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Misaligned spin and orbital axes cause the anomalous precession of DI Herculis


The orbits of binary stars precess as a result of general relativistic effects, forces arising from the asphericity of the stars, and forces from any additional stars or planets in the system. For most binaries, the theoretical and observed precession rates are in agreement1. One system, however—DI Herculis—has resisted explanation for 30 years2,3,4. The observed precession rate is a factor of four slower than the theoretical rate, a disagreement that once was interpreted as evidence for a failure of general relativity5. Among the contemporary explanations are the existence of a circumbinary planet6 and a large tilt of the stellar spin axes with respect to the orbit7,8. Here we report that both stars of DI Herculis rotate with their spin axes nearly perpendicular to the orbital axis (contrary to the usual assumption for close binary stars). The rotationally induced stellar oblateness causes precession in the direction opposite to that of relativistic precession, thereby reconciling the theoretical and observed rates.

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Figure 1: Distortion of stellar absorption lines during eclipses.
Figure 2: Apparent radial velocities of DI Herculis.
Figure 3: Apsidal motion of DI Herculis, calculated and observed.


  1. Claret, A. & Giménez, Á. The apsidal motion test of the internal stellar structure—comparison between theory and observations. Astron. Astrophys. 277, 487–502 (1993)

    ADS  Google Scholar 

  2. Martynov, D. I. & Khaliullin, K. F. On the relativistic motion of the periastron in the eclipsing binary system DI Herculis. Astrophys. Space Sci. 71, 147–170 (1980)

    Article  ADS  CAS  Google Scholar 

  3. Guinan, E. F. & Maloney, F. P. The apsidal motion of the eccentric eclipsing binary DI Herculis—an apparent discrepancy with general relativity. Astron. J. 90, 1519–1528 (1985)

    Article  ADS  Google Scholar 

  4. Claret, A. Some notes on the relativistic apsidal motion of DI Herculis. Astron. Astrophys. 330, 533–540 (1998)

    ADS  Google Scholar 

  5. Moffat, J. W. The orbital motion of DI Herculis as a test of a theory of gravitation. Astrophys. J. 287, L77–L79 (1984)

    Article  ADS  Google Scholar 

  6. Hsuan, K. & Mardling, R. A. A Three body solution for the DI Her system. Astrophys. Space Sci. 304, 243–246 (2006)

    Article  ADS  Google Scholar 

  7. Shakura, N. I. On the apsidal motion in binary stars. Sov. Astron. L, 224–226 (1985)

    ADS  Google Scholar 

  8. Company, R., Portilla, M. & Giménez, Á. On the apsidal motion of DI Herculis. Astrophys. J. 335, 962–964 (1988)

    Article  ADS  Google Scholar 

  9. Popper, D. M. Rediscussion of eclipsing binaries. XIII—DI Herculis, a B-type system with an eccentric orbit. Astrophys. J. 254, 203–213 (1982)

    Article  ADS  CAS  Google Scholar 

  10. Perruchot, S. et al. The SOPHIE spectrograph: design and technical key-points for high throughput and high stability. SPIE Conf. Ser. 7014 10.1117/12.787379 (2008)

  11. Holt, J. R. Spectroscopic determination of stellar rotation. Astron. Astrophys. 12, 646 (1893)

    Google Scholar 

  12. Rossiter, R. A. On the detection of an effect of rotation during eclipse in the velocity of the brighter component of beta Lyrae, and on the constancy of velocity of this system. Astrophys. J. 60, 15–21 (1924)

    Article  ADS  Google Scholar 

  13. McLaughlin, D. B. Some results of a spectrographic study of the Algol system. Astrophys. J. 60, 22–31 (1924)

    Article  ADS  Google Scholar 

  14. Albrecht, S., Reffert, S., Snellen, I., Quirrenbach, A. & Mitchell, D. S. The spin axes orbital alignment of both stars within the eclipsing binary system V1143 Cyg using the Rossiter-McLaughlin effect. Astron. Astrophys. 474, 565–573 (2007)

