Probing the ringdown perturbation in binary black hole coalescences with an improved quasinormal mode extraction algorithm
Creators
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1.
Cornell University
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2.
California Institute of Technology
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3.
Columbia University
- 4. Flatiron Institute
Abstract
Using gravitational waves to probe the geometry of the ringing remnant black hole formed in a binary black hole coalescence is a well-established way to test Einstein’s theory of general relativity. However, doing so requires knowledge of when the predictions of black hole perturbation theory, i.e., quasinormal modes (QNMs), are a valid description of the emitted gravitational wave as well as what the amplitudes of these excitations are. In this work, we develop an algorithm to systematically extract QNMs from the ringdown of black hole merger simulations. Our algorithm improves upon previous ones in three ways: it fits over the two-sphere, enabling a complete model of the strain; it performs a reverse search in time for QNMs using a more robust nonlinear least squares routine called varpro; and it checks the variance of QNM amplitudes, which we refer to as “stability,” over an interval matching the natural timescale of each QNM. Using this algorithm, we not only demonstrate the stability of a multitude of QNMs and their overtones across the parameter space of quasicircular, nonprecessing binary black holes, but we also identify new quadratic QNMs that may be detectable in the near future using ground-based interferometers. Furthermore, we provide evidence which suggests that the source of remnant black hole perturbations is roughly independent of the overtone index in a given angular harmonic across binary parameter space, at least for overtones with 𝑛 ≲2. This finding may hint at the spatiotemporal structure of ringdown perturbations in black hole coalescences, as well as the regime of validity of perturbation theory in the ringdown of these events
Copyright and License
© 2025 American Physical Society.
Acknowledgement
The authors thank Will Farr and Max Isi for useful and insightful discussions, Sizheng Ma and Neev Khera for clarifications regarding quadratic QNM excitations and for sharing the excitation factor data used in Fig. 9, and Leo Stein for suggesting the non-Gaussian noise test. K. M. is supported by NASA through the NASA Hubble Fellowship Grant No. HST-HF2-51562.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA Contract No. NAS5-26555. H. S. is supported by Yuri Levin’s Simons Investigator Award No. 827103. This material is based upon work supported by the National Science Foundation under Grants No. PHY-2309211, No. PHY-2309231, No. OAC-2209656 at Caltech, and No. PHY-2407742, No. PHY-2207342, and No. OAC-2209655 at Cornell. This work was supported by the Sherman Fairchild Foundation at Caltech and Cornell.
Data Availability
The data that support the findings of this article are openly available [98], embargo periods may apply.
Additional Information
K. M. developed the published version of the algorithm, wrote the majority of the manuscript, and created all of the figures, besides Fig. 1. I. P. developed an earlier version of the algorithm, conducted initial analyses on the stability of QNMs with respect to white noise, performed tests to assess the algorithm’s capabilities and accuracy, and also created Fig. 1. H. S. principally contributed conceptual design, analysis, and writing to Sec. III D and its associated figures.
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2503.09678 (arXiv)
- Is supplemented by
- Dataset: https://www.black-holes.org/waveforms/ (URL)
Funding
- National Aeronautics and Space Administration
- HST-HF2-51562.001-A
- Space Telescope Science Institute
- National Aeronautics and Space Administration
- NAS5-26555
- Yuri Levin's Simons Investigator
- 827103
- National Science Foundation
- PHY-2309211
- National Science Foundation
- PHY-2309231
- National Science Foundation
- OAC-2209656
- National Science Foundation
- PHY-2407742
- National Science Foundation
- PHY-2207342
- National Science Foundation
- OAC-2209655
- Sherman Fairchild Foundation
Dates
- Accepted
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2025-08-11