Relativistic Shapiro delay measurements of an extremely massive millisecond pulsar


Despite its importance to our understanding of physics at supranuclear densities, the equation of state (EoS) of matter deep within neutron stars remains poorly understood. Millisecond pulsars (MSPs) are among the most useful astrophysical objects in the Universe for testing fundamental physics, and place some of the most stringent constraints on this high-density EoS. Pulsar timing—the process of accounting for every rotation of a pulsar over long time periods—can precisely measure a wide variety of physical phenomena, including those that allow the measurement of the masses of the components of a pulsar binary system1. One of these, called relativistic Shapiro delay2, can yield precise masses for both an MSP and its companion; however, it is only easily observed in a small subset of high-precision, highly inclined (nearly edge-on) binary pulsar systems. By combining data from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 12.5-yr data set with recent orbital-phase-specific observations using the Green Bank Telescope, we have measured the mass of the MSP J0740+6620 to be \({\mathbf{2}}{\mathbf{.14}}_{ - {\mathbf{0}}{\mathbf{.09}}}^{ + {\mathbf{0}}{\mathbf{.10}}}\)M (68.3% credibility interval; the 95.4% credibility interval is \({\mathbf{2}}{\mathbf{.14}}_{ - {\mathbf{0}}{\mathbf{.18}}}^{ + {\mathbf{0}}{\mathbf{.20}}}\)M). It is highly likely to be the most massive neutron star yet observed, and serves as a strong constraint on the neutron star interior EoS.

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Fig. 1: Timing residuals from all observations of J0740+6620 as a function of orbital phase, with superior conjunction at orbital phase = 0.25.
Fig. 2: Map of fitted χ2 distributions and corresponding probability density functions for mp, mc and i.
Fig. 3: Timing residuals and DMX for all epochs of J0740+6620 data.

Data availability

PSR J0740+6620 TOAs from both the 12.5-yr data set and from the two supplemental GBT observations will be available at on publication of this manuscript.

Code availability

All code mentioned in this work is open source and available at the links provided in the manuscript.


  1. 1.

    Lorimer, D. R. & Kramer, M. Handbook of Pulsar Astronomy (Cambridge University Press, 2005).

  2. 2.

    Shapiro, I. I. Fourth test of general relativity. Phys. Rev. Lett. 13, 789–791 (1964).

    ADS  MathSciNet  Article  Google Scholar 

  3. 3.

    Freire, P. C. C. & Wex, N. The orthometric parametrization of the Shapiro delay and an improved test of general relativity with binary pulsars. Mon. Not. R. Astron. Soc. 409, 199–212 (2010).

    ADS  Article  Google Scholar 

  4. 4.

    Demorest, P. B., Pennucci, T., Ransom, S. M., Roberts, M. S. E. & Hessels, J. W. T. A two-solar-mass neutron star measured using Shapiro delay. Nature 467, 1081–1083 (2010).

    ADS  Article  Google Scholar 

  5. 5.

    Fonseca, E. et al. The NANOGrav nine-year data set: mass and geometric measurements of binary millisecond pulsars. Astrophys. J. 832, 167 (2016).

    ADS  Article  Google Scholar 

  6. 6.

    Antoniadis, J. et al. A massive pulsar in a compact relativistic binary. Science 340, 448 (2013).

    ADS  Article  Google Scholar 

  7. 7.

    Friere, P. C. C. et al. On the nature and evolution of the unique binary pulsar J1903+0327. Mon. Not. R. Astron. Soc. 412, 2763–2780 (2011).

    ADS  Article  Google Scholar 

  8. 8.

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

    ADS  Article  Google Scholar 

  9. 9.

    Linares, M., Shahbaz, T. & Casares, J. Peering into the dark side: magnesium lines establish a massive neutron star in PSR J2215+5135. Astrophys. J. 859, 54 (2018).

    ADS  Article  Google Scholar 

  10. 10.

    Arzoumanian, Z. et al. The NANOGrav 11-year data set: pulsar-timing constraints on the stochastic gravitational-wave background. Astrophys. J. 859, 47 (2018).

    ADS  Article  Google Scholar 

  11. 11.

    Stovall, K. et al. The Green Bank Northern Celestial Cap pulsar survey. I. Survey description, data analysis, and initial results. Astrophys. J. 791, 67 (2014).

    ADS  Article  Google Scholar 

  12. 12.

    Lynch, R. S. et al. The Green Bank North Celestial Cap pulsar survey. III. 45 new pulsar timing solutions. Astrophys. J. 859, 93 (2018).

    ADS  Article  Google Scholar 

  13. 13.

    Beronya, D. M. et al. The ultracool helium-atmosphere white dwarf companion of PSR J0740+6620?. Mon. Not. R. Astron. Soc. 485, 3715–3720 (2019).

    ADS  Article  Google Scholar 

  14. 14.

    Watts, A. et al. Probing the neutron star interior and the Equation of State of cold dense matter with the SKA. Proc. Sci. 215, 43 (2015).

