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.

Universality of free fall from the orbital motion of a pulsar in a stellar triple system

Abstract

Einstein’s theory of gravity—the general theory of relativity1—is based on the universality of free fall, which specifies that all objects accelerate identically in an external gravitational field. In contrast to almost all alternative theories of gravity2, the strong equivalence principle of general relativity requires universality of free fall to apply even to bodies with strong self-gravity. Direct tests of this principle using Solar System bodies3,4 are limited by the weak self-gravity of the bodies, and tests using pulsar–white-dwarf binaries5,6 have been limited by the weak gravitational pull of the Milky Way. PSR J0337+1715 is a hierarchical system of three stars (a stellar triple system) in which a binary consisting of a millisecond radio pulsar and a white dwarf in a 1.6-day orbit is itself in a 327-day orbit with another white dwarf. This system permits a test that compares how the gravitational pull of the outer white dwarf affects the pulsar, which has strong self-gravity, and the inner white dwarf. Here we report that the accelerations of the pulsar and its nearby white-dwarf companion differ fractionally by no more than 2.6 × 10−6. For a rough comparison, our limit on the strong-field Nordtvedt parameter, which measures violation of the universality of free fall, is a factor of ten smaller than that obtained from (weak-field) Solar System tests3,4 and a factor of almost a thousand smaller than that obtained from other strong-field tests5,6.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

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

Fig. 1: Difference between our pulsar time-of-arrival measurements and model (fit residuals).
Fig. 2: Quasi-Fourier representation of fit residuals.
Fig. 3: Constraints on quasi-Brans–Dicke theories of gravity.

References

  1. Einstein, A. Die Grundlage der allgemeinen Relativitätstheorie. Ann. Phys. 354, 769–822 (1916).

    Article  MATH  Google Scholar 

  2. Deruelle, N. Nordström’s scalar theory of gravity and the equivalence principle. Gen. Relativ. Gravit. 43, 3337–3354 (2011).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Genova, A. et al. Solar system expansion and strong equivalence principle as seen by the NASA MESSENGER mission. Nat. Commun. 9, 289 (2018).

    Article  ADS  PubMed  PubMed Central  CAS  Google Scholar 

  4. Hofmann, F. & Müller, J. Relativistic tests with lunar laser ranging. Class. Quantum Gravity 35, 035015 (2018).

    Article  ADS  MATH  Google Scholar 

  5. Freire, P. C. C., Kramer, M. & Wex, N. Tests of the universality of free fall for strongly self-gravitating bodies with radio pulsars. Class. Quantum Gravity 29, 184007 (2012).

    Article  ADS  MATH  Google Scholar 

  6. Zhu, W. W. et al. Tests of gravitational symmetries with pulsar binary J1713+0747. Preprint at https://arxiv.org/abs/1802.09206 (2018).

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

    Article  ADS  Google Scholar 

  8. Ransom, S. M. et al. A millisecond pulsar in a stellar triple system. Nature 505, 520–524 (2014).

    Article  ADS  PubMed  CAS  Google Scholar 

  9. Will, C. M. & Nordtvedt, K. Jr. Conservation laws and preferred frames in relativistic gravity. I. Preferred-frame theories and an extended PPN formalism. Astrophys. J. 177, 757–774 (1972).

    Article  ADS  MathSciNet  Google Scholar 

  10. Nordtvedt, K. A post-Newtonian gravitational Lagrangian formalism for celestial body dynamics in metric gravity. Astrophys. J. 297, 390–404 (1985).

    Article  ADS  Google Scholar 

  11. Meurer, A. et al. Sympy: symbolic computing in python. PeerJ Comput. Sci. 3, e103 (2017).

    Article  Google Scholar 

  12. Damour, T. & Schaefer, G. New tests of the strong equivalence principle using binary-pulsar data. Phys. Rev. Lett. 66, 2549–2552 (1991).

    Article  ADS  PubMed  CAS  Google Scholar 

  13. Baker, T., Psaltis, D. & Skordis, C. Linking tests of gravity on all scales: from the strong-field regime to cosmology. Astrophys. J. 802, 63 (2015).

    Article  ADS  Google Scholar 

  14. Will, C. M. in Theory and Experiment in Gravitational Physics Ch. 4 (Cambridge Univ. Press, Cambridge, 1981).

    MATH  Google Scholar 

  15. Damour, T. & Taylor, J. H. Strong-field tests of relativistic gravity and binary pulsars. Phys. Rev. D 45, 1840–1868 (1992).

