Helioseismology shows that the Sun's radiative interior rotates nearly uniformly from the base of the convective envelope down to about 0.2 solar radii, yet stellar-evolution models with only hydrodynamic angular-momentum (AM) transport predict strong radial differential rotation: an efficient additional mechanism, most plausibly magnetic, must operate in radiative zones. The two analytical prescriptions in use — the original Tayler-Spruit dynamo (Spruit 2002) and the revised Tayler-instability closure of Fuller, Piro & Jermyn (2019) — differ in effective viscosity by about four orders of magnitude, and the nonlinear viability of the underlying dynamo long lacked numerical demonstration. Eggenberger, Buldgen & Salmon (2019) showed that a measurement of the solar core rotation rate from gravity-mode rotational splittings would calibrate the magnetic-transport efficiency in chemically stratified layers independently of the Sun's unknown rotational history, and would cleanly discriminate the two prescriptions (a fast core favoring the original Tayler-Spruit dynamo). The problem remains open: solar g modes still elude confirmed detection; asteroseismic tests of the prescriptions in subgiants, red giants, and Gamma Doradus stars pull in different directions; simulations now realize Tayler-Spruit-like dynamos but not at stellar parameters; wind-braking laws are under active revision; and the combined action of internal gravity waves has only begun to be modeled.

Background

The Sun's internal rotation is mapped by helioseismology. The frequencies of the five-minute solar oscillations — pressure modes (p modes), standing sound waves trapped in the outer layers — are split into multiplets by rotation, and these rotational splittings reveal that the radiative zone (the stably stratified region between the convective envelope and the center, from roughly 0.7 to 0 of the solar radius) rotates nearly uniformly down to about 0.2 solar radii. Stellar-evolution models that transport angular momentum (AM) only through hydrodynamic processes — meridional circulation (large-scale flows driven by rotation) and turbulent shear instability — instead predict a strongly differential rotation in the radiative interior, contradicting the observations. An efficient additional AM-transport process must therefore be at work. Spruit (2002) proposed one candidate: a weak magnetic field wound up by differential rotation becomes unstable to the Tayler instability (a current-driven instability of toroidal magnetic fields in stable stratification), and the interplay of winding and instability can sustain a small-scale turbulent dynamo — the Tayler-Spruit (TS) dynamo — whose Maxwell stresses enforce nearly uniform rotation. Two uncertainties attach to this picture. First, Spruit's analytical derivation deliberately discarded multiplicative factors of order unity, so the predicted effective viscosity is uncertain at that level. Second, early numerical simulations gave contrasting results: Braithwaite (2006) found a differential-rotation-driven dynamo in a stably stratified star, while Zahn, Brun & Mathis (2007) found none; simulations at realistic stellar parameters were considered out of reach. Fuller, Piro & Jermyn (2019) then proposed a revised Tayler-instability-based closure whose effective viscosity in the solar radiative zone is typically four orders of magnitude larger than the TS value, implying essentially uniform rotation down to the solar center rather than a faster-turning core. The deepest 0.2 solar radii of the Sun are not probed by p modes. Gravity modes (g modes), whose restoring force is buoyancy and which are confined to the radiative interior, would measure the core rotation through their rotational splittings. Reported g-mode detections (García et al. 2007; Fossat et al. 2017) favor a core rotating several times faster than the envelope, but both claims are disputed (Schunker et al. 2018; Appourchaux & Corbard 2019), and amplitude theory places the strongest modes near or below current instrumental detection thresholds (Belkacem et al. 2022). Surface rotation constrains the problem only jointly with the adopted magnetized-wind braking law — the torque by which the magnetized stellar wind spins a star down (e.g. Matt et al. 2015) — and internal gravity waves (buoyancy-driven waves excited by convective motion, e.g. Pinçon et al. 2017) constitute a further AM-transport channel that magnetic-transport models typically omit. Eggenberger, Buldgen & Salmon (2019) computed solar models with AM transport by meridional circulation, shear, and the TS dynamo, calibrated the wind-braking torque on open-cluster surface-rotation data, and showed that (i) a fast-rotating core, as suggested by the disputed g-mode claims, is compatible with TS transport once the stabilizing effect of chemical-composition gradients (stratification by mean molecular weight that resists radial motion and inhibits magnetic AM transport) is accounted for; (ii) the mean core rotation rate would calibrate the magnetic-transport efficiency in chemically stratified layers independently of the Sun's unknown past rotational history; and (iii) the original TS prescription and the Fuller et al. (2019) closure are easily distinguished by exactly this measurement, with a fast core favoring the original prescription. They framed the remaining task as obtaining a firm, confirmed g-mode detection of the solar core rotation rate and converting that measurement into a definitive calibration of magnetic AM transport in stellar interiors.

