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Weakened magnetic braking supported by asteroseismic rotation rates of Kepler dwarfs


Studies using asteroseismic ages and rotation rates from star-spot rotation have indicated that standard age–rotation relations may break down roughly half way through the main sequence lifetime, a phenomenon referred to as weakened magnetic braking. Although rotation rates from spots can be difficult to determine for older, less active stars, rotational splitting of asteroseismic oscillation frequencies can provide rotation rates for both active and quiescent stars, and so can confirm whether this effect really takes place on the main sequence. We obtained asteroseismic rotation rates of 91 main sequence stars showing high signal-to-noise modes of oscillation. Using these new rotation rates, along with effective temperatures, metallicities and seismic masses and ages, we built a hierarchical Bayesian mixture model to determine whether the ensemble more closely agreed with a standard rotational evolution scenario, or one where weakened magnetic braking takes place. The weakened magnetic braking scenario was found to be 98.4% more likely for our stellar ensemble, adding to the growing body of evidence for this stage of stellar rotational evolution. This work presents a large catalogue of seismic rotation rates for stars on the main sequence, which opens up possibilities for more detailed ensemble analysis of rotational evolution with Kepler.

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Fig. 1: Our sample of 95 stars from the Kages and LEGACY catalogues.
Fig. 2: Comparisons between asteroseismic and photometric measures of stellar rotation for 48 stars.
Fig. 3: Stars for which rotation was measured in this work plotted over two stellar population models of rotational evolution.
Fig. 4: Posterior estimates of the mixture model parameter QWMB by stellar classification.

Data availability

The core input data and results are summarized in Supplementary Table 1, which is available in a machine-readable format as Supplementary Data 1. Larger data files, such as stellar model populations and individual posterior distribution chains from the asteroseismic and gyrochronology model fitting are fully available on request from the corresponding author. This work made use of publicly available data. Kepler power spectral densities were obtained from the KASOC webpages for the majority of stars, and from the MAST for 16 Cyg A and B. This work used asteroseismic data from refs. 7,22,23,24. Parameter distributions of the Kepler field used to alter our stellar population models were taken from ref. 36.

Code availability

The code required to replicate our results has been placed in a curated online repository at All code written in the duration of this project, along with a full commit history, can be found in an uncurated online repository at The code used to construct the stellar population models used in this work is available upon request from the corresponding author.


  1. 1.

    Barnes, S. A. Ages for illustrative field stars using gyrochronology: viability, limitations, and errors. Astrophys. J. 669, 1167–1189 (2007).

    ADS  Article  Google Scholar 

  2. 2.

    Meibom, S. et al. A spin-down clock for cool stars from observations of a 2.5-billion-year-old cluster. Nature 517, 589–591 (2015).

    ADS  Article  Google Scholar 

  3. 3.

    Leiner, E., Mathieu, R. D., Vanderburg, A., Gosnell, N. M. & Smith, J. C. Blue Lurkers: hidden blue stragglers on the M67 main sequence identified from their Kepler/K2 rotation periods. Astrophys. J. 881, 47 (2019).

    ADS  Article  Google Scholar 

  4. 4.

    Claytor, Z. R. et al. Chemical evolution in the Milky Way: rotation-based ages for APOGEE-Kepler cool dwarf stars. Astrophys. J. 888, 43 (2020).

    ADS  Article  Google Scholar 

  5. 5.

    Barnes, S. A., Weingrill, J., Fritzewski, D., Strassmeier, K. G. & Platais, I. Rotation periods for cool stars in the 4 Gyr old Open Cluster M67, the solar-stellar connection, and the applicability of gyrochronology to at least solar age. Astrophys. J. 823, 16 (2016).

    ADS  Article  Google Scholar 

  6. 6.

    Borucki, W. J. et al. Kepler planet-detection mission: introduction and first results. Science 327, 977–980 (2010).

    ADS  Article  Google Scholar 

  7. 7.

    Silva Aguirre, V. et al. Ages and fundamental properties of Kepler exoplanet host stars from asteroseismology. Mon. Not. R. Astron. Soc. 452, 2127–2148 (2015).

    ADS  Article  Google Scholar 

  8. 8.

    Angus, R., Aigrain, S., Foreman-Mackey, D. & McQuillan, A. Calibrating gyrochronology using Kepler asteroseismic targets. Mon. Not. R. Astron. Soc. 450, 1787–1798 (2015).

    ADS  Article  Google Scholar 

  9. 9.

