Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Stringent constraints on neutron-star radii from multimessenger observations and nuclear theory

Abstract

The properties of neutron stars are determined by the nature of the matter that they contain. These properties can be constrained by measurements of the star’s size. We obtain stringent constraints on neutron-star radii by combining multimessenger observations of the binary neutron-star merger GW170817 with nuclear theory that best accounts for density-dependent uncertainties in the equation of state. We construct equations of state constrained by chiral effective field theory and marginalize over these using the gravitational-wave observations. Combining this with the electromagnetic observations of the merger remnant that imply the presence of a short-lived hypermassive neutron star, we find that the radius of a 1.4 M neutron star is \({R}_{1.4{M}_{\odot }}={11.0}_{-0.6}^{+0.9}\ {\rm{km}}\) (90% credible interval). Using this constraint, we show that neutron stars are unlikely to be disrupted in neutron star–black hole mergers; subsequently, such events will not produce observable electromagnetic emission.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Comparison of the estimated \({R}_{1.4{M}_{\odot }}\) at different stages of our analysis.
Fig. 2: Mass–radius relation for the two equation-of-state sets.
Fig. 3: Implications for electromagnetic counterparts to neutron star–black hole mergers.

Similar content being viewed by others

Data availability

All data are available in the manuscript or the Supplementary Information. Full posterior data samples are available at https://github.com/sugwg/gw170817-eft-eos. The gravitational-wave data used in this work were obtained from the Gravitational Wave Open Science Center (GWOSC) at https://www.gw-openscience.org.

Code availability

All software used in this analysis is open source and available from https://github.com/gwastro/pycbc.

References

  1. Lattimer, J. M. & Prakash, M. Neutron star structure and the equation of state. Astrophys. J. 550, 426–442 (2001).

    ADS  Google Scholar 

  2. Özel, F. & Freire, P. Masses, radii, and the equation of state of neutron stars. Annu. Rev. Astron. Astrophys. 54, 401–440 (2016).

    ADS  Google Scholar 

  3. Gendreau, K., Arzoumanian, Z. & Okajima, T. The Neutron star Interior Composition ExploreR (NICER): an explorer mission of opportunity for soft X-ray timing spectroscopy. Proc. SPIE 8443 844313 (2012).

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  6. De, S. et al. Tidal deformabilities and radii of neutron stars from the observation of GW170817. Phys. Rev. Lett. 121, 091102 (2018); erratum 121, 259902 (2018).

  7. Abbott, B. P. et al. GW170817: measurements of neutron star radii and equation of state. Phys. Rev. Lett. 121, 161101 (2018).

    ADS  Google Scholar 

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

    Google Scholar 

  9. Radice, D. & Dai, L. Multimessenger parameter estimation of GW170817. Eur. Phys. J. A 55, 50 (2019).

    ADS  Google Scholar 

  10. Weinberg, S. Nuclear forces from chiral lagrangians. Phys. Lett. B 251, 288–292 (1990).

    ADS  Google Scholar 

  11. Weinberg, S. Effective chiral lagrangians for nucleon–pion interactions and nuclear forces. Nucl. Phys. B 363, 3–18 (1991).

    ADS  Google Scholar 

  12. van Kolck, U. Few nucleon forces from chiral lagrangians. Phys. Rev. C 49, 2932–2941 (1994).

    ADS  Google Scholar 

  13. Epelbaum, E., Hammer, H. W. & Meissner, U. G. Modern theory of nuclear forces. Rev. Mod. Phys. 81, 1773–1825 (2009).

    ADS  Google Scholar 

  14. Machleidt, R. & Entem, D. R. Chiral effective field theory and nuclear forces. Phys. Rep. 503, 1–75 (2011).

    ADS  Google Scholar 

  15. Carlson, J. et al. Quantum Monte Carlo methods for nuclear physics. Rev. Mod. Phys. 87, 1067–1118 (2015).

    ADS  MathSciNet  Google Scholar 

  16. Tews, I., Margueron, J. & Reddy, S. Critical examination of constraints on the equation of state of dense matter obtained from GW170817. Phys. Rev. C 98, 045804 (2018).

