Nonlinear interaction between dynamo-generated magnetic fields, mean flows and internal gravity waves in stellar stably-stratified layers: From 3D to 1D

Magnetic fields have been constrained at the surface of several massive and intermediate-mass stars, but their origin and properties in deep stellar radiative interiors are still debated, despite recent detections in the core of some red giant stars. Therefore, the modelling of AM transport in stellar radiative layers only relies on theoretical and numerical estimates of magnetic fields. Recent 3D numerical simulations show that a dynamo could occur in deep radiative regions. A realistic setup for understanding AM transport in such layers thus requires to take into account the mutual interactions of IGW and dynamo-generated magnetic field. We model the dynamics induced by IGW and dynamo in rotating radiative stellar layers using a simple description applicable to various evolutionary stages. As dynamo action and the propagation of IGW are 3D processes that have characteristic timescales short compared to periods associated with structural evolution of stars, we propose a mean-field 1D model by taking advantage of the dynamo coefficients computed from 3D spherical simulations. In this model, the necessary mean shear flow to trigger the dynamo results from the dissipation of monochromatic IGW generated in existing adjacent convective layers, which are expected to drive the formation of an oscillating rotational shear layer, the so-called Shear Layer Oscillation (SLO). In turn, magnetic effects can act on the mean flow through the Lorentz force. We show that the inclusion of magnetic fields adds up to the already very complex nonlinear problem and gives rise to the emergence of new dynamical regimes. Particularly, the fast SLO generated very close to the place where IGW are generated is perturbed by magnetic fields. This dynamical change can filter the wave energy spectrum transmitted towards further layers, with potential influence on the long-term evolution of the inner rotation.

💡 Research Summary

This paper investigates the nonlinear coupling between internal gravity waves (IGW) and dynamo‑generated magnetic fields in the stably‑stratified radiative layers of stars. Observations have constrained surface magnetic fields in many massive and intermediate‑mass stars and have even detected internal fields in red‑giant cores, yet the origin and structure of magnetic fields deep inside radiative zones remain uncertain. Angular‑momentum (AM) transport in these zones is thought to involve a variety of processes—stellar winds, meridional circulation, turbulence, IGW, and magnetic torques—but the interplay between IGW and magnetic fields has not been treated self‑consistently.

The authors build on recent three‑dimensional (3D) spherical magnetohydrodynamic (MHD) simulations that demonstrated a sub‑critical dynamo operating in radiative shells under realistic stellar parameters (Ekman numbers 10⁻⁷–10⁻⁴, Reynolds numbers 3×10²–10⁵, Rayleigh numbers 10⁸–10¹⁰, magnetic Prandtl numbers 0.5–25). In those simulations, a temperature gradient establishes stable stratification, while differential rotation is imposed by rotating the inner and outer spheres at slightly different rates. The simulations employ the pseudo‑spectral PaRoDy code and resolve the full set of incompressible Boussinesq MHD equations, allowing the authors to extract mean‑field dynamo coefficients (α‑effect, β‑effect, effective magnetic diffusivity η) directly from the flow.

A key insight is that the shear required to sustain the dynamo does not need to be externally imposed. Instead, monochromatic IGW generated at an adjacent convective boundary deposit momentum as they propagate into the radiative zone, producing an oscillating shear layer known as a Shear Layer Oscillation (SLO). The SLO is analogous to the Earth’s Quasi‑Biennial Oscillation (QBO) and the Jovian Quasi‑Quadrennial Oscillation, where wave‑driven momentum deposition creates a periodic reversal of the mean flow. In the stellar context, the SLO can filter the wave spectrum that reaches deeper layers, thereby influencing long‑term AM redistribution.

To capture the essential physics on evolutionary timescales, the authors construct a one‑dimensional (1D) mean‑field model. The model couples three equations: (i) the angular‑momentum balance including viscous diffusion, wave‑driven AM flux, and the Lorentz force; (ii) a wave‑energy transport equation with radiative, viscous, and magnetic damping terms; and (iii) the mean‑field induction equation with the measured α‑effect and turbulent diffusivity. The wave source is taken as a single monochromatic mode (frequency ω₀, wavenumber k₀), which allows analytical expressions for the wave‑induced Reynolds stress and the resulting SLO growth rate. The dynamo term feeds back on the shear through the Lorentz force, while the magnetic field modifies wave propagation by altering the effective Brunt‑Väisälä frequency and adding magnetic damping.

Parameter scans reveal two distinct dynamical regimes. In the “fast SLO” regime, the wave‑driven shear is strong enough to generate large‑amplitude oscillations, but the magnetic field remains too weak to significantly affect the flow; consequently, a broad wave spectrum penetrates to deeper layers. In the “magnetically‑controlled SLO” regime, the Tayler instability triggered by the shear amplifies a toroidal field to the point where the Lorentz force suppresses the shear amplitude. This suppression preferentially damps high‑frequency waves, leaving only low‑frequency components to propagate inward. The resulting spectral filtering reduces the net AM flux delivered to the core and can lead to markedly different rotation profiles over stellar evolutionary timescales.

The authors compare their 1D results with the full 3D simulations, finding good qualitative agreement in the onset of dynamo action, the emergence of SLOs, and the transition between the two regimes as magnetic Prandtl number or wave amplitude is varied. They argue that the traditional Spruit‑Taylor dynamo model, which assumes a strong, large‑scale shear imposed a priori, is overly restrictive; the wave‑driven shear provides a natural, self‑consistent source of differential rotation that can sustain a dynamo even at modest shear levels.

In the discussion, the paper highlights the astrophysical implications. The coupled IGW‑dynamo system offers a mechanism for the observed near‑solid‑body rotation of the solar radiative interior, as well as the slowed core rotation in sub‑giant and red‑giant stars inferred from asteroseismology. Moreover, the magnetic filtering of wave energy could explain why some massive main‑sequence stars retain significant differential rotation while others do not. The authors suggest that incorporating the derived nonlinear terms into 1D stellar evolution codes (e.g., MESA, GENEC) would improve predictions of internal rotation, chemical mixing, and magnetic braking.

In conclusion, the study demonstrates that (1) IGW can generate the shear needed to trigger a sub‑critical dynamo in radiative zones, (2) the resulting magnetic field feeds back on both the shear and the wave propagation, and (3) this three‑way coupling creates new nonlinear dynamical regimes that substantially alter angular‑momentum transport. The work provides a bridge between computationally intensive 3D DNS and tractable 1D models, offering a practical framework for future investigations of magnetic‑wave interactions in stellar interiors.