant No. EP/Y008251/1]). O. B. acknowledges financial support from the Grant No. UKRI972 awarded via the UK Space Agency. O. S. K. acknowledges the support of the NUS Research Scholarship. J. M. and A. J. K. C. acknowledge support from the NUS Faculty of Science, under the research Grant No. 22-5478-A0001. H. K. acknowledges the support from the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Colleges and Universities. J. E. T. and A. J. K. C. acknowledge support from the NASA LISA Preparatory Science Grant No. 20-LPS20-0005. S. I. and A. J. K. C. acknowledge support from the Ministry of Education, Singapore, under the Academic Research Fund Tier 1 A-800149200-00 (FY2023). S. A. H. acknowledges support from NSF Grants No. PHY-2110384 and No. PHY-2409644. N. W. acknowledges support from a Royal Society—Research Ireland University Research Fellowship. This publication has emanated from research conducted with the financial support of Research Ireland under Grants No. 16/RS-URF/3428, No. 17/RS-URF-RG/3490 and No. 22/RS-URF-R/3825. This research was also done using services provided by the OSG Consortium [234,313–315], which is supported by the National Science Foundation Awards No. 2030508 and No. 2323298.

Contributions

C. E. A. C.-B.: Conceptualization, data curation, formal analysis, investigation, methodology, project administration, resources, software, supervision, validation, visualization, writing—original draft, writing—review and editing. L. S.: Conceptualization, formal analysis, investigation, methodology, supervision, validation, visualization, writing—original draft, writing—review and editing. Z. N.: Conceptualization, data curation, formal analysis, investigation, methodology, resources, software, validation, visualization, writing—original draft, writing—review and editing. O. B.: Formal analysis, investigation, methodology, validation, visualization, writing—original draft, writing—review and editing. M. L. K.: Conceptualization, investigation, methodology, resources, software, supervision, writing—review and editing. A. S.: Formal analysis, investigation, methodology, visualization, writing—original draft. S. K.: Formal analysis, investigation, validation, visualization, software, writing—original draft, writing—review and editing. P. L.: Investigation, validation, visualization, software, writing—original draft, writing—review and editing. J. M.: Formal analysis, investigation, validation, visualization, writing—original draft, writing—review and editing. H. K.: Investigation, validation, visualization, writing—original draft, writing—review and editing. J. E. T.: Validation, visualization, writing—reviewing and editing. S. I.: Data curation, formal analysis, investigation, supervision, validation, writing—original draft, writing—review and editing. S. A. H.: Conceptualization, data curation, formal analysis, investigation, methodology, validation, writing—review and editing. N. W.: Conceptualization, writing—original draft, writing—review and editing. A. J. K. C.: Conceptualization, supervision, writing—review and editing. M. P.: Software.

Data Availability

The data that support the findings of this article are openly available [316,317], embargo periods may apply.

Files

scbp-75pf.pdf

Files (13.7 MB)

Name Size
md5:465907cf83dc5e6249a11feb8a9163a3
13.7 MB Preview Download

Additional details

Additional titles

Alternative title
The Fast and the Frame-Dragging: Efficient waveforms for asymmetric-mass eccentric equatorial inspirals into rapidly-spinning black holes

Related works

Is new version of
Discussion Paper: arXiv:2506.09470 (arXiv)
Is supplemented by
Dataset: 10.5281/zenodo.15631641 (DOI)
Dataset: 10.5281/zenodo.15624459 (DOI)

Funding

United Kingdom Space Agency
UKRI971
European Space Agency
European Research Council
UK Research and Innovation
EP/Y008251/1
United Kingdom Space Agency
UKRI972
National University of Singapore
22-5478-A0001
Perimeter Institute
Government of Canada
Ministry of Colleges and Universities
National Aeronautics and Space Administration
20-LPS20-0005
Ministry of Education
A-800149200-00
National Science Foundation
PHY-2110384
National Science Foundation
PHY-2409644
Royal Society
Taighde Éireann - Research Ireland
16/RS-URF/3428
Taighde Éireann - Research Ireland
17/RS-URF-RG/3490
Taighde Éireann - Research Ireland
22/RS-URF-R/3825
National Science Foundation
2030508
National Science Foundation
2323298

Dates

Submitted
2025-06-12
Accepted
2025-09-26

Caltech Custom Metadata