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

TL;DR

This study investigates how IGW-driven mean flows interact nonlinearly with dynamo-generated magnetic fields in stably stratified stellar radiative layers. It builds a 1D mean-field model, calibrated with α-effect measurements from 3D DNS, to capture the coupled dynamics of wave-induced shear and a Tayler-Spruit–like dynamo, including Maxwell-stress feedback on the flow. The results reveal new dynamical regimes, where magnetic fields can modify the SLO, alter wave-energy filtering, and shift oscillation frequencies, thereby potentially influencing long-term angular momentum evolution in stellar interiors. The framework offers a computationally light pathway to incorporate Maxwell-stress transport into 1D stellar evolution codes, while acknowledging substantial idealisations and the need for further validation with more complete DNS and observations.

Abstract

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.

Figures (8)

• Figure 1: A measure of the $\alpha$-effect. (a) Meridional section of the component $\alpha_{\phi\phi}$ measured with the SVD technique applied to the simulation $Ek=10^{-5}$, $Ra=10^9$, $Re=27500$, $Pr=0.1$ and $Pm=1$PetitdemangeMG23. Isovalues of the time-averaged azimuthal magnetic field $B_\phi$ are visible. (b) Linear regression of $\mathcal{N}(\alpha_{\phi\phi})$ for our data set.
• Figure 2: Geometry of the domain (in red) (not to scale). Left: Global view where the domain is located at the base of the convective zone (CZ) and at the top of the radiative zone (RZ). Right:Radial representation of the computational domain of extent $d=r_o-r_i \ll r_o$.
• Figure 3: Typical profile for $B$ (left, dashed black) and $\alpha$ (right, red) (the values are in code units). The waves are excited on the right of the domain, at $r/d=10$.
• Figure 4: Bifurcation diagram of $\sigma(V_1)$ the standard deviation of $V_1$ (see text for definition) for $Pr=0.01,Pm=10,Ek=10^{-5},L=0.25, D=3.10^{-3}$ and increasing $F$, normalised by the measured critical value of the onset of oscillations $F_c=117$. a-e: Phase portraits in the $(V_1,V_2)$ plane for $F/F_c=\left\{1,2.56,6.84,10.26,12.82\right\}$ (a,b,c,d and e respectively). Simulations are here reported without (HD, black crosses) or with magnetic field, being either initialised from the condition described in the text (MHD scratch, red squares) or restarted from a previously computed solution (MHD restart, green crosses).
• Figure 5: Comparison of the simulation at $Pr=0.01,Pm=10,Ek=10^{-5},L=0.25,D=3.10^{-3},F=200$ with (MHD) or without magnetic field (HD). a: Timeseries of the energies. b and c: Hovmöller diagrams of the velocity field for the MHD case (b) and the HD (c) one. The dashed line corresponds to the location of the second probe $X_2$. d: Fourier spectra of $V_1$. e: Time evolution of $V_2$ in the two cases.