Fast core rotation in red-giant stars as revealed by gravity-dominated mixed modes



When the core hydrogen is exhausted during stellar evolution, the central region of a star contracts and the outer envelope expands and cools, giving rise to a red giant. Convection takes place over much of the star’s radius. Conservation of angular momentum requires that the cores of these stars rotate faster than their envelopes; indirect evidence supports this1,2. Information about the angular-momentum distribution is inaccessible to direct observations, but it can be extracted from the effect of rotation on oscillation modes that probe the stellar interior. Here we report an increasing rotation rate from the surface of the star to the stellar core in the interiors of red giants, obtained using the rotational frequency splitting of recently detected ‘mixed modes’3,4. By comparison with theoretical stellar models, we conclude that the core must rotate at least ten times faster than the surface. This observational result confirms the theoretical prediction of a steep gradient in the rotation profile towards the deep stellar interior1,5,6.

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Figure 1: Oscillation spectrum of KIC 8366239.
Figure 2: Contributions to the total rotational splitting.
Figure 3: Rotational splitting versus mode linewidth for KIC 8366239.


  1. 1

    Sills, A. & Pinsonneault, M. H. Rotation of horizontal-branch stars in globular clusters. Astrophys. J. 540, 489–503 (2000)

    ADS  Article  Google Scholar 

  2. 2

    Sweigart, A. V. & Mengel, J. G. Meridional circulation and CNO anomalies in red giant stars. Astrophys. J. 229, 624–641 (1979)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Beck, P. G. et al. Kepler detected gravity-mode period spacings in a red giant star. Science 332, 205 (2011)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Bedding, T. R. et al. Gravity modes as a way to distinguish between hydrogen- and helium-burning red giant stars. Nature 471, 608–611 (2011)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Zahn, J.-P. Circulation and turbulence in rotating stars. Astron. Astrophys. 265, 115–132 (1992)

    ADS  Google Scholar 

  6. 6

    Eggenberger, P. et al. Effects of rotation on the evolution and asteroseismic properties of red giants. Astron. Astrophys. 509, A72 (2010)

    Article  Google Scholar 

  7. 7

    Aerts, C., Christensen-Dalsgaard, J. & Kurtz, D. W. Asteroseismology Ch. 3 (Springer-Verlag, 2010)

    Google Scholar 

  8. 8

    De Ridder, J. et al. Non-radial oscillation modes with long lifetimes in giant stars. Nature 459, 398–400 (2009)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Dziembowski, W. A. et al. Oscillations of α UMa and other red giants. Mon. Not. R. Astron. Soc. 328, 601–610 (2001)

    ADS  Article  Google Scholar 

  10. 10

    Christensen-Dalsgaard, J. Physics of solar-like oscillations. Sol. Phys. 220, 137–168 (2004)

    ADS  Article  Google Scholar 

  11. 11

    Dupret, M.-A. et al. Theoretical amplitudes and lifetimes of non-radial solar-like oscillations in red giants. Astron. Astrophys. 506, 57–67 (2009)

    ADS  Article  Google Scholar 

  12. 12

    Montalbán, J., Miglio, A., Noels, A., Scuflaire, R. & Ventura, P. Seismic diagnostics of red giants: first comparison with stellar models. Astrophys. J. 721, L182–L188 (2010)

    ADS  Article  Google Scholar 

  13. 13

    Mosser, B. et al. The universal red-giant oscillation pattern. An automated determination with CoRoT data. Astron. Astrophys. 525, L9 (2011)

    ADS  Article  Google Scholar 

  14. 14

    Kallinger, T. et al. Asteroseismology of red giants from the first four months of Kepler data: fundamental stellar parameters. Astron. Astrophys. 522, A1 (2010)

    Article  Google Scholar 

  15. 15

    García, R. A. et al. Tracking solar gravity modes: the dynamics of the solar core. Science 316, 1591–1593 (2007)

    ADS  Article  Google Scholar 

  16. 16

    Elsworth, Y. et al. Slow rotation of the Sun's interior. Nature 376, 669–672 (1995)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Chaplin, W. J. et al. Rotation of the solar core from BiSON and LOWL frequency observations. Mon. Not. R. Astron. Soc. 308, 405–414 (1999)

    ADS  Article  Google Scholar 

  18. 18

    Thompson, M. J. et al. The internal rotation of the Sun. Annu. Rev. Astron. Astrophys. 41, 599–643 (2003)

    ADS  Article  Google Scholar 

  19. 19

    Aerts, C. et al. Asteroseismology of HD 129929: core overshooting and nonrigid rotation. Science 300, 1926–1928 (2003)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Pamyatnykh, A. A. et al. Asteroseismology of the β Cephei star ν Eridani: interpretation and applications of the oscillation spectrum. Mon. Not. R. Astron. Soc. 350, 1022–1028 (2004)

    ADS  Article  Google Scholar 

  21. 21

    Kawaler, S. D., Sekii, T. & Gough, D. Prospects for measuring differential rotation in white dwarfs through asteroseismology. Astrophys. J. 516, 349–365 (1999)

    ADS  Article  Google Scholar 

  22. 22

    Bedding, T. R. et al. Solar-like oscillations in low-luminosity red giants: first results from Kepler . Astrophys. J. Lett. 713, L176–L181 (2010)

    ADS  Article  Google Scholar 

  23. 23

    García, R. A. et al. Preparation of Kepler light curves for asteroseismic analyses. Mon. Not. R. Astron. Soc. 414, L6–L10 (2011)

    ADS  Article  Google Scholar 

  24. 24

    Ledoux, P. The nonradial oscillations of gaseous stars and the problem of beta Canis Majoris. Astrophys. J. 114, 373–384 (1951)

    ADS  Article  Google Scholar 

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We acknowledge the work of the team behind Kepler. Funding for the Kepler Mission is provided by NASA's Science Mission Directorate. P.G.B. and C.A. were supported by the European Community’s Seventh Framework Programme (ERC grant PROSPERITY); J.D.R. and T.K. were supported by the Fund for Scientific Research, Flanders. S.H. was supported by the Netherlands Organisation for Scientific Research. J.M. and M.V. were supported by the Belgian Science Policy Office. The work is partly based on observations with the High Efficiency and Resolution Mercator Echelle Spectrograph at the Mercator Telescope, which is operated at La Palma in Spain by the Flemish Community.

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P.G.B., T.K., J.D.R., C.A., R.A.G., S.H., B.M., Y.E., S.F., F.C. and M.G. measured the mode parameters, and derived and interpreted the rotational splitting and period spacings. J.M., M.-A.D., P.E., J.C.-D. and A.M. calculated stellar models and provided theoretical interpretation of the rotational splitting. M.H. and M.V. observed and analysed the spectra. J.D.R., S.H., S.F., Y.E., D.S., T.R.B., H.K., F.R.G., J.R.H. and K.A.I. contributed to the coordination of the project, including the acquisition and distribution of the data. C.A. defined and supervised the research. All authors discussed the results and commented on the manuscript.

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Correspondence to Paul G. Beck.

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Beck, P., Montalban, J., Kallinger, T. et al. Fast core rotation in red-giant stars as revealed by gravity-dominated mixed modes. Nature 481, 55–57 (2012).

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