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The internal rotation of the Sun and its link to the solar Li and He surface abundances


The Sun serves as a natural reference for the modelling of the various physical processes at work in stellar interiors. Helioseismology results, which inform us on the characterization of the interior of the Sun (such as, for example, the helium abundance in its envelope), are, however, at odds with heavy element abundances. Moreover, the solar internal rotation and surface abundance of lithium have always been challenging to explain. We present results of solar models that account for transport of angular momentum and chemicals by both hydrodynamic and magnetic instabilities. We show that these transport processes reconcile the internal rotation of the Sun, its surface lithium abundance, and the helioseismic determination of the envelope helium abundance. We also show that the efficiency of the transport of chemicals required to account for the solar surface lithium abundance also predicts the correct value of helium, independently from a specific transport process.

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Fig. 1: Rotation profiles in the solar radiative interior for models computed with the AGSS09 photospheric abundances.
Fig. 2: Lithium surface abundance as a function of age for different solar models.
Fig. 3: Beryllium surface abundance as a function of age for different solar models.
Fig. 4: Evolution of the surface helium mass fraction as a function of age for different solar models.
Fig. 5: Relative differences in the squared adiabatic sound speed c2 between the Sun and solar models obtained by inversion.
Fig. 6: Lithium surface abundance as a function of age for the different non-rotating solar models.
Fig. 7: Evolution of the surface helium mass fraction as a function of age for non-rotating solar models.

Data availability

The solar lithium abundances used in this paper are publicly available in the papers by Asplund et al.5 and Wang et al.42. The beryllium abundance is publicly available in the paper by Asplund et al.5. The solar inverted rotation profile shown in Fig. 1 is available in the paper by Couvidat et al.58. The Global Oscillations at Low Frequencies (GOLF) dataset used for the frequency ratios is publicly available from Salabert et al.59. The dataset used for the sound speed inversions is publicly available from the Birmingham Solar Oscillation Network (BiSON) network website ( and the Joint Science Operations Center portal ( All data obtained within this paper are available from the corresponding author upon reasonable request.

Code availability

The Geneva stellar evolution code is a proprietary software, but all solar evolution models will be made available upon request. The software used to compute the sound speed inversions is publicly available on the following SpaceInn webpage:


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We thank T. Dumont and C. Charbonnel for providing us with their compilation of observations of lithium and beryllium abundances available for solar-type stars. P.E. and S.J.A.J.S. have received funding from the European Research Council under the European Union's Horizon 2020 research and innovation programme (grant agreement No 833925, project STAREX). G.B. acknowledges fundings from the SNF AMBIZIONE grant No 185805 (Seismic inversions and modelling of transport processes in stars).

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P.E. led the project with the help from G.B. P.E. computed the models with the Geneva code and G.B. computed the inversions. P.E., G.B., S.J.A.J.S. and A.N. interpreted the data regarding helioseismic constraints and input physics of solar models. N.G. and M.A. interpreted the results in the context of solar spectroscopic abundance determinations. All authors have contributed to the discussion of the results and to the writing of the paper.

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Correspondence to P. Eggenberger.

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Nature Astronomy thanks Ana Palacios, Alessandro Lanzafame and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Table 1 and Figs. 1–5.

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Eggenberger, P., Buldgen, G., Salmon, S. et al. The internal rotation of the Sun and its link to the solar Li and He surface abundances. Nat Astron 6, 788–795 (2022).

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