    Article  ADS  CAS  Google Scholar 

  16. Berti, E. et al. Testing general relativity with present and future astrophysical observations. Class. Quantum Gravity 32, 243001 (2015).

    Article  ADS  Google Scholar 

  17. Damour, T. & Esposito-Farèse, G. Tensor-scalar gravity and binary-pulsar experiments. Phys. Rev. D 54, 1474–1491 (1996).

    Article  ADS  CAS  Google Scholar 

  18. Brans, C. & Dicke, R. H. Mach’s principle and a relativistic theory of gravitation. Phys. Rev. 124, 925–935 (1961).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Damour, T. & Esposito-Farese, G. Tensor-multi-scalar theories of gravitation. Class. Quantum Gravity 9, 2093–2176 (1992).

    Article  ADS  MathSciNet  MATH  CAS  Google Scholar 

  20. Bertotti, B., Iess, L. & Tortora, P. A test of general relativity using radio links with the Cassini spacecraft. Nature 425, 374–376 (2003).

    Article  ADS  PubMed  CAS  Google Scholar 

  21. Freire, P. C. C. et al. The relativistic pulsar–white dwarf binary PSR J1738+0333 – II. The most stringent test of scalar–tensor gravity. Mon. Not. R. Astron. Soc. 423, 3328–3343 (2012).

    Article  ADS  Google Scholar 

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

    Article  CAS  Google Scholar 

  23. Mignard, F. & Klioner, S. A. Gaia: relativistic modelling and testing. Proc. Int. Astron. Union 261, 306–314 (2010).

    Google Scholar 

  24. Shao, L., Sennett, N., Buonanno, A., Kramer, M. & Wex, N. Constraining nonperturbative strong-field effects in scalar-tensor gravity by combining pulsar timing and laser-interferometer gravitational-wave detectors. Phys. Rev. X 7, 041025 (2017).

    Google Scholar 

  25. Haensel, P., Proszynski, M. & Kutschera, M. Uncertainty in the saturation density of nuclear matter and neutron star models. Astron. Astrophys. 102, 299–302 (1981).

    ADS  CAS  Google Scholar 

  26. DuPlain, R. et al. Launching GUPPI: the Green Bank ultimate pulsar processing instrument. Proc. SPIE 7019, 70191D (2008).

    Article  Google Scholar 

  27. Karuppusamy, R., Stappers, B. & van Straten, W. PuMa-II: a wide band pulsar machine for the Westerbork Synthesis Radio Telescope. Publ. Astron. Soc. Pacif. 120, 191–202 (2008).

    Article  ADS  Google Scholar 

  28. Hankins, T. H. & Rickett, B. J. in Methods in Computational Physics. Volume 14 – Radio Astronomy (eds Alder, B. et al.) 55–129 (Academic Press, New York, 1975).

  29. van Straten, W. Radio astronomical polarimetry and high-precision pulsar timing. Astrophys. J. 642, 1004–1011 (2006).

    Article  ADS  Google Scholar 

  30. Lambert, H. C. & Rickett, B. J. On the theory of pulse propagation and two-frequency field statistics in irregular interstellar plasmas. Astrophys. J. 517, 299–317 (1999).

    Article  ADS  Google Scholar 

  31. Archibald, A. M., Kondratiev, V. I., Hessels, J. W. T. & Stinebring, D. R. Millisecond pulsar scintillation studies with LOFAR: initial results. Astrophys. J. 790, L22 (2014).

    Article  ADS  Google Scholar 

  32. Bulirsch, R. & Stoer, J. Asymptotic upper and lower bounds for results of extrapolation methods. Numer. Math. 8, 93–104 (1966).

    Article  MathSciNet  MATH  Google Scholar 

  33. Hobbs, G. B., Edwards, R. T. & Manchester, R. N. TEMPO2, a new pulsar-timing package – I. An overview. Mon. Not. R. Astron. Soc. 369, 655–672 (2006).

    Article  ADS  Google Scholar 

  34. Kopeikin, S. M. On possible implications of orbital parallaxes of wide orbit binary pulsars and their measurability. Astrophys. J. 439, L5–L8 (1995).

    Article  ADS  Google Scholar 

  35. Nordtvedt, K. Testing relativity with laser ranging to the Moon. Phys. Rev. 170, 1186–1187 (1968).

    Article  ADS  Google Scholar 

  36. Thirring, H. Über die Wirkung rotierender ferner Massen in der Einsteinschen Gravitationstheorie. Phys. Z. 19, 33 (1918).

