The Sun's deepest ~20% is the only directly observable stellar core whose rotation would cleanly discriminate between competing prescriptions for magnetic angular-momentum (AM) transport by the Tayler instability — the original Tayler–Spruit dynamo and its revised variants — yet no rotation-sensitive mode reaching the core has been confirmed. The problem is to (i) obtain a definitive measurement of the solar core rotation rate, via detection of gravity-mode (g-mode) rotational splittings or an equivalent core-sensitive observable, and (ii) establish the correct physical prescription for magnetic AM transport in radiative zones so that this measurement becomes a quantitative, history-independent calibration of the transport efficiency in chemically stratified regions, with the surface wind-braking history and the internal-gravity-wave channel consistently accounted for. As of 2026 both halves remain open: the claimed g-mode detection is considered fragile and unconfirmed, and evolution models still cannot simultaneously reproduce the internal rotation of the Sun, subgiants, and red giants with any single Tayler-based closure.

Background

Helioseismology — the study of the Sun's oscillations — has measured the solar rotation profile precisely down to about 0.2 R⊙0.2\,R_\odot (20% of the solar radius) using pressure modes (pp modes), oscillations restored by pressure, whose rotational splitting (the frequency separation between modes of the same structure traveling in opposite directions) probes rotation where the modes have amplitude. Below 0.2 R⊙0.2\,R_\odot, p modes lose sensitivity, so the rotation of the core is unmeasured by this route. Gravity modes (gg modes), restored by buoyancy, are trapped in the core and would measure it through their rotational splittings, but they are damped in the convection zone and have amplitudes at or below current detection limits; the claimed detection by Fossat et al. (2017, A&A 604, A40) from 16.5 years of GOLF data (the spectrometer aboard the SOHO spacecraft), implying a core rotating at 1644±231644\pm23 nHz — about 3.83.8 times faster than the radiative envelope — was shown by Schunker et al. (2018) to vanish under a shift of the series' start time by a few hours, and Scherrer & Gough (2019) found it nearly inconsistent with p-mode splittings and mode-amplitude upper limits; the claim remains unconfirmed.

Why the core rotation matters: rotating stellar-evolution models that include only hydrodynamic transport (meridional circulation and shear turbulence) predict a solar core spinning orders of magnitude faster than allowed by helioseismology, and predict far too rapid core rotation for subgiant and red-giant stars observed with the CoRoT/Kepler missions. Some efficient extra AM-transport process operates in radiative zones. A leading candidate is magnetic transport by the Tayler instability — a kink-type instability of the mostly horizontal toroidal field that differential rotation winds up — organized as the Tayler–Spruit (TS) dynamo proposed by Spruit (2002) as a scaling-argument theory with undetermined order-unity factors. Fuller, Piro & Jermyn (2019, MNRAS 485, 3661) proposed a revised Tayler prescription with a different saturation assumption, predicting transport efficiencies differing by orders of magnitude from the original, and claimed it reproduces the nearly rigid rotation of the present Sun, red-giant core rotation, and white-dwarf spins. Eggenberger, Buldgen & Salmon (2019, A&A 626, L1) — the source of this problem — showed that solar models with magnetic-instability transport plus a modern prescription for the braking of the stellar surface by magnetized winds reproduce open-cluster surface-rotation data, and that a rapid core (as suggested by the reported g-mode detection) is compatible with such transport: chemical stratification stabilizes the core, so it can keep rotating faster than the envelope. Crucially, they showed the core rotation rate calibrates the transport efficiency inside strongly stratified regions independently of the Sun's unknown rotational history, and that the two closures are empirically distinguishable — a faster core supports the original TS prescription over the revised one. Their paper, which defines this problem, flags what is still missing: a definitive g-mode confirmation; a physically settled prescription (order-unity factors, orders-of-magnitude disagreement between closures, and numerical simulations unable to reach stellar parameter regimes); residual uncertainty from the wind-braking law; and the unquantified complementary channel of internal gravity waves (buoyancy waves excited at the convective boundary, which can themselves extract core angular momentum).

Problem Statement

Turn the Sun's core rotation rate into a definitive calibration of magnetic angular-momentum transport in stellar radiative zones. Concretely, with the conventions of Eggenberger, Buldgen & Salmon (2019):

  1. Obtain a definitive measurement of the solar core rotation rate inside r≲0.2 R⊙r\lesssim0.2\,R_\odot — through a confirmed detection of gravity-mode rotational splittings (e.g., in time series from GOLF, BiSON, or VIRGO — the dedicated solar-oscillation instruments: the GOLF spectrometer and the VIRGO photometer aboard the SOHO spacecraft, and the ground-based BiSON network — or by any equivalent core-sensitive observable, such as rotational inversions using mixed f/g modes, i.e., modes of hybrid surface-gravity and core-gravity character) — with a stated significance that survives the known artifact tests (window-function leakage from p modes, sensitivity to the start time of the time series, consistency with p-mode rotation inversions and g-mode amplitude upper limits). Treat this item as resolved only by an unambiguous detection that is independently corroborated — reproduced from an independent data set or by an independent analysis — and whose significance is stated as a quantified detection statistic (e.g., a false-alarm probability); a marginal, single-analysis, or otherwise unreplicated claim does not resolve it.

  2. Establish the correct prescription for angular-momentum transport by the Tayler instability in radiative zones — the original Tayler–Spruit dynamo, the revised closure of Fuller et al. (2019), or a successor derived from first principles or validated simulations — such that stellar-evolution models with that prescription simultaneously reproduce: the measured solar core rotation rate from item 1 together with the helioseismically inferred near-uniform rotation of the radiative zone above 0.2 R⊙0.2\,R_\odot; the core rotation rates of subgiant and red-giant stars; and the surface rotation of stars in open clusters, with the surface wind-braking law and the possible complementary transport by internal gravity waves (and their interaction with the magnetic field) consistently accounted for rather than tuned away. Here "reproduce" means agreeing with each listed data set to within the stated uncertainties of its measurements, and the surface wind-braking law and the internal-gravity-wave treatment must be fixed a priori or calibrated on data independent of the targets being reproduced, not re-tuned per data set to force agreement.

The overarching objective, which binds these components: determine how fast the solar core rotates and what that measurement implies, quantitatively, for the efficiency and physical origin of magnetic angular-momentum transport in the chemically stratified interiors of low-mass stars.

References

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