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Internal mixing of rotating stars inferred from dipole gravity modes


During most of their life, stars fuse hydrogen into helium in their cores. The mixing of chemical elements in the radiative envelope of stars with a convective core is able to replenish the core with extra fuel. If effective, such deep mixing allows stars to live longer and change their evolutionary path. Yet localized observations to constrain internal mixing are absent so far. Gravity modes probe the deep stellar interior near the convective core and allow us to calibrate internal mixing processes. Here we provide core-to-surface mixing profiles inferred from observed dipole gravity modes in 26 rotating stars with masses between 3 and 10 solar masses. We find a wide range of internal mixing levels across the sample. Stellar models with stratified mixing profiles in the envelope reveal the best asteroseismic performance. Our results provide observational guidance for three-dimensional hydrodynamical simulations of transport processes in the deep interiors of stars.

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Fig. 1: Light curves overplotted with amplitude spectra of six SPB stars.
Fig. 2: Gravity-mode period spacing patterns of six SPB stars.
Fig. 3: Schematic representation of the considered mixing profiles.
Fig. 4: Population of the eight model grids in terms of model capacity.
Fig. 5: Inferred internal mixing profiles for 26 SPB stars.
Fig. 6: Correlations among estimated parameters and inferred quantities for the sample.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The iterative prewhitening code is freely available and documented at The stellar evolution code, MESA, is freely available and documented at The stellar pulsation code, GYRE, is freely available and documented at


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We thank the MESA and GYRE code developers for their efforts, public dissemination and training initiatives to make their software so accessible to the worldwide astrophysics community. We thank S. Ekström of the Geneva Observatory for providing mixing profiles from Georgy et al.4 in electronic format. We acknowledge the work of the teams behind the NASA Kepler and ESA Gaia space missions. This work is based on observations with the HERMES spectrograph at the Mercator Telescope, which is operated at La Palma, Spain, by the Flemish Community. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, and NASA’s Astrophysics Data System. The research leading to these results has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 670519: MAMSIE), from the National Science Foundation (grant number NSF PHY-1748958), from the KU Leuven Research Council (grant number C16/18/005: PARADISE) and from the Research Foundation Flanders (FWO) by means of PhD Fellowships to M.M. and S. Gebruers under contract numbers 11F7120N and 11E5620N and a senior post-doctoral fellowship to D.M.B. under grant agreement number 1286521N. Funding for the Kepler Mission was provided by NASA’s Science Mission Directorate. Gaia data are being processed by the Gaia Data Processing and Analysis Consortium (DPAC); funding for the DPAC is provided by national institutions, in particular the institutions participating in the Gaia MultiLateral Agreement (MLA).

Author information




M.G.P. performed frequency analysis and mode identification, wrote code to include mixing profiles in MESA, computed asteroseismic observables, implemented and applied the modelling procedures, interpreted the results and wrote part of the text. C.A. defined the research, developed the modelling procedure, interpreted the results and wrote part of the text. P.I.P. constructed light curves from the raw Kepler data and discovered the targets to be new SPB stars. M.M. wrote code to include mixing profiles in MESA and assessed the capacity of observables used for the modelling. S. Gebruers determined abundances from spectroscopy. T.M.R. computed and provided envelope mixing profiles due to internal gravity waves. G.M. provided advice on the parameter estimation and statistical model selection and performed the cluster analysis. S.B., S. Garcia and D.M.B. contributed to the frequency analysis and interpretation. All authors contributed to the discussions and have read and iterated upon the text of the final manuscript.

Corresponding author

Correspondence to May G. Pedersen.

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The authors declare no competing interests.

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Peer review information Nature Astronomy thanks Joyce Guzik, Ernst Paunzen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Discussion, Figs. 1–34 and Tables 1–8.

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Pedersen, M.G., Aerts, C., Pápics, P.I. et al. Internal mixing of rotating stars inferred from dipole gravity modes. Nat Astron 5, 715–722 (2021).

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