    MATH  Google Scholar 

  37. Einstein, A. Über Gravitationswellen 154–167 (Königlich-Preußischen Akademie der Wissenschaften, Berlin, 1918).

    MATH  Google Scholar 

  38. Russell, H. N. On the advance of periastron in eclipsing binaries. Mon. Not. R. Astron. Soc. 88, 641–643 (1928).

    Article  ADS  Google Scholar 

  39. Smarr, L. L. & Blandford, R. The binary pulsar: physical processes, possible companions, and evolutionary histories. Astrophys. J. 207, 574–588 (1976).

    Article  ADS  Google Scholar 

  40. Gusinskaia, N. V. et al. Conquering systematics in the timing of the pulsar triple system J0337+1715: towards a unique and robust test of the strong equivalence principle. J. Phys. Conf. Ser. 932, 012003 (2017).

    Article  Google Scholar 

  41. Prodan, S. & Murray, N. On the dynamics and tidal dissipation rate of the white dwarf in 4U 1820−30. Astrophys. J. 747, 4 (2012).

    Article  ADS  Google Scholar 

  42. Wex, N. in Frontiers in Relativistic Celestial Mechanics. Volume 2: Applications and Experiments (ed. Kopeikin, S. M.) 39–102 (De Gruyter, Berlin, 2014).

  43. Luan, J. & Goldreich, P. Secular evolution of the pulsar triple system J0337+1715. Astrophys. J. 790, 82 (2014).

    Article  ADS  Google Scholar 

  44. Di Casola, E., Liberati, S. & Sonego, S. Nonequivalence of equivalence principles. Am. J. Phys. 83, 39–46 (2015).

    Article  ADS  Google Scholar 

  45. Damour, T. & Esposito-Farèse, G. Testing gravity to second post-Newtonian order: a field-theory approach. Phys. Rev. D 53, 5541–5578 (1996).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  46. Horbatsch, M. W. & Burgess, C. P. Model-independent comparisons of pulsar timings to scalar-tensor gravity. Class. Quantum Gravity 29, 245004 (2012).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. Bekenstein, J. D. Relativistic gravitation theory for the modified Newtonian dynamics paradigm. Phys. Rev. D 70, 083509 (2004).

    Article  ADS  CAS  Google Scholar 

  48. Shao, L. & Wex, N. Tests of gravitational symmetries with radio pulsars. Sci. China Phys. Mech. Astron. 59, 699501 (2016).

    Article  Google Scholar 

  49. Taylor, J. H., Wolszczan, A., Damour, T. & Weisberg, J. M. Experimental constraints on strong-field relativistic gravity. Nature 355, 132–136 (1992).

    Article  ADS  Google Scholar 

  50. Stairs, I. H. et al. Discovery of three wide-orbit binary pulsars: implications for binary evolution and equivalence principles. Astrophys. J. 632, 1060–1068 (2005).

    Article  ADS  Google Scholar 

  51. Arzoumanian, Z. et al. The neutron star interior composition explorer (NICER): mission definition. Proc. SPIE 9144, 914420 (2014).

    Article  Google Scholar 

  52. Irwin, A. W. & Fukushima, T. A numerical time ephemeris of the Earth. Astron. Astrophys. 348, 642–652 (1999).

    ADS  Google Scholar 

  53. Lorimer, D. R. & Kramer, M. in Handbook of Pulsar Astronomy Ch. 8, Appendix 2 (Cambridge Univ. Press, Cambridge, 2004).

    Google Scholar 

  54. Shklovskii, I. S. Possible causes of the secular increase in pulsar periods. Sov. Astron. 13, 562–565 (1970).

    ADS  Google Scholar 

  55. Pathak, D. & Bagchi, M. GalDynPsr: A package to estimate dynamical contributions in the rate of change of the period of radio pulsars. Preprint at https://arxiv.org/abs/1712.06590 (2017).