Problem Statement

Obtain a definitive measurement of the rotation rate of the solar core — the innermost roughly 20 percent of the solar radius that pressure modes cannot reach — and use this measurement to deliver a definitive calibration of angular-momentum transport by magnetic instabilities in stellar radiative interiors. The calibration must fix the unknown order-unity multiplicative factors of the original Tayler-Spruit prescription of Spruit (2002) and discriminate it against the revised Tayler-instability closure of Fuller, Piro & Jermyn (2019), whose effective viscosities differ by about four orders of magnitude and whose solar-model predictions — a faster-rotating core versus uniform rotation down to the center — are distinguishable precisely by this measurement; and it must be consistent with the surface-rotation constraints that link the interior to the magnetized-wind braking law. The single scientific objective is to convert the Sun's core rotation into the definitive empirical calibrator of magnetic angular-momentum transport for stellar evolution models, exploiting the fact established by the source that the core rate constrains the transport efficiency in chemically stratified layers independently of the Sun's unknown rotational history. The calibration requires a secure determination (or an equivalent constraint) of the solar core rotation rate precise enough to discriminate the two prescriptions' distinguishable predictions and to fix the order-unity factors of the Spruit (2002) prescription.

References

  1. Eggenberger P., Buldgen G., Salmon S. J. A. J. (2019). Rotation rate of the solar core as a key constraint to magnetic angular momentum transport in stellar interiors. Astronomy & Astrophysics 626, L1. doi:10.1051/0004-6361/201935509, https://doi.org/10.1051/0004-6361/201935509
  2. Spruit H. C. (2002). Dynamo action by differential rotation in a stably stratified stellar interior. Astronomy & Astrophysics 381, 923-932. doi:10.1051/0004-6361:20011465, https://doi.org/10.1051/0004-6361:20011465
  3. Fuller J., Piro A. L., Jermyn A. S. (2019). Slowing the spins of stellar cores. Monthly Notices of the Royal Astronomical Society 485, 3661-3680. doi:10.1093/mnras/stz514, https://doi.org/10.1093/mnras/stz514
  4. Fossat E., Boumier P., Corbard T., Provost J., Salabert D., Schmider F. X., Gabriel A. H., Grec G., Renaud C., Robillot J. M., Roca-Cortés T., Turck-Chièze S., Ulrich R. K., Lazrek M. (2017). Asymptotic g modes: Evidence for a rapid rotation of the solar core. Astronomy & Astrophysics 604, A40. doi:10.1051/0004-6361/201730460, https://doi.org/10.1051/0004-6361/201730460
  5. García R. A., Turck-Chièze S., Jiménez-Reyes S. J., Ballot J., Pallé P. L., Eff-Darwich A., Mathur S., Provost J. (2007). Tracking solar gravity modes: The dynamics of the solar core. Science 316, 1591-1593. doi:10.1126/science.1140598, https://doi.org/10.1126/science.1140598
  6. Schunker H., Schou J., Gaulme P., Gizon L. (2018). Fragile detection of solar g modes by Fossat et al. Solar Physics 293, 95. doi:10.1007/s11207-018-1313-6, https://doi.org/10.1007/s11207-018-1313-6
  7. Appourchaux T., Corbard T. (2019). Searching for g modes. Astronomy & Astrophysics 624, A106. doi:10.1051/0004-6361/201935196, https://doi.org/10.1051/0004-6361/201935196