    ADS  Google Scholar 

  17. Hebeler, K., Lattimer, J. M., Pethick, C. J. & Schwenk, A. Constraints on neutron star radii based on chiral effective field theory interactions. Phys. Rev. Lett. 105, 161102 (2010).

    ADS  Google Scholar 

  18. Antoniadis, J. et al. A massive pulsar in a compact relativistic binary. Science 340, 1233232 (2013).

    Google Scholar 

  19. Tews, I., Carlson, J., Gandolfi, S. & Reddy, S. Constraining the speed of sound inside neutron stars with chiral effective field theory interactions and observations. Astrophys. J. 860, 149 (2018).

    ADS  Google Scholar 

  20. Biwer, C. M. et al. PyCBC inference: a Python-based parameter estimation toolkit for compact binary coalescence signals. Publ. Astron. Soc. Pac. 131, 024503 (2019).

    ADS  Google Scholar 

  21. Soares-Santos, M. et al. The electromagnetic counterpart of the binary neutron star merger LIGO/Virgo GW170817. I. Discovery of the optical counterpart using the dark energy camera. Astrophys. J. 848, L16 (2017).

    ADS  Google Scholar 

  22. Cantiello, M. et al. A precise distance to the host galaxy of the binary neutron star merger GW170817 using surface brightness fluctuations. Astrophys. J. 854, L31 (2018).

    ADS  Google Scholar 

  23. Margalit, B. & Metzger, B. D. Constraining the maximum mass of neutron stars from multi-messenger observations of GW170817. Astrophys. J. 850, L19 (2017).

    ADS  Google Scholar 

  24. Bauswein, A., Just, O., Janka, H. T. & Stergioulas, N. Neutron-star radius constraints from GW170817 and future detections. Astrophys. J. 850, L34 (2017).

    ADS  Google Scholar 

  25. Bauswein, A., Baumgarte, T. W. & Janka, H.-T. Prompt merger collapse and the maximum mass of neutron stars. Phys. Rev. Lett. 111, 131101 (2013).

    ADS  Google Scholar 

  26. Köppel, S., Bovard, L. & Rezzolla, L. A general-relativistic determination of the threshold mass to prompt collapse in binary neutron star mergers. Astrophys. J. 872, L16 (2019).

    ADS  Google Scholar 

  27. Shibata, M., Zhou, E., Kiuchi, K. & Fujibayashi, S. Constraint on the maximum mass of neutron stars using GW170817 event. Phys. Rev. D 100, 023015 (2019).

    ADS  Google Scholar 

  28. Cromartie, H. T. et al. Relativistic Shapiro delay measurements of an extremely massive millisecond pulsar. Nat. Astron. 4, 72–76 (2020).

  29. Bedaque, P. & Steiner, A. W. Sound velocity bound and neutron stars. Phys. Rev. Lett. 114, 031103 (2015).

    ADS  Google Scholar 

  30. Lattimer, J. M. & Prakash, M. in From Nuclei to Stars (ed. Lee, S) 275–304 (UK World Scientific, 2011).

  31. Hannam, M., Brown, D. A., Fairhurst, S., Fryer, C. L. & Harry, I. W. When can gravitational-wave observations distinguish between black holes and neutron stars? Astrophys. J. 766, L14 (2013).

    ADS  Google Scholar 

  32. Abbott, B. P. et al. Model comparison from LIGO-Virgo data on GW170817’s binary components and consequences for the merger remnant. Class. Quant. Grav. 37, 045006 (2020).

    ADS  Google Scholar 

  33. Advanced LIGO Anticipated Sensitivity Curves LIGO-DCC-T0900288 (LIGO Scientific Collaboration, 2010): https://dcc.ligo.org/LIGO-T0900288/public

  34. Hinderer, T. et al. Distinguishing the nature of comparable-mass neutron star binary systems with multimessenger observations: GW170817 case study. Phys. Rev. D 100, 06321 (2019).

    Google Scholar 

  35. Foucart, F. Black hole–neutron star mergers: disk mass predictions. Phys. Rev. D 86, 124007 (2012).

    ADS  Google Scholar 

  36. Bauswein, A., Goriely, S. & Janka, H.-T. Systematics of dynamical mass ejection, nucleosynthesis, and radioactively powered electromagnetic signals from neutron-star mergers. Astrophys. J. 773, 78 (2013).

