Conversion and Damping of Non-axisymmetric Internal Gravity Waves in Magnetized Stellar Cores

TL;DR

This paper extends the understanding of IGW–magnetic field interactions from axisymmetric to non-axisymmetric cases by employing a 3D Cartesian radiative-core model and a WKB amplitude framework. It shows that down-going IGWs convert to a mixture of SM and AW modes that develop fine-scale structure and damp, leading to overall energy loss in magnetized stellar cores. The work reveals parity-dependent pathways near SM cutoff and Alfvén boundaries, with diffusion playing a critical role in damping AWs and shaping the observable wave field. These findings bolster magnetic-field inference from asteroseismology and imply that both axisymmetric and non-axisymmetric dipole modes can be suppressed by sufficiently strong core fields, informing interpretations of red-giant and massive-star pulsations.

Abstract

Magnetism is thought to play an important role in the evolution and dynamics of stars, though little is known about magnetic fields deep within stellar interiors. A promising avenue for probing these fields uses asteroseismic observations of global oscillations that result from the coupling of acoustic waves in the convective zone to internal gravity waves (IGWs) in the radiative interior. Recent modeling efforts implicate deep magnetic fields in the suppression of dipole mixed modes observed in 20% of red giants and a number of high-mass main sequence stars. Previous numerical and theoretical work shows that core magnetic fields could suppress axisymmetric global modes by refracting down-going IGWