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The use of hypermodels to understand binary neutron star collisions

Abstract

Gravitational waves from the collision of binary neutron stars provide a unique opportunity to study the behaviour of supranuclear matter, the fundamental properties of gravity and the cosmic history of our Universe. However, given the complexity of Einstein's field equations, theoretical models that enable source–property inference suffer from systematic uncertainties due to simplifying assumptions. We develop a hypermodel approach to compare and measure the uncertainty of gravitational-wave approximants. Using state-of-the-art models, we apply this new technique to the binary neutron star observations GW170817 and GW190425 and to the sub-threshold candidate GW200311_103121. Our analysis reveals subtle systematic differences (with Bayesian odds of ~2) between waveform models. A frequency-dependence study suggests that this may be due to the treatment of the tidal sector. This new technique provides a proving ground for model development and a means to identify waveform systematics in future observing runs where detector improvements will increase the number and clarity of binary neutron star collisions we observe.

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Fig. 1: The evolution of the posterior probability of each waveform for GW170817 as the maximum frequency of the analysis data is varied.

Data availability

The results for the primary analyses of GW170817, GW190425 and GW200311_103121 are available in the data release50.

Code availability

The program for the primary analyses of GW170817, GW190425 and GW200311_103121 is described and available in the data release50.

References

  1. Abbott, B. P. et al. GW170817: observation of gravitational waves from a binary neutron star inspiral. Phys. Rev. Lett. 119, 161101 (2017).

    ADS  Article  Google Scholar 

  2. Abbott, B. P. et al. A gravitational-wave standard siren measurement of the Hubble constant. Nature 551, 85–88 (2017).

    ADS  Article  Google Scholar 

  3. Hotokezaka, K. et al. A Hubble constant measurement from superluminal motion of the jet in GW170817. Nat. Astron. 3, 940–944 (2019).

    ADS  Article  Google Scholar 

  4. Dietrich, T. et al. Multimessenger constraints on the neutron-star equation of state and the Hubble constant. Science 370, 1450–1453 (2020).

    ADS  MathSciNet  MATH  Article  Google Scholar 

  5. Cowperthwaite, P. S. et al. The electromagnetic counterpart of the binary neutron star merger LIGO/Virgo GW170817. II. UV, optical, and near-infrared light curves and comparison to kilonova models. Astrophys. J. 848, L17 (2017).

    ADS  Article  Google Scholar 

  6. Smartt, S. J. et al. A kilonova as the electromagnetic counterpart to a gravitational-wave source. Nature 551, 75–79 (2017).

    ADS  Article  Google Scholar 

  7. Kasliwal, M. M. et al. Illuminating gravitational waves: a concordant picture of photons from a neutron star merger. Science 358, 1559–1565 (2017).

    ADS  Article  Google Scholar 

  8. Kasen, D., Metzger, B., Barnes, J., Quataert, E. & Ramirez-Ruiz, E. Origin of the heavy elements in binary neutron-star mergers from a gravitational wave event. Nature 551, 80–84 (2017).

    ADS  Article  Google Scholar 

  9. Ezquiaga, J. M. & Zumalacárregui, M. Dark energy after GW170817: dead ends and the road ahead. Phys. Rev. Lett. 119, 251304 (2017).

    ADS  Article  Google Scholar 

  10. Baker, T. et al. Strong constraints on cosmological gravity from GW170817 and GRB 170817A. Phys. Rev. Lett. 119, 251301 (2017).

    ADS  Article  Google Scholar 

  11. Creminelli, P. & Vernizzi, F. Dark energy after GW170817 and GRB170817A. Phys. Rev. Lett. 119, 251302 (2017).

    ADS  Article  Google Scholar 

  12. Abbott, B. P. et al. Multi-messenger observations of a binary neutron star merger. Astrophys. J. 848, L12 (2017).

    ADS  Article  Google Scholar 

  13. Abbott, B. P. et al. GW190425: observation of a compact binary coalescence with total mass ~ 3.4M. Astrophys. J. Lett. 892, L3 (2020).

    ADS  Article  Google Scholar 

  14. Abbott, R. et al. GWTC-3: compact binary coalescences observed by LIGO and Virgo during the second part of the third observing run. Preprint at https://arxiv.org/abs/2111.03606 (2021).