    ADS  Google Scholar 

  37. Hotokezaka, K. et al. Mass ejection from the merger of binary neutron stars. Phys. Rev. D 87, 024001 (2013).

    ADS  Google Scholar 

  38. LIGO Scientific Collaboration & the Virgo Collaboration GRB Coordinates Network Circular Service 25333 (2019).

  39. Foucart, F., Hinderer, T. & Nissanke, S. Remnant baryon mass in neutron star–black hole mergers: predictions for binary neutron star mimickers and rapidly spinning black holes. Phys. Rev. D 98, 081501 (2018).

    ADS  Google Scholar 

  40. Margalit, B. & Metzger, B. D. The multi-messenger matrix: the future of neutron star merger constraints on the nuclear equation of state. Astrophys. J. 880, L15 (2019).

    ADS  Google Scholar 

  41. Wijnands, R., Degenaar, N. & Page, D. Cooling of accretion-heated neutron stars. J. Astrophys. Astron. 38, 49 (2017).

    ADS  Google Scholar 

  42. Brown, E. F. & Cumming, A. Mapping crustal heating with the cooling lightcurves of quasi-persistent transients. Astrophys. J. 698, 1020 (2009).

    ADS  Google Scholar 

  43. Lewin, W. H. G. & van der Klis, M. Compact Stellar X-ray Sources (Cambridge Univ. Press, 2006).

  44. Barkett, K. et al. Gravitational waveforms for neutron star binaries from binary black hole simulations. Phys. Rev. D 93, 044064 (2016).

    ADS  Google Scholar 

  45. Narikawa, T. et al. Reanalysis of the binary neutron star merger GW170817 using numerical-relativity calibrated waveform models. Preprint at https://arxiv.org/abs/1910.08971 (2019).

  46. Abbott, B. P. et al. Prospects for observing and localizing gravitational-wave transients with advanced LIGO, Advanced Virgo and KAGRA. Living Rev. Rel. 21, 3 (2018).

    Google Scholar 

  47. 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 

  48. Melendez, J. A., Wesolowski, S. & Furnstahl, R. J. Bayesian truncation errors in chiral effective field theory: nucleon-nucleon observables. Phys. Rev. C 96, 024003 (2017).

    ADS  Google Scholar 

  49. Lynn, J. E. et al. Chiral three-nucleon interactions in light nuclei, neutron-α scattering, and neutron matter. Phys. Rev. Lett. 116, 062501 (2016).

    ADS  Google Scholar 

  50. Lonardoni, D. et al. Properties of nuclei up to A = 16 using local chiral interactions. Phys. Rev. Lett. 120, 122502 (2018).

    ADS  Google Scholar 

  51. Lynn, J. E., Tews, I., Gandolfi, S. & Lovato, A. Quantum Monte Carlo methods in nuclear physics: recent advances. Annu. Rev. Nucl. Part. Sci. 69, 279–305 (2019).

    ADS  Google Scholar 

  52. Tews, I. Spectrum of shear modes in the neutron-star crust: estimating the nuclear-physics uncertainties. Phys. Rev. C 95, 015803 (2017).

    ADS  Google Scholar 

  53. Tews, I., Margueron, J. & Reddy, S. Confronting gravitational-wave observations with modern nuclear physics constraints. Eur. Phys. J. A 55, 97 (2019).

    ADS  Google Scholar 

  54. Vallisneri, M., Kanner, J., Williams, R., Weinstein, A. & Stephens, B. The LIGO Open Science Center. J. Phys. Conf. Ser. 610, 012021 (2015).

    Google Scholar 

  55. Allen, B., Anderson, W. G., Brady, P. R., Brown, D. A. & Creighton, J. D. E. FINDCHIRP: an algorithm for detection of gravitational waves from inspiraling compact binaries. Phys. Rev. D 85, 122006 (2012).

    ADS  Google Scholar 

  56. Foreman-Mackey, D., Hogg, D. W., Lang, D. & Goodman, J. emcee: the MCMC hammer. Publ. Astron. Soc. Pac. 125, 306–312 (2013).