    Nielsen, M. B., Schunker, H., Gizon, L. & Ball, W. H. Constraining differential rotation of Sun-like stars from asteroseismic and starspot rotation periods. Astron. Astrophys. 582, A10 (2015).

    ADS  Article  Google Scholar 

  10. 10.

    Davies, G. R. et al. Asteroseismic inference on rotation, gyrochronology and planetary system dynamics of 16 Cygni. Mon. Not. R. Astron. Soc. 446, 2959–2966 (2015).

    ADS  Article  Google Scholar 

  11. 11.

    van Saders, J. L. et al. Weakened magnetic braking as the origin of anomalously rapid rotation in old field stars. Nature 529, 181–184 (2016).

    ADS  Article  Google Scholar 

  12. 12.

    Réville, V., Brun, A. S., Matt, S. P., Strugarek, A. & Pinto, R. F. The effect of magnetic topology on thermally driven wind: toward a general formulation of the braking law. Astrophys. J. 798, 116 (2015).

    ADS  Article  Google Scholar 

  13. 13.

    Garraffo, C., Drake, J. J. & Cohen, O. The missing magnetic morphology term in stellar rotation evolution. Astron. Astrophys. 595, A110 (2016).

    ADS  Article  Google Scholar 

  14. 14.

    Metcalfe, T. S., Egeland, R. & van Saders, J. Stellar evidence that the solar dynamo may be in transition. Astrophys. J. Lett. 826, L2 (2016).

    ADS  Article  Google Scholar 

  15. 15.

    Metcalfe, T. S. et al. LBT/PEPSI spectropolarimetry of a magnetic morphology shift in old solar-type stars. Astrophys. J. 887, L38 (2019).

    ADS  Article  Google Scholar 

  16. 16.

    See, V. et al. Do non-dipolar magnetic fields contribute to spin-down torques? Astrophys. J. 886, 120 (2019).

    ADS  Article  Google Scholar 

  17. 17.

    McQuillan, A., Mazeh, T. & Aigrain, S. Rotation periods of 34,030 Kepler main-sequence stars: the full autocorrelation sample. Astrophys. J. Suppl. Ser. 211, 24 (2014).

    ADS  Article  Google Scholar 

  18. 18.

    Matt, S. P., Brun, A. S., Baraffe, I., Bouvier, J. & Chabrier, G. The mass-dependence of angular momentum evolution in Sun-like stars. Astrophys. J. 799, L23 (2015).

    ADS  Article  Google Scholar 

  19. 19.

    Reinhold, T. et al. The Sun is less active than other solar-like stars. Science 368, 518–521 (2020).

    ADS  Article  Google Scholar 

  20. 20.

    van Saders, J. L., Pinsonneault, M. H. & Barbieri, M. Forward modeling of the Kepler stellar rotation period distribution: interpreting periods from mixed and biased stellar populations. Astrophys. J. 872, 128 (2019).

    ADS  Article  Google Scholar 

  21. 21.

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

    ADS  Article  Google Scholar 

  22. 22.

    Davies, G. R. et al. Oscillation frequencies for 35 Kepler solar-type planet-hosting stars using Bayesian techniques and machine learning. Mon. Not. R. Astron. Soc. 456, 2183–2195 (2016).

    ADS  Article  Google Scholar 

  23. 23.

    Lund, M. N. et al. Standing on the shoulders of dwarfs: the Kepler Asteroseismic LEGACY sample. I. Oscillation mode parameters. Astrophys. J. 835, 172 (2017).

    ADS  Article  Google Scholar 

  24. 24.

    Silva Aguirre, V. et al. Standing on the shoulders of dwarfs: the Kepler asteroseismic LEGACY sample. II. Radii, masses, and ages. Astrophys. J. 835, 173 (2017).

    ADS  Article  Google Scholar 

  25. 25.

    García, R. A. et al. Rotation and magnetism of Kepler pulsating solar-like stars. Towards asteroseismically calibrated age-rotation relations. Astron. Astrophys. 572, A34 (2014).

    Article  Google Scholar 

  26. 26.

    Kraft, R. P. Studies of stellar rotation. V. The dependence of rotation on age among solar-type stars. Astrophys. J. 150, 551 (1967).

    ADS  Article  Google Scholar 

  27. 27.

    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 

  28. 28.

    Benomar, O. et al. Asteroseismic detection of latitudinal differential rotation in 13 Sun-like stars. Science 361, 1231–1234 (2018).

    ADS  Article  Google Scholar 

  29. 29.