  15. Brügmann, B. Fundamentals of numerical relativity for gravitational wave sources. Science 361, 366–371 (2018).

    ADS  Article  Google Scholar 

  16. Dietrich, T. et al. CoRe database of binary neutron star merger waveforms. Class. Quantum Gravity 35, 24LT01 (2018).

    Article  Google Scholar 

  17. Kiuchi, K., Kawaguchi, K., Kyutoku, K., Sekiguchi, Y. & Shibata, M. Sub-radian-accuracy gravitational waves from coalescing binary neutron stars in numerical relativity. II. Systematic study on the equation of state, binary mass, and mass ratio. Phys. Rev. D 101, 084006 (2020).

    ADS  Article  Google Scholar 

  18. Aasi, J. et al. Advanced LIGO. Class. Quantum Gravity 32, 074001 (2015).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  20. Blanchet, L. Gravitational radiation from post-Newtonian sources and inspiralling compact binaries. Living Rev. Relativ. 17, 2 (2014).

    ADS  MATH  Article  Google Scholar 

  21. Buonanno, A. & Damour, T. Effective one-body approach to general relativistic two-body dynamics. Phys. Rev. D 59, 084006 (1999).

    ADS  MathSciNet  Article  Google Scholar 

  22. Buonanno, A. & Damour, T. Transition from inspiral to plunge in binary black hole coalescences. Phys. Rev. D 62, 064015 (2000).

    ADS  Article  Google Scholar 

  23. Dietrich, T., Bernuzzi, S. & Tichy, W. Closed-form tidal approximants for binary neutron star gravitational waveforms constructed from high-resolution numerical relativity simulations. Phys. Rev. D 96, 121501 (2017).

    ADS  Article  Google Scholar 

  24. Bernuzzi, S., Nagar, A., Dietrich, T. & Damour, T. Modeling the dynamics of tidally interacting binary neutron stars up to the merger. Phys. Rev. Lett. 114, 161103 (2015).

    ADS  Article  Google Scholar 

  25. Hotokezaka, K., Kyutoku, K., Okawa, H. & Shibata, M. Exploring tidal effects of coalescing binary neutron stars in numerical relativity. II. Long-term simulations. Phys. Rev. D 91, 064060 (2015).

    ADS  Article  Google Scholar 

  26. Hinderer, T. et al. Effects of neutron-star dynamic tides on gravitational waveforms within the effective-one-body approach. Phys. Rev. Lett. 116, 181101 (2016).

    ADS  Article  Google Scholar 

  27. Dietrich, T. et al. Improving the NRTidal model for binary neutron star systems. Phys. Rev. D 100, 044003 (2019).

    ADS  Article  Google Scholar 

  28. Kawaguchi, K. et al. Frequency-domain gravitational waveform models for inspiraling binary neutron stars. Phys. Rev. D 97, 044044 (2018).

    ADS  Article  Google Scholar 

  29. Dudi, R. et al. Relevance of tidal effects and post-merger dynamics for binary neutron star parameter estimation. Phys. Rev. D 98, 084061 (2018).

    ADS  Article  Google Scholar 

  30. Samajdar, A. & Dietrich, T. Waveform systematics for binary neutron star gravitational wave signals: effects of the point-particle baseline and tidal descriptions. Phys. Rev. D 98, 124030 (2018).

    ADS  Article  Google Scholar 

  31. Gamba, R., Breschi, M., Bernuzzi, S., Agathos, M. & Nagar, A. Waveform systematics in the gravitational-wave inference of tidal parameters and equation of state from binary neutron star signals. Phys. Rev. D 103, 124015 (2021).

    ADS  MathSciNet  Article  Google Scholar 

  32. Pratten, G., Schmidt, P. & Williams, N. Impact of dynamical tides on the reconstruction of the neutron star equation of state. Preprint at https://arxiv.org/abs/2109.07566 (2021).

  33. Kunert, N., Pang, P. T. H., Tews, I., Coughlin, M. W. & Dietrich, T. Quantifying modelling uncertainties when combining multiple gravitational-wave detections from binary neutron star sources. Phys. Rev. D 105, L061301 (2022).

    ADS  Article  Google Scholar 

  34. Ashton, G. & Khan, S. Multiwaveform inference of gravitational waves. Phys. Rev. D 101, 064037 (2020).

    ADS  MathSciNet  Article  Google Scholar 

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

    MathSciNet  MATH  Article  Google Scholar 

  36. Jan, A. Z., Yelikar, A. B., Lange, J. & O’Shaughnessy, R. Assessing and marginalizing over compact binary coalescence waveform systematics with RIFT. Phys. Rev. D 102, 124069 (2020).