    ADS  Google Scholar 

  57. Vousden, W. D., Farr, W. M. & Mandel, I. Dynamic temperature selection for parallel tempering in Markov chain Monte Carlo simulations. Mon. Not. R. Astron. Soc. 455, 1919–1937 (2015).

    ADS  Google Scholar 

  58. Speagle, J. S. dynesty: a dynamic nested sampling package for estimating bayesian posteriors and evidences. Preprint at https://arxiv.org/abs/1904.02180 (2019).

  59. Burgay, M. et al. An increased estimate of the merger rate of double neutron stars from observations of a highly relativistic system. Nature 426, 531–533 (2003).

    ADS  Google Scholar 

  60. Ade, P. A. R. et al. Planck 2015 results. XIII. cosmological parameters. Astron. Astrophys 594, A13 (2016).

    Google Scholar 

  61. Sathyaprakash, B. S. & Dhurandhar, S. V. Choice of filters for the detection of gravitational waves from coalescing binaries. Phys. Rev. D 44, 3819–3834 (1991).

    ADS  Google Scholar 

  62. Buonanno, A., Iyer, B., Ochsner, E., Pan, Y. & Sathyaprakash, B. S. Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors. Phys. Rev. D 80, 084043 (2009).

    ADS  Google Scholar 

  63. Mikoczi, B., Vasuth, M. & Gergely, L. A. Self-interaction spin effects in inspiralling compact binaries. Phys. Rev. D 71, 124043 (2005).

    ADS  Google Scholar 

  64. Arun, K. G., Buonanno, A., Faye, G. & Ochsner, E. Higher-order spin effects in the amplitude and phase of gravitational waveforms emitted by inspiraling compact binaries: ready-to-use gravitational waveforms. Phys. Rev. D 79, 104023 (2009); erratum 84, 049901 (2011).

  65. Bohé, A., Marsat, S. & Blanchet, L. Next-to-next-to-leading order spin-orbit effects in the gravitational wave flux and orbital phasing of compact binaries. Class. Quant. Grav. 30, 135009 (2013).

    ADS  MathSciNet  MATH  Google Scholar 

  66. Vines, J., Flanagan, E. E. & Hinderer, T. Post-1-Newtonian tidal effects in the gravitational waveform from binary inspirals. Phys. Rev. D 83, 084051 (2011).

    ADS  Google Scholar 

  67. 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  Google Scholar 

  68. Dietrich, T. et al. Matter imprints in waveform models for neutron star binaries: tidal and self-spin effects. Phys. Rev. D 99, 024029 (2019).

    ADS  Google Scholar 

  69. 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  Google Scholar 

  70. 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  Google Scholar 

  71. Villar, V. A. et al. The combined ultraviolet, optical, and near-infrared light curves of the kilonova associated with the binary neutron star merger GW170817: unified data set, analytic models, and physical implications. Astrophys. J. 851, L21 (2017).

    ADS  Google Scholar 

  72. Kiuchi, K., Kyutoku, K., Shibata, M. & Taniguchi, K. Revisiting the lower bound on tidal deformability derived by at 2017gfo. Astrophys. J. 876, L31 (2019).

    ADS  Google Scholar 

  73. Bauswein, A. & Stergioulas, N. Semi-analytic derivation of the threshold mass for prompt collapse in binary neutron star mergers. Mon. Not. R. Astron. Soc. 471, 4956–4965 (2017).

    ADS  Google Scholar 

  74. Shibata, M. et al. Modeling GW170817 based on numerical relativity and its implications. Phys. Rev. D 96, 123012 (2017).

    ADS  Google Scholar 

  75. Rezzolla, L., Most, E. R. & Weih, L. R. Using gravitational-wave observations and quasi-universal relations to constrain the maximum mass of neutron stars. Astrophys. J. 852, L25 (2018).

    ADS  Google Scholar 

  76. Ruiz, M., Shapiro, S. L. & Tsokaros, A. GW170817, general relativistic magnetohydrodynamic simulations, and the neutron star maximum mass. Phys. Rev. D 97, 021501 (2018).

    ADS  Google Scholar 

  77. Lattimer, J. M. & Schramm, D. N. Black-hole–neutron-star collisions. Astrophys. J. 192, L145 (1974).

    ADS  Google Scholar 

  78. Shibata, M. & Taniguchi, K. Merger of black hole and neutron star in general relativity: tidal disruption, torus mass, and gravitational waves. Phys. Rev. D 77, 084015 (2008).