    Lund, M. N., Miesch, M. S. & Christensen-Dalsgaard, J. Differential rotation in main-sequence solar-like stars: qualitative inference from asteroseismic data. Astrophys. J. 790, 121 (2014).

    ADS  Article  Google Scholar 

  30. 30.

    Benomar, O., Takata, M., Shibahashi, H., Ceillier, T. & García, R. A. Nearly uniform internal rotation of solar-like main-sequence stars revealed by space-based asteroseismology and spectroscopic measurements. Mon. Not. R. Astron. Soc. 452, 2654–2674 (2015).

    ADS  Article  Google Scholar 

  31. 31.

    Gizon, L. et al. Seismic constraints on rotation of Sun-like star and mass of exoplanet. Proc. Natl Acad. Sci. USA 110, 13267–13271 (2013).

    ADS  Article  Google Scholar 

  32. 32.

    Chaplin, W. J. et al. Asteroseismic determination of obliquities of the exoplanet systems Kepler-50 and Kepler-65. Astrophys. J. 766, 101 (2013).

    ADS  Article  Google Scholar 

  33. 33.

    Skumanich, A. Time scales for Ca II emission decay, rotational braking, and lithium depletion. Astrophys. J. 171, 565 (1972).

    ADS  Article  Google Scholar 

  34. 34.

    Kawaler, S. D. Angular momentum loss in low-mass stars. Astrophys. J. 333, 236 (1988).

    ADS  Article  Google Scholar 

  35. 35.

    Girardi, L. et al. in Red Giants as Probes of the Structure and Evolution of the Milky Way (eds Miglio, A. et al.) 165–170 (Springer, 2013).

  36. 36.

    Berger, T. A., Huber, D., Gaidos, E., van Saders, J. L. & Weiss, L. M. The Gaia-Kepler Stellar Properties Catalog. II. Planet radius demographics as a function of stellar mass and age. Astron. J. 160, 108 (2020).

    ADS  Article  Google Scholar 

  37. 37.

    Gelman, A. & Rubin, D. B. Inference from iterative simulation using multiple sequences. Stat. Sci. 7, 457–472 (1992).

    MATH  Google Scholar 

  38. 38.

    Salvatier, J., Wiecki, T. V. & Fonnesbeck, C. Probabilistic programming in Python using PyMC3. PeerJ Comp. Sci. 2, e55 (2016).

    Article  Google Scholar 

  39. 39.

    Metcalfe, T. S. & Egeland, R. Understanding the limitations of gyrochronology for old field stars. Astrophys. J. 871, 39 (2019).

    ADS  Article  Google Scholar 

  40. 40.

    Lorenzo-Oliveira, D. et al. Constraining the evolution of stellar rotation using solar twins. Mon. Not. R. Astron. Soc. 485, L68–L72 (2019).

    ADS  Article  Google Scholar 

  41. 41.

    van Saders, J. L. & Pinsonneault, M. H. Fast star, slow star; old star, young star: subgiant rotation as a population and stellar physics diagnostic. Astrophys. J. 776, 67 (2013).

    ADS  Article  Google Scholar 

  42. 42.

    Barnes, S. A. A simple nonlinear model for the rotation of main-sequence cool stars. I. Introduction, implications for gyrochronology, and color-period diagrams. Astrophys. J. 722, 222–234 (2010).

    ADS  Article  Google Scholar 

  43. 43.

    Deng, L.-C. et al. LAMOST Experiment for Galactic Understanding and Exploration (LEGUE)—the survey’s science plan. Res. Astron. Astrophys. 12, 735–754 (2012).

    ADS  Article  Google Scholar 

  44. 44.

    de Jong, R. S. et al. 4MOST: 4-metre multi-object spectroscopic telescope. Proc. SPIE 9147, 91470M (2014).

    Article  Google Scholar 

  45. 45.

    Dalton, G. et al. Project overview and update on WEAVE: the next generation wide-field spectroscopy facility for the William Herschel Telescope. Proc SPIE 9147, 91470L (2014).

    Google Scholar 

  46. 46.

    Blanton, M. et al. The Sloan Digital Sky Survey as an Archetypal Mid-Scale Program. Bull. Am. Astron. Soc. 51, 196 (2019).

  47. 47.

    Kollmeier, J. et al. SDSS-V pioneering panoptic spectroscopy. Bull. Am. Astron. Soc. 51, 274 (2019).

  48. 48.