    ADS  Google Scholar 

  15. 15.

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

    ADS  Article  Google Scholar 

  16. 16.

    Bedaque, P. F. & Steiner, A. W. Hypernuclei and the hyperon problem in neutron stars. Phys. Rev. C 92, 025803 (2015).

    ADS  Article  Google Scholar 

  17. 17.

    Antoniadis, J. et al. The millisecond pulsar mass distribution: Evidence for bimodality and constraints on the maximum neutron star mass. Preprint at (2016).

  18. 18.

    Tauris, T. M., Langer, N. & Kramer, M. Formation of millisecond pulsars with CO white dwarf companions—I. PSR J1614-2230: evidence for a neutron star born massive. Mon. Not. R. Astron. Soc. 416, 2130–2142 (2011).

    ADS  Article  Google Scholar 

  19. 19.

    Cognard, I. et al. A massive-born neutron star with a massive white dwarf companion. Astrophys. J. 844, 128 (2017).

    ADS  Article  Google Scholar 

  20. 20.

    Rappaport, S., Podsiadlowski, P., Joss, P. C., Di Stefano, R. & Han, Z. The relation between white dwarf mass and orbital period in wide binary radio pulsars. Mon. Not. R. Astron. Soc. 273, 731–741 (1995).

    ADS  Article  Google Scholar 

  21. 21.

    Tauris, T. M. & Savonije, G. J. Formation of millisecond pulsars. I. Evolution of low-mass X-ray binaries with P orb > 2 days. Astron. Astrophys. 350, 928–944 (1999).

    ADS  Google Scholar 

  22. 22.

    Ng, C. Pulsar science with the CHIME telescope. In Proc. International Astronomical Union Vol. 13, Symp. 337: Pulsar AstrophysicsThe Next Fifty Years (eds Weltevrede, P. et al.) 179–182 (Cambridge University Press, 2018).

  23. 23.

    DuPlain, R. et al. Launching GUPPI: the Green Bank Ultimate Pulsar Processing Instrument. Proc. SPIE 7019, 70191D (2008).

    Article  Google Scholar 

  24. 24.

    Arzoumanian, Z. et al. The NANOGrav nine-year data set: observations, arrival time measurements, and analysis of 37 millisecond pulsars. Astrophys. J. 813, 65 (2015).

    ADS  Article  Google Scholar 

  25. 25.

    Demorest, P. B. nanopipe: calibration and data reduction pipeline for pulsar timing. Astrophysics Source Code Library ascl:1803.004 (2018).

  26. 26.

    van Straten, W. et al. PSRCHIVE: development library for the analysis of pulsar astronomical data. Astrophysics Source Code Library ascl:1105.014 (2011).

  27. 27.

    Hobbs, G. & Edwards, R. Tempo2: pulsar timing package. Astrophysics Source Code Library ascl:1210.015 (2012).

  28. 28.

    Lange, Ch et al. Precision timing measurements of PSR J1012+5307. Mon. Not. R. Astron. Soc. 326, 274–282 (2001).

    ADS  Article  Google Scholar 

  29. 29.

    Lam, M. T. et al. Systematic and stochastic variations in pulsar dispersion measures. Astrophys. J. 821, 66 (2015).

    ADS  Article  Google Scholar 

  30. 30.

    Jones, M. L. et al. The NANOGrav nine-year data set: measurement and interpretation of variations in dispersion measures. Astrophys. J. 841, 125 (2017).

    ADS  Article  Google Scholar 

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The NANOGrav Project receives support from NSF Physics Frontiers Center award no. 1430284. Pulsar research at UBC is supported by an NSERC Discovery Grant and by the Canadian Institute for Advanced Research (CIFAR). The National Radio Astronomy Observatory and the Green Bank Observatory are facilities of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. S.M.R is a CIFAR Senior Fellow. W.W.Z. is supported by the CAS Pioneer Hundred Talents Program, the Strategic Priority Research Program of the Chinese Academy of Sciences grant no. XDB23000000 and the National Natural Science Foundation of China grant nos. 11690024, 11743002 and 11873067. Supplementary Green Bank conjunction-phase observing project codes were 18B-289 and 18B-372 (DDT).

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The creation of the NANOGrav 12.5-yr data set was made possible through extensive observations and pulsar-timing activities conducted by all the authors. H.T.C. was responsible for the NANOGrav-adjacent concentrated observing campaigns and the majority of this manuscript’s contents. H.T.C., E.F., S.M.R. and P.B.D. were responsible for the extended J0740+6620 data analysis (the merging of NANOGrav and conjunction-phase observations) and modelling effort. E.F. was responsible for much of the initial work on J0740+6620 that informed the supplementary observing proposals, and for the development of the gridding code that yielded both the mass and inclination credibility intervals and Fig. 2.

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Correspondence to H. T. Cromartie.

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Peer review information Nature Astronomy thanks John Antoniadis and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

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