    ADS  Article  Google Scholar 

  37. Husa, S. et al. Frequency-domain gravitational waves from nonprecessing black-hole binaries. I. New numerical waveforms and anatomy of the signal. Phys. Rev. D 93, 044006 (2016).

    ADS  Article  Google Scholar 

  38. Khan, S. et al. Frequency-domain gravitational waves from nonprecessing black-hole binaries. II. A phenomenological model for the advanced detector era. Phys. Rev. D 93, 044007 (2016).

    ADS  Article  Google Scholar 

  39. Bohé, A. et al. Improved effective-one-body model of spinning, nonprecessing binary black holes for the era of gravitational-wave astrophysics with advanced detectors. Phys. Rev. D 95, 044028 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  40. Lackey, B. D., Pürrer, M., Taracchini, A. & Marsat, S. Surrogate model for an aligned-spin effective one body waveform model of binary neutron star inspirals using Gaussian process regression. Phys. Rev. D 100, 024002 (2019).

    ADS  Article  Google Scholar 

  41. Nagar, A. et al. Time-domain effective-one-body gravitational waveforms for coalescing compact binaries with nonprecessing spins, tides and self-spin effects. Phys. Rev. D 98, 104052 (2018).

    ADS  Article  Google Scholar 

  42. Abbott, B. P. et al. Properties of the binary neutron star merger GW170817. Phys. Rev. X 9, 011001 (2019).

    Google Scholar 

  43. Littenberg, T. B. & Cornish, N. J. Bayesian inference for spectral estimation of gravitational wave detector noise. Phys. Rev. D 91, 084034 (2015).

    ADS  Article  Google Scholar 

  44. Payne, E., Talbot, C., Lasky, P. D., Thrane, E. & Kissel, J. S. Gravitational-wave astronomy with a physical calibration model. Phys. Rev. D 102, 122004 (2020).

    ADS  Article  Google Scholar 

  45. Abbott, B. P. et al. GW170817: observation of gravitational waves from a binary neutron star inspiral. Phys. Rev. Lett. 119, 161101 (2017).

    ADS  Article  Google Scholar 

  46. Veitch, J. et al. Parameter estimation for compact binaries with ground-based gravitational-wave observations using the LALInference software library. Phys. Rev. D 91, 042003 (2015).

    ADS  Article  Google Scholar 

  47. Flanagan, E. E. & Hinderer, T. Constraining neutron star tidal Love numbers with gravitational wave detectors. Phys. Rev. D 77, 021502 (2008).

    ADS  Article  Google Scholar 

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

    MathSciNet  MATH  Article  Google Scholar 

  49. Harry, I. & Hinderer, T. Observing and measuring the neutron-star equation-of-state in spinning binary neutron star systems. Class. Quantum Gravity 35, 145010 (2018).

    ADS  Article  Google Scholar 

  50. Ashton, G. Data release: understanding binary neutron star collisions with hypermodels. Zenodo https://doi.org/10.5281/zenodo.5707911 (2021).

  51. Dietrich, T., Ujevic, M., Tichy, W., Bernuzzi, S. & Brügmann, B. Gravitational waves and mass ejecta from binary neutron star mergers: effect of the mass-ratio. Phys. Rev. D 95, 024029 (2017).

    ADS  Article  Google Scholar 

  52. Abbott, B. P. et al. Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA. Living Rev. Relativ. 23, 3 (2020).

    ADS  Article  Google Scholar 

  53. Abbott, B. P. et al. 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).

    Google Scholar 

  54. Abbott, R. et al. 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).

    Google Scholar 

  55. Abbott, R. et al. GWTC-2.1: deep extended catalog of compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run. Preprint at https://arxiv.org/abs/2108.01045 (2021).

  56. Christensen, N. & Meyer, R. Markov chain Monte Carlo methods for Bayesian gravitational radiation data analysis. Phys. Rev. D 58, 082001 (1998).

    ADS  Article  Google Scholar 

  57. Veitch, J. & Vecchio, A. A Bayesian approach to the follow-up of candidate gravitational wave signals. Phys. Rev. D 78, 022001 (2008).

    ADS  Article  Google Scholar 

  58. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. & Teller, E. Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 1087–1092 (1953).

    ADS  MATH  Article  Google Scholar 

  59. Hastings, W. K. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97–109 (1970).

    MathSciNet  MATH  Article  Google Scholar 

  60. Pankow, C., Brady, P., Ochsner, E. & O’Shaughnessy, R. Novel scheme for rapid parallel parameter estimation of gravitational waves from compact binary coalescences. Phys. Rev. D 92, 023002 (2015).