    Handberg, R. & Lund, M. N. Automated preparation of Kepler time series of planet hosts for asteroseismic analysis. Mon. Not. R. Astron. Soc. 445, 2698–2709 (2014).

    ADS  Article  Google Scholar 

  49. 49.

    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 

  50. 50.

    Christensen-Dalsgaard, J. ASTEC—the Aarhus STellar Evolution Code. Astrophys. Space Sci. 316, 13 (2008).

    ADS  Article  Google Scholar 

  51. 51.

    Buchhave, L. A. & Latham, D. W. The metallicities of stars with and without transiting planets. Astrophys. J. 808, 187 (2015).

    ADS  Article  Google Scholar 

  52. 52.

    Astropy Collaboration et al. Astropy: A community Python package for astronomy. Astron. Astrophys. 558, A33 (2013).

  53. 53.

    Astropy Collaboration et al. The Astropy Project: building an open-science project and status of the v2.0 core package. Astron. J. 156, 123 (2018).

  54. 54.

    Ginsburg, A. et al. Astroquery: an astronomical web-querying package in Python. Astron. J. 157, 98 (2019).

    ADS  Article  Google Scholar 

  55. 55.

    McKinney, W. Data structures for statistical computing in Python. In Proc. 9th Python in Science Conference 51–56 (2010);

  56. 56.

    Harvey, J. High-resolution helioseismology. In Future Missions in Solar, Heliospheric & Space Plasma Physics (eds Rolfe, E. & Battrick, B.) 199 (ESA Scientific & Technical Publications Branch, 1985).

  57. 57.

    Tassoul, M. Asymptotic approximations for stellar nonradial pulsations. Astrophys. J. Suppl. Ser. 43, 469–490 (1980).

    ADS  Article  Google Scholar 

  58. 58.

    Vrard, M., Mosser, B. & Samadi, R. Period spacings in red giants. II. Automated measurement. Astron. Astrophys. 588, A87 (2016).

    ADS  Google Scholar 

  59. 59.

    Hogg, D. W., Bovy, J. & Lang, D. Data analysis recipes: fitting a model to data. Preprint at (2010).

  60. 60.

    Hall, O. J. et al. Testing asteroseismology with Gaia DR2: hierarchical models of the Red Clump. Mon. Not. R. Astron. Soc. 486, 3569–3585 (2019).

    ADS  Article  Google Scholar 

  61. 61.

    Mazumdar, A. et al. Measurement of acoustic glitches in solar-type stars from oscillation frequencies observed by Kepler. Astrophys. J. 782, 18 (2014).

    ADS  Article  Google Scholar 

  62. 62.

    Chaplin, W. J. & Basu, S. Asteroseismic Data Analysis: Foundations and Techniques 1st edn (Princeton Univ. Press, 2017).

  63. 63.

    Van Hoey, S., van der Kwast, J., Nopens, I. & Seuntjens, P. Python package for model STructure ANalysis (pySTAN). In EGU General Assembly Conference Abstracts EGU2013–10059 (2013).

  64. 64.

    Carpenter, B. et al. Stan: a probabilistic programming language. J. Stat. Softw. 76, (2017).

  65. 65.

    van der Walt, S., Colbert, S. C. & Varoquaux, G. The NumPy array: a structure for efficient numerical computation. Comput. Sci. Eng. 13, 22–30 (2011).

    Article  Google Scholar 

  66. 66.

    Theano Development Team et al. Theano: a Python framework for fast computation of mathematical expressions. Preprint at (2016).

  67. 67.

    Gaia Collaboration et al. Gaia Data Release 2 – summary of the contents and survey properties. Astron. Astrophys. 616, A1 (2018).

  68. 68.

    Raghavan, D. et al. A survey of stellar families: multiplicity of solar-type stars. Astrophys. J. Suppl. Ser. 190, 1 (2010).

    ADS  Article  Google Scholar 

  69. 69.

    Chaplin, W. J. et al. Ensemble asteroseismology of solar-type stars with the NASA Kepler mission. Science 332, 213–216 (2011).

    ADS  Article  Google Scholar 

  70. 70.

    Seabold, S. & Perktold, J. Statsmodels: econometric and statistical modeling with Python. In Proc. 9th Python in Science Conference (eds van der Walt, S. & Millman, J.) 92–96 (2010);

  71. 71.

    Betancourt, M. J. & Girolami, M. Hamiltonian Monte Carlo for hierarchical models. Preprint (2013).

  72. 72.