    ADS  Google Scholar 

  79. Kyutoku, K., Ioka, K., Okawa, H., Shibata, M. & Taniguchi, K. Dynamical mass ejection from black hole–neutron star binaries. Phys. Rev. D 92, 044028 (2015).

    ADS  Google Scholar 

  80. Pannarale, F. & Ohme, F. Prospects for joint gravitational-wave and electromagnetic observations of neutron-star–black-hole coalescing binaries. Astrophys. J. 791, L7 (2014).

    ADS  Google Scholar 

  81. Barbieri, C., Salafia, O. S., Perego, A., Colpi, M. & Ghirlanda, G. Electromagnetic counterparts of black hole–neutron star mergers: dependence on the neutron star properties. Eur. Phys. J. A 56, 8 (2020).

    ADS  Google Scholar 

  82. Bardeen, J. M., Press, W. H. & Teukolsky, S. A. Rotating black holes: locally nonrotating frames, energy extraction, and scalar synchrotron radiation. Astrophys. J. 178, 347–370 (1972).

    ADS  Google Scholar 

Download references

Acknowledgements

We thank B. Allen, W. Kastaun, J. Lattimer and B. Metzger for valuable discussions. This work was supported by US National Science Foundation grants PHY-1430152 to the JINA Center for the Evolution of the Elements (S.R.), PHY-1707954 (D.A.B. and S.D.); US Department of Energy grant DE-FG02-00ER41132 (S.R.); NASA Hubble Fellowship grant number HST-HF2-51412.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555 (B.M.); and the US Department of Energy, Office of Science, Office of Nuclear Physics, under contract DE-AC52-06NA25396, the Los Alamos National Laboratory (LANL) LDRD programme and the NUCLEI SciDAC programme (I.T.). D.A.B., S.D. and B.M. thank the Kavli Institute for Theoretical Physics (KITP) where portions of this work were completed. KITP is supported in part by the National Science Foundation under grant number NSF PHY-1748958. Computational resources have been provided by Los Alamos Open Supercomputing via the Institutional Computing (IC) programme, by the National Energy Research Scientific Computing Center (NERSC), by the Jülich Supercomputing Center, by the ATLAS Cluster at the Albert Einstein Institute in Hannover, and by Syracuse University. GWOSC is a service of LIGO Laboratory, the LIGO Scientific Collaboration and the Virgo Collaboration. LIGO is funded by the National Science Foundation. Virgo is funded by the French Centre National de Recherche Scientifique (CNRS), the Italian Istituto Nazionale della Fisica Nucleare (INFN) and the Dutch Nikhef, with contributions by Polish and Hungarian institutes. B.M. is a NASA Einstein Fellow.

Author information

Authors and Affiliations

Authors

Contributions

Conceptualization: D.A.B., C.D.C., B.K., B.M., S.R., I.T. Data curation: D.A.B., C.D.C., S.D., I.T. Formal analysis, C.D.C., S.M.B., I.T., S.D. Funding acquisition: D.A.B., B.K., B.M., S.R., I.T. Methodology: D.A.B., C.D.C., S.D., B.K., B.M., S.R., I.T. Project administration: D.A.B., B.K., S.R., I.T. Resources: D.A.B., B.K., I.T. Software: D.A.B., S.M.B., C.D.C., S.D., S.K., B.M., I.T. Supervision: D.A.B., B.K., S.R. Validation: D.A.B., S.M.B., C.D.C., S.D., I.T. Visualization: S.M.B., C.D.C., B.M. Writing—original draft: D.A.B., S.M.B., C.D.C., I.T. Writing—review and editing: D,.A.B., S.M.B., C.D.C., S.D., B.K., B.M., S.R., I.T.

Corresponding author

Correspondence to Collin D. Capano.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Capano, C.D., Tews, I., Brown, S.M. et al. Stringent constraints on neutron-star radii from multimessenger observations and nuclear theory. Nat Astron 4, 625–632 (2020). https://doi.org/10.1038/s41550-020-1014-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41550-020-1014-6

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing