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
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Einstein, A. Die Grundlage der allgemeinen Relativitätstheorie. Ann. Phys. 354, 769–822 (1916).
Deruelle, N. Nordström’s scalar theory of gravity and the equivalence principle. Gen. Relativ. Gravit. 43, 3337–3354 (2011).
Genova, A. et al. Solar system expansion and strong equivalence principle as seen by the NASA MESSENGER mission. Nat. Commun. 9, 289 (2018).
Hofmann, F. & Müller, J. Relativistic tests with lunar laser ranging. Class. Quantum Gravity 35, 035015 (2018).
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).
Zhu, W. W. et al. Tests of gravitational symmetries with pulsar binary J1713+0747. Preprint at https://arxiv.org/abs/1802.09206 (2018).
The NANOGrav Collaboration. The NANOGrav nine-year data set: observations, arrival time measurements, and analysis of 37 millisecond pulsars. Astrophys. J. 813, 65 (2015).
Ransom, S. M. et al. A millisecond pulsar in a stellar triple system. Nature 505, 520–524 (2014).
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).
Nordtvedt, K. A post-Newtonian gravitational Lagrangian formalism for celestial body dynamics in metric gravity. Astrophys. J. 297, 390–404 (1985).
Meurer, A. et al. Sympy: symbolic computing in python. PeerJ Comput. Sci. 3, e103 (2017).
Damour, T. & Schaefer, G. New tests of the strong equivalence principle using binary-pulsar data. Phys. Rev. Lett. 66, 2549–2552 (1991).
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).
Will, C. M. in Theory and Experiment in Gravitational Physics Ch. 4 (Cambridge Univ. Press, Cambridge, 1981).
Damour, T. & Taylor, J. H. Strong-field tests of relativistic gravity and binary pulsars. Phys. Rev. D 45, 1840–1868 (1992).
Berti, E. et al. Testing general relativity with present and future astrophysical observations. Class. Quantum Gravity 32, 243001 (2015).
Damour, T. & Esposito-Farèse, G. Tensor-scalar gravity and binary-pulsar experiments. Phys. Rev. D 54, 1474–1491 (1996).
Brans, C. & Dicke, R. H. Mach’s principle and a relativistic theory of gravitation. Phys. Rev. 124, 925–935 (1961).
Damour, T. & Esposito-Farese, G. Tensor-multi-scalar theories of gravitation. Class. Quantum Gravity 9, 2093–2176 (1992).
Bertotti, B., Iess, L. & Tortora, P. A test of general relativity using radio links with the Cassini spacecraft. Nature 425, 374–376 (2003).
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).
Antoniadis, J. et al. A massive pulsar in a compact relativistic binary. Science 340, 1233232 (2013).
Mignard, F. & Klioner, S. A. Gaia: relativistic modelling and testing. Proc. Int. Astron. Union 261, 306–314 (2010).
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).
Haensel, P., Proszynski, M. & Kutschera, M. Uncertainty in the saturation density of nuclear matter and neutron star models. Astron. Astrophys. 102, 299–302 (1981).
DuPlain, R. et al. Launching GUPPI: the Green Bank ultimate pulsar processing instrument. Proc. SPIE 7019, 70191D (2008).
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).
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).
van Straten, W. Radio astronomical polarimetry and high-precision pulsar timing. Astrophys. J. 642, 1004–1011 (2006).
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).
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).
Bulirsch, R. & Stoer, J. Asymptotic upper and lower bounds for results of extrapolation methods. Numer. Math. 8, 93–104 (1966).
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).
Kopeikin, S. M. On possible implications of orbital parallaxes of wide orbit binary pulsars and their measurability. Astrophys. J. 439, L5–L8 (1995).
Nordtvedt, K. Testing relativity with laser ranging to the Moon. Phys. Rev. 170, 1186–1187 (1968).
Thirring, H. Über die Wirkung rotierender ferner Massen in der Einsteinschen Gravitationstheorie. Phys. Z. 19, 33 (1918).
Einstein, A. Über Gravitationswellen 154–167 (Königlich-Preußischen Akademie der Wissenschaften, Berlin, 1918).
Russell, H. N. On the advance of periastron in eclipsing binaries. Mon. Not. R. Astron. Soc. 88, 641–643 (1928).
Smarr, L. L. & Blandford, R. The binary pulsar: physical processes, possible companions, and evolutionary histories. Astrophys. J. 207, 574–588 (1976).
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).
Prodan, S. & Murray, N. On the dynamics and tidal dissipation rate of the white dwarf in 4U 1820−30. Astrophys. J. 747, 4 (2012).
Wex, N. in Frontiers in Relativistic Celestial Mechanics. Volume 2: Applications and Experiments (ed. Kopeikin, S. M.) 39–102 (De Gruyter, Berlin, 2014).
Luan, J. & Goldreich, P. Secular evolution of the pulsar triple system J0337+1715. Astrophys. J. 790, 82 (2014).
Di Casola, E., Liberati, S. & Sonego, S. Nonequivalence of equivalence principles. Am. J. Phys. 83, 39–46 (2015).
Damour, T. & Esposito-Farèse, G. Testing gravity to second post-Newtonian order: a field-theory approach. Phys. Rev. D 53, 5541–5578 (1996).
Horbatsch, M. W. & Burgess, C. P. Model-independent comparisons of pulsar timings to scalar-tensor gravity. Class. Quantum Gravity 29, 245004 (2012).
Bekenstein, J. D. Relativistic gravitation theory for the modified Newtonian dynamics paradigm. Phys. Rev. D 70, 083509 (2004).
Shao, L. & Wex, N. Tests of gravitational symmetries with radio pulsars. Sci. China Phys. Mech. Astron. 59, 699501 (2016).
Taylor, J. H., Wolszczan, A., Damour, T. & Weisberg, J. M. Experimental constraints on strong-field relativistic gravity. Nature 355, 132–136 (1992).
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).
Arzoumanian, Z. et al. The neutron star interior composition explorer (NICER): mission definition. Proc. SPIE 9144, 914420 (2014).
Irwin, A. W. & Fukushima, T. A numerical time ephemeris of the Earth. Astron. Astrophys. 348, 642–652 (1999).
Lorimer, D. R. & Kramer, M. in Handbook of Pulsar Astronomy Ch. 8, Appendix 2 (Cambridge Univ. Press, Cambridge, 2004).
Shklovskii, I. S. Possible causes of the secular increase in pulsar periods. Sov. Astron. 13, 562–565 (1970).
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).
Bovy, J. galpy: a python library for galactic dynamics. Astrophys. J. Suppl. Ser. 216, 29 (2015).
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
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
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.
Rights and permissions
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41586-018-0265-1