  56. Bovy, J. galpy: a python library for galactic dynamics. Astrophys. J. Suppl. Ser. 216, 29 (2015).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank P. Freire for pointing out how useful PSR J0337+1715 could be for testing the SEP, L. Shao for providing an independent cross-check on the signature of Δ and K. Nordvedt for explaining why the signature of Δ differs from that in lunar laser ranging. A.M.A. is supported by a Netherlands Foundation for Scientific Research (NWO) Veni grant. N.V.G. is supported by NOVA. J.W.T.H. acknowledges funding from an NWO Vidi fellowship and from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Starting Grant agreement number 337062 (‘DRAGNET’). A.T.D. is the recipient of an Australian Research Council Future Fellowship (FT150100415). D.R.L. also received support from NSF award OIA-1458952. S.M.R. and I.H.S. are Senior Fellows of the Canadian Institute for Advanced Research. I.H.S. is also supported by an NSERC Discovery Grant. The NANOGrav project (involving D.L.K., D.R.L., R.S.L., S.M.R. and I.H.S.) receives support from National Science Foundation (NSF) Physics Frontiers Center award number 1430284. The National Radio Astronomy Observatory is a facility of the NSF operated under cooperative agreement by Associated Universities. The Arecibo Observatory is operated by SRI International under a cooperative agreement with the NSF (AST-1100968), and in alliance with Ana G. Mendez-Universidad Metropolitana and the Universities Space Research Association. The Green Bank Observatory is a facility of the NSF operated under cooperative agreement by Associated Universities. The WSRT is operated by ASTRON with contributions from NWO.

Reviewer information

Nature thanks P. Freire and C. Will for their contribution to the peer review of this work.

Author information

Authors and Affiliations

Authors

Contributions

A.M.A. wrote the processing pipeline, orbital modelling, fitting and equation-of-state integration code, ran the data processing and fitting operations, wrote the manuscript, with substantial contributions from co-authors, and produced all figures and tables unless otherwise indicated. N.V.G. wrote the systematics analysis code, inspected observations for quality, carried out the systematics analysis, produced Table 1, Figs. 1, 2 and Extended Data Fig. 4, and wrote the section on orbital effects. J.W.T.H. carried out an intensive observing campaign with the WSRT. A.M.A., N.V.G., J.W.T.H., D.R.L., R.S.L., S.M.R. and I.H.S. carried out observations with Arecibo and the GBT. J.W.T.H., S.M.R. and I.H.S. carried out a preliminary version of the data processing. A.T.D. consulted on the astrometry. N.V.G. and D.L.K. carried out the tidal-effects analysis. All authors participated in discussions of the content of the paper.

Corresponding author

Correspondence to Anne M. Archibald.

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.

Extended data figures and tables

Extended Data Fig. 1 Template pulse profile used for timing.

This figure is based on the average 1,300–1,900-MHz profile from the GBT observation on MJD 56,412. The Stokes IQUV data have been smoothed by a wavelet-based algorithm (psrsmooth, PSRCHIVE). a, Total intensity (I) and linear (Q, U) and circular (V) polarization after correcting for Faraday rotation. An offset c has been subtracted; see below. b, Polarization angle (P.A.) at the centre frequency of the observation. The linear polarization (red) at some phases is responsible for almost half the flux density and its profile has complicated polarization structure. Offsets have been added to I and to \(\sqrt{{Q}^{2}+{U}^{2}}\) to ensure that I2 ≥ Q2 + U2 + V2.

Extended Data Fig. 2 Timing-model truncation error.

The root-mean-square (RMS) arrival-time error caused by the finite time steps of the orbital integrator is shown as a function of the tolerance parameter. The vertical dotted line is the value used for all orbits in this work; the RMS error from truncation is below 0.1 ns. Blue triangles are calculations done in hardware 80-bit floating point; black stars are calculations done in software 128-bit floating point, which are much slower to compute. To estimate the errors in this plot, we compute a fiducial solution with 128-bit precision and a tolerance parameter of 10−22 and compare all other solutions to this one.

Extended Data Fig. 3 Covariances between parameters that affect the orbit.

This plot does not include the parameters that are evaluated by linear least-squares fitting and marginalized out. Plots on the diagonal are single-parameter histograms; plots off the diagonal are pairwise two-dimensional histograms. See Extended Data Table 2 for parameter definitions.

Extended Data Fig. 4 Distribution of residuals divided by uncertainty, for each telescope.

The standard deviation σ represents the factor by which the scatter of the post-fit residuals exceeds the claimed uncertainties on pulse arrival times; μ is the mean of the distribution. Each colour represents a different telescope. Only observations in the 1,400-MHz frequency band are shown here. Here Δν and Δt are the bandwidth and time, respectively, over which the data are averaged to produce each pulse arrival time.

Extended Data Table 1 Fixed values and characteristics of the dataset
Extended Data Table 2 Fitted values
Extended Data Table 3 Inferred values

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Archibald, A.M., Gusinskaia, N.V., Hessels, J.W.T. et al. Universality of free fall from the orbital motion of a pulsar in a stellar triple system. Nature 559, 73–76 (2018). https://doi.org/10.1038/s41586-018-0265-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-018-0265-1

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

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