    Article  ADS  Google Scholar 

  15. Queloz, D. et al. Detection of a spectroscopic transit by the planet orbiting the star HD209458. Astron. Astrophys. 359, L13–L17 (2000)

    ADS  Google Scholar 

  16. Winn, J. N. et al. Measurement of spin-orbit alignment in an extrasolar planetary system. Astrophys. J. 631, 1215–1226 (2005)

    Article  ADS  Google Scholar 

  17. Gray, D. F. The Observation and Analysis of Stellar Photospheres 3rd edn (Cambridge Univ. Press, 2005)

    Book  Google Scholar 

  18. Markwardt, C. B. Non-linear least squares fitting in IDL with MPFIT. Preprint at 〈〉 2009

  19. Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. Numerical Recipes in C. The Art of Scientific Computing 2nd edn 689–699 (Cambridge Univ. Press, 1992)

    MATH  Google Scholar 

  20. Von Zeipel, H. The radiative equilibrium of a slightly oblate rotating star. Mon. Not. R. Astron. Soc. 84, 684–701 (1924)

    Article  ADS  Google Scholar 

  21. Guinan, E. F., Marshall, J. J. & Maloney, F. P. A new apsidal motion determination for DI Herculis. Inform. Bull. Variable Stars 4101, 1–44 (1994)

    ADS  Google Scholar 

  22. Fabrycky, D. & Tremaine, S. Shrinking binary and planetary orbits by Kozai cycles with tidal friction. Astrophys. J. 669, 1298–1315 (2007)

    Article  ADS  CAS  Google Scholar 

  23. Chelli, A. & Petrov, R. G. Model fitting and error analysis for differential interferometry. II. Application to rotating stars and binary systems. Astron. Astrophys. 109 (Suppl.). 401–415 (1995)

    ADS  Google Scholar 

  24. Le Bouquin, J. B. The spin-orbit alignment of the Fomalhaut planetary system probed by optical long baseline interferometry. Astron. Astrophys. 498, L41–L44 (2009)

    Article  ADS  Google Scholar 

  25. Reisenberger, M. P. & Guinan, E. F. A possible rescue of general relativity in DI Herculis. Astron. J. 97, 216–221 (1989)

    Article  ADS  CAS  Google Scholar 

  26. Van Dien, E. Axial rotation of the brighter stars in the Pleiades cluster. J. R. Astron. Soc. Can. 42, 249–261 (1948)

    ADS  Google Scholar 

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We are grateful to Á. Giménez, E. Guinan and T. Mazeh for bringing DI Herculis to our attention. We thank J. Lub, R. Tubbs, C. Hopman, Y. Levin and D. Fabrycky for discussions about double stars and their properties. We also thank H. Reckman for essential help during one observing run. We are grateful to the Sophie team for building the spectrograph and reduction pipeline. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, and the Vienna Atomic Line database (VALD) located at S.A. acknowledges support during part of this project by a Rubicon fellowship from the Netherlands Organisation for Scientific Research (NWO). J.N.W. acknowledges support from a NASA Origins grant (NNX09AD36G). S.A. and S.R. acknowledge funding from the Optical Infrared Coordination network (OPTICON).

Author Contributions S.A. participated in the development of the concept of this research and the analysis code, participated in the observations, the analysis and interpretation of the data and writing the manuscript. S.R. participated in the development of the concept of this research and the analysis code and the observations. I.A.G.S. participated in the analysis and interpretation of the data and in writing the manuscript. J.N.W. participated in the analysis and interpretation of the data and in writing the manuscript.

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Correspondence to Simon Albrecht.

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Albrecht, S., Reffert, S., Snellen, I. et al. Misaligned spin and orbital axes cause the anomalous precession of DI Herculis. Nature 461, 373–376 (2009).

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