    ADS  Article  Google Scholar 

  61. Lange, J., O’Shaughnessy, R. & Rizzo, M. Rapid and accurate parameter inference for coalescing, precessing compact binaries. Preprint at https://arxiv.org/abs/1805.10457 (2018).

  62. Ashton, G. & Talbot, C. Bilby-MCMC: an MCMC sampler for gravitational-wave inference (2021). Mon. Not. R. Astron. Soc. 507, 2037–2051 (2021).

    ADS  Article  Google Scholar 

  63. Estellés, H. et al. A detailed analysis of GW190521 with phenomenological waveform models. Astrophys. J. 924, 79 (2022).

    ADS  Article  Google Scholar 

  64. Mateu-Lucena, M. et al. Adding harmonics to the interpretation of the black hole mergers of GWTC-1. Preprint at https://arxiv.org/abs/2105.05960 (2021).

  65. Colleoni, M. et al. Towards the routine use of subdominant harmonics in gravitational-wave inference: reanalysis of GW190412 with generation X waveform models. Phys. Rev. D 103, 024029 (2021).

    ADS  MathSciNet  Article  Google Scholar 

  66. Hogg, D. W. & Foreman-Mackey, D. Data analysis recipes: using Markov chain Monte Carlo. Astrophys. J. Suppl. Ser. 236, 11 (2018).

    ADS  Article  Google Scholar 

  67. Green, P. J. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711–732 (1995).

    MathSciNet  MATH  Article  Google Scholar 

  68. Cornish, N. J. & Littenberg, T. B. Tests of Bayesian model selection techniques for gravitational wave astronomy. Phys. Rev. D 76, 083006 (2007).

    ADS  Article  Google Scholar 

  69. Cornish, N. J. & Littenberg, T. B. BayesWave: Bayesian inference for gravitational wave bursts and instrument glitches. Class. Quantum Gravity 32, 135012 (2015).

    ADS  Article  Google Scholar 

  70. Farr, W. M. et al. The mass distribution of stellar-mass black holes. Astrophys. J. 741, 103 (2011).

    ADS  Article  Google Scholar 

  71. Speagle, J. dynesty: A dynamic nested sampling package for estimating Bayesian posteriors and evidences. Mon. Not. R. Astron. Soc. 493, 3132–3158 (2020).

    ADS  Article  Google Scholar 

  72. Smith, R. J. E., Ashton, G., Vajpeyi, A. & Talbot, C. Massively parallel Bayesian inference for transient gravitational-wave astronomy. Mon. Not. R. Astron. Soc. 498, 4492–4502 (2020).

    ADS  Article  Google Scholar 

  73. Virtanen, P. et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272 (2020).

    Article  Google Scholar 

  74. Oliphant, T. E. A Guide to NumPy Vol. 1 (Trelgol, 2006).

  75. Van Der Walt, S., Colbert, S. C. & Varoquaux, G. The NumPy array: a structure for efficient numerical computation. Comput. Sci. Eng. 13, 22–30 (2011).

    Article  Google Scholar 

  76. Harris, C. R. et al. Array programming with NumPy. Nature 585, 357–362 (2020).

    ADS  Article  Google Scholar 

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Acknowledgements

We thank S. Akcay for valuable comments on the manuscript and comments about the tidal sector of the TEOBResumS model. We are also grateful for discussions with S. Bernuzzi, R. Gamba and A. Nagar. Finally, we thank J. Tissino for pointing out a mistake in equation (5) in an early draft of this work. All nested sampling analyses made use of the dynesty package71 and the higher-order mode analysis of TEOBResumS additionally used the massively parallelized software Parallel Bilby72. G.A. thanks the UKRI Future Leaders Fellowship for support through the grant MR/T01881X/1. T.D. thanks the Max Planck Society for financial support. We are grateful for computational resources provided by Cardiff University and funded by an STFC grant ST/I006285/1 supporting UK Involvement in the Operation of Advanced LIGO. This work makes use of the SciPy73 and NumPy74,75,76 packages for data analysis and visualization.

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G.A. wrote the code and carried out the data curation, analysis and visualization. G.A. and T.D. carried out the remaining aspects of the work.

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Correspondence to Gregory Ashton.

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Nature Astronomy thanks Jacob Lange and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Ashton, G., Dietrich, T. The use of hypermodels to understand binary neutron star collisions. Nat Astron 6, 961–967 (2022). https://doi.org/10.1038/s41550-022-01707-x

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