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High precision ringdown modeling: Multimode fits and BMS frames

Magaña Zertuche, Lorena and Mitman, Keefe and Khera, Neev and Stein, Leo C. and Boyle, Michael and Deppe, Nils and Hébert, François and Iozzo, Dante A. B. and Kidder, Lawrence E. and Moxon, Jordan and Pfeiffer, Harald P. and Scheel, Mark A. and Teukolsky, Saul A. and Throwe, William and Vu, Nils (2022) High precision ringdown modeling: Multimode fits and BMS frames. Physical Review D, 105 (10). Art. No. 104015. ISSN 2470-0010. doi:10.1103/physrevd.105.104015.

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Quasinormal mode (QNM) modeling is an invaluable tool for characterizing remnant black holes, studying strong gravity, and testing general relativity. Only recently have QNM studies begun to focus on multimode fitting to numerical relativity strain waveforms. As gravitational wave observatories become even more sensitive they will be able to resolve higher-order modes. Consequently, multimode QNM fits will be critically important, and in turn require a more thorough treatment of the asymptotic frame at I⁺. The first main result of this work is a method for systematically fitting a QNM model containing many modes to a numerical waveform produced using Cauchy-characteristic extraction (CCE), a waveform extraction technique which is known to resolve memory effects. We choose the modes to model based on their power contribution to the residual between numerical and model waveforms. We show that the all-mode strain mismatch improves by a factor of ∼10⁵ when using multimode fitting as opposed to only fitting the (2, ±2, n) modes. Our most significant result addresses a critical point that has been overlooked in the QNM literature: the importance of matching the Bondi-van der Burg-Metzner-Sachs (BMS) frame of the numerical waveform to that of the QNM model. We show that by mapping the numerical waveforms—which exhibit the memory effect—to a BMS frame known as the super rest frame, there is an improvement of ∼10⁵ in the all-mode strain mismatch compared to using a strain waveform whose BMS frame is not fixed. Furthermore, we find that by mapping CCE waveforms to the super rest frame, we can obtain all-mode mismatches that are, on average, a factor of ∼4 better than using the publicly available extrapolated waveforms. We illustrate the effectiveness of these modeling enhancements by applying them to families of waveforms produced by numerical relativity and comparing our results to previous QNM studies.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Magaña Zertuche, Lorena0000-0003-1888-9904
Mitman, Keefe0000-0003-0276-3856
Khera, Neev0000-0003-3515-2859
Stein, Leo C.0000-0001-7559-9597
Boyle, Michael0000-0002-5075-5116
Deppe, Nils0000-0003-4557-4115
Hébert, François0000-0001-9009-6955
Iozzo, Dante A. B.0000-0002-7244-1900
Kidder, Lawrence E.0000-0001-5392-7342
Moxon, Jordan0000-0001-9891-8677
Pfeiffer, Harald P.0000-0001-9288-519X
Scheel, Mark A.0000-0001-6656-9134
Teukolsky, Saul A.0000-0001-9765-4526
Throwe, William0000-0001-5059-4378
Vu, Nils0000-0002-5767-3949
Additional Information:© 2022 American Physical Society. (Received 11 November 2021; accepted 11 March 2022; published 11 May 2022) We thank Max Isi for fruitful discussions, Matt Giesler for sharing his work, which helped us clarify the differences between our results and those of [18,19], and Arnab Dhani for detailed discussions on the methods used in his work [25]. We also thank Greg Cook, Arnab Dhani, Matt Giesler, Max Isi, and Xiang Li for reviewing an earlier version of this manuscript. Calculations were performed with the Wheeler cluster at the California Institute of Technology (Caltech), which is supported by the Sherman Fairchild Foundation and by Caltech. The work of L. M. Z. was partially supported by the MSSGC Graduate Research Fellowship, awarded through the NASA Cooperative Agreement No. 80NSSC20M0101. Part of this research was performed while L. M. Z. was visiting the Institute for Pure and Applied Mathematics (IPAM), which is supported by the National Science Foundation (Grant No. DMS-1925919) The work of K. M was partially supported by NSF Grants No. PHY-2011961, No. PHY-2011968, and No. OAC-1931266. The work of N. K. was partially supported by NSF Grant No. PHY-1806356, Grant No. UN2017-92945 from the Urania Stott Fund of the Pittsburgh Foundation, the Eberly research funds of Penn State at Penn State and the Mebus fellowship. The work of L. C. S. was partially supported by NSF CAREER Grant No. PHY–2047382. All plots were made using the python package matplotlib [80].
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Mississippi Space Grant Consortium80NSSC20M0101
Pittsburgh FoundationUN2017-92945
Pennsylvania State UniversityUNSPECIFIED
Issue or Number:10
Record Number:CaltechAUTHORS:20220601-257716000
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:114989
Deposited By: George Porter
Deposited On:01 Jun 2022 22:33
Last Modified:01 Jun 2022 22:33

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