  8. Fossat E., Schmider F. X. (2018). More about solar g modes. Astronomy & Astrophysics 612, L1. doi:10.1051/0004-6361/201832626, https://doi.org/10.1051/0004-6361/201832626
  9. Matt S. P., Brun A. S., Baraffe I., Bouvier J., Chabrier G. (2015). The mass-dependence of angular momentum evolution in Sun-like stars. The Astrophysical Journal 799, L23. doi:10.1088/2041-8205/799/2/L23, https://doi.org/10.1088/2041-8205/799/2/L23
  10. Pinçon C., Belkacem K., Goupil M. J., Marques J. P. (2017). Can plume-induced internal gravity waves regulate the core rotation of subgiant stars? Astronomy & Astrophysics 605, A31. doi:10.1051/0004-6361/201730998, https://doi.org/10.1051/0004-6361/201730998
  11. Eggenberger P., Maeder A., Meynet G. (2005). Stellar evolution with rotation and magnetic fields. Astronomy & Astrophysics 440, L9-L12. doi:10.1051/0004-6361:200500156, https://doi.org/10.1051/0004-6361:200500156
  12. Braithwaite J. (2006). A differential rotation driven dynamo in a stably stratified star. Astronomy & Astrophysics 449, 451-460. doi:10.1051/0004-6361:20054241, https://doi.org/10.1051/0004-6361:20054241
  13. Zahn J.-P., Brun A. S., Mathis S. (2007). On magnetic instabilities and dynamo action in stellar radiation zones. Astronomy & Astrophysics 474, 145-154. doi:10.1051/0004-6361:20077653, https://doi.org/10.1051/0004-6361:20077653
  14. Eggenberger P., den Hartogh J. W., Buldgen G., Meynet G., Salmon S. J. A. J., Deheuvels S. (2019). Asteroseismology of evolved stars to constrain the internal transport of angular momentum. Astronomy & Astrophysics 631, L6. doi:10.1051/0004-6361/201936348, https://doi.org/10.1051/0004-6361/201936348
  15. Eggenberger P., Buldgen G., Salmon S. J. A. J., Noels A., Grevesse N., Asplund M. (2022). The internal rotation of the Sun and its link to the solar Li and He surface abundances. Nature Astronomy 6, 788-795. doi:10.1038/s41550-022-01677-0, https://doi.org/10.1038/s41550-022-01677-0
  16. Moyano F. D., Eggenberger P., Meynet G., Gehan C., Mosser B., Buldgen G., Salmon S. J. A. J. (2022). Asteroseismology of evolved stars to constrain the internal transport of angular momentum. Astronomy & Astrophysics 663, A180. doi:10.1051/0004-6361/202243389, https://doi.org/10.1051/0004-6361/202243389
  17. Moyano F. D., Eggenberger P., Salmon S. J. A. J. (2024). Angular momentum transport near convective-core boundaries of Gamma Doradus stars. Astronomy & Astrophysics 681, L16. doi:10.1051/0004-6361/202348704, https://doi.org/10.1051/0004-6361/202348704
  18. Deheuvels S., Ballot J., Eggenberger P., Spada F., Noll A., den Hartogh J. W. (2020). Seismic evidence for near solid-body rotation in two Kepler subgiants and implications for angular momentum transport. Astronomy & Astrophysics 641, A117. doi:10.1051/0004-6361/202038578, https://doi.org/10.1051/0004-6361/202038578
  19. Li G., Deheuvels S., Li T., Ballot J., Lignières F. (2023). Internal magnetic fields in 13 red giants detected by asteroseismology. Astronomy & Astrophysics 680, A26. doi:10.1051/0004-6361/202347260, https://doi.org/10.1051/0004-6361/202347260
  20. Petitdemange L., Marcotte F., Gissinger C. (2023). Spin-down by dynamo action in simulated radiative stellar layers. Science 379, 300-303. doi:10.1126/science.abk2169, https://doi.org/10.1126/science.abk2169