    Foreman-Mackey, D., Hogg, D. W., Lang, D. & Goodman, J. Emcee: the MCMC hammer. Publ. Astron. Soc. Pac. 125, 306–312 (2013).

    ADS  Article  Google Scholar 

  73. 73.

    Foreman-Mackey, D. scatterplot matrices in Python. J. Open Source Softw. 1, 24 (2016);

  74. 74.

    Bonanno, A. & Fröhlich, H.-E. A Bayesian estimation of the helioseismic solar age. Astron. Astrophys. 580, A130 (2015).

    ADS  Article  Google Scholar 

  75. 75.

    Paxton, B. et al. Modules for Experiments in Stellar Astrophysics (MESA): convective boundaries, element diffusion, and massive star explosions. Astrophys. J. Suppl. Ser. 234, 34 (2018).

    ADS  Article  Google Scholar 

  76. 76.

    Hunter, J. D. Matplotlib: a 2D graphics environment. Comput. Sci. Eng. 9, 90–95 (2007).

    Article  Google Scholar 

  77. 77.

    Nielsen, M. B., Gizon, L., Schunker, H. & Karoff, C. Rotation periods of 12 000 main-sequence Kepler stars: dependence on stellar spectral type and comparison with v sin i observations. Astron. Astrophys. 557, L10 (2013).

    ADS  Article  Google Scholar 

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We thank S. Matt, E. Avallone, A. Dixon, W. Ball and B. Morris for helpful discussions. O.J.H., G.R.D. and W.J.C. acknowledge support from the UK Science and Technology Facilities Council (STFC). J.v.S. acknowledges support from the TESS Guest Investigator Program (grant number 80NSSC18K18584). M.B.N. acknowledges support from the UK Space Agency. This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (CartographY GA. 804752). Funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation (Grant agreement number DNRF106). L.A., A.A.B. and V.S. acknowledge funding from the ERC under the European Union’s Horizon 2020 research and innovation program (grant agreement number 682393 AWESoMeStars). A.A.B. also acknowledges support from the College of Engineering, Mathematics and Physical Sciences at the University of Exeter. R.A.G. acknowledges support from the PLATO and GOLF CNES grants. J.T. acknowledges that support for this work was provided by NASA through NASA Hubble Fellowship grant number 51424 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract number NAS5-26555. The computations described in this paper were performed using the University of Birmingham’s BlueBEAR HPC service. This paper includes data collected by the Kepler mission and obtained from the MAST data archive at the Space Telescope Science Institute (STScI). Funding for the Kepler mission is provided by the NASA Science Mission Directorate. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract number NAS 5-26555.

Author information




O.J.H. led the project, with help from G.R.D., J.v.S., M.B.N. and W.J.C. J.v.S. also led the development of the stellar population models. M.N.L., R.A.G. and S.K. provided data or stellar models and, along with J.T., assessed the validity of our asteroseismic results. L.A., A.A.B. and V.S. provided the assessment of the theoretical implications of the gyrochronology results. All authors have contributed to the interpretation of the data and the results, and all discussed and provided comments for all drafts of the paper.

Corresponding author

Correspondence to Oliver J. Hall.

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The authors declare no competing interests.

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Peer review informationNature Astronomy thanks Cecilia Garraffo and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 A probabilistic graphical model (PGM) represented algebraically in Equation 2.

The shaded circle indicates observed data, and solid black points represent other fixed information, such as the KDEs and observational uncertainties. The remaining circles represent parameters. The underline indicates that the symbol represents a set of parameters or data. Here, κs and κWMB represent the KDEs of standard and WMB model populations respectively. QWMB is the mixture model weighting factor. The latent parameters θ, our observations \({\mathcal{D}}\) and their uncertainties \({\sigma }_{{\mathcal{D}}}\) include temperature Teff), mass (M), log-age (\(\mathrm{ln}\,(t)\)), metallicity [Fe/H]) and log-rotation (\(\mathrm{ln}\,(P)\)). This model is hierarchical, as all the latent parameters are drawn from the common probability distribution set by QWMB and described in Equation (3).

Supplementary information

Supplementary Information

Supplementary Figs. 1–5, Table 1 and asteroseismic model, verifying asteroseismic results and verifying consequences for gyrochronology sections.

Supplementary Data 1

A .csv file with the contents of Supplementary Table 1.

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Hall, O.J., Davies, G.R., van Saders, J. et al. Weakened magnetic braking supported by asteroseismic rotation rates of Kepler dwarfs. Nat Astron 5, 707–714 (2021).

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