  21. Petitdemange L., Marcotte F., Gissinger C., Daniel F. (2024). Tayler-Spruit dynamo simulations for the modeling of radiative stellar layers. Astronomy & Astrophysics 681, A75. doi:10.1051/0004-6361/202347241, https://doi.org/10.1051/0004-6361/202347241
  22. Barrère P., Reboul-Salze A., Eggenberger P., Deheuvels S., Rodríguez C., Marchand M. (2026). Coexisting Tayler instability-driven dynamos in radiative zones: New dynamo solution and its impacts on stellar physics. Astronomy & Astrophysics (in press). doi:10.1051/0004-6361/202558158, https://doi.org/10.1051/0004-6361/202558158
  23. Barrère P., Guilet J., Gallet B., Raynaud R. (2026). Complex dynamical regimes of the Tayler-Spruit dynamo. arXiv:2601.02182, https://arxiv.org/abs/2601.02182
  24. Skoutnev V. A., Beloborodov A. M. (2024). Tayler instability revisited. The Astrophysical Journal 974, 290. doi:10.3847/1538-4357/ad71c8, https://doi.org/10.3847/1538-4357/ad71c8 (preprint arXiv:2404.19103, https://arxiv.org/abs/2404.19103)
  25. Gusakov M. E., Becerra L., Kantor E. M., Reisenegger A., Valdivia J. A. (2026). Beyond the Tayler instability: A new global instability of toroidal magnetic fields in stars. Physical Review D 114, 023019. doi:10.1103/2h7n-g6nq, https://doi.org/10.1103/2h7n-g6nq
  26. Belkacem K., Pinçon C., Buldgen G. (2022). Amplitudes of solar gravity modes: A review. Solar Physics 297, 147. doi:10.1007/s11207-022-02075-5, https://doi.org/10.1007/s11207-022-02075-5
  27. Leclerc A., Le Saux A., Ong J. M. J., García R. A. (2026). On the feasibility of inverting the rotation of the solar core with mixed f/g modes. arXiv:2607.04830, https://arxiv.org/abs/2607.04830
  28. Awasthi A. (2026). Detection prospects of solar g-modes with LISA. arXiv:2602.18385, https://arxiv.org/abs/2602.18385
  29. Amard L., Mathis S. (2026). Coexistence of internal gravity waves and Tayler-Spruit magnetic fields in the radiative cores of low-mass stars. Astronomy & Astrophysics 708, A327. doi:10.1051/0004-6361/202453460, https://doi.org/10.1051/0004-6361/202453460
  30. Finley A. J. (2025). Reconstructing the Sun's Alfvén surface and wind braking torque with Parker Solar Probe. Astronomy & Astrophysics 702, A252. doi:10.1051/0004-6361/202556391, https://doi.org/10.1051/0004-6361/202556391
  31. Hall O. J., Davies G. R., van Saders J., Nielsen M. B., Lund M. N., Chaplin W. J., García R. A., Amard L., Breimann A. A., Khan S., See V., Tayar J. (2021). Weakened magnetic braking supported by asteroseismic rotation rates of Kepler dwarfs. Nature Astronomy 5, 707-714. doi:10.1038/s41550-021-01335-x, https://doi.org/10.1038/s41550-021-01335-x
  32. Metcalfe T. S., van Saders J. L., Pinsonneault M. H., Ayres T. R., Kochukhov O., Stassun K. G., Finley A. J., See V., Ilyin I. V., Strassmeier K. G. (2025). Weakened magnetic braking signals the collapse of the global stellar dynamo. The Astrophysical Journal Letters 991, L17. doi:10.3847/2041-8213/ae03bc, https://doi.org/10.3847/2041-8213/ae03bc
  33. Mombarg J. S. G., Mathis S. (2026). Calibrating angular momentum transport in intermediate-mass stars from gravity-mode asteroseismology. II. Modelling 2937 BAF-type stars. arXiv:2606.23819, https://arxiv.org/abs/2606.23819
  34. Spada F., Lanzafame A. C. (2020). Competing effect of wind braking and interior coupling in the rotational evolution of solar-like stars. Astronomy & Astrophysics 636, A76. doi:10.1051/0004-6361/201936384, https://doi.org/10.1051/0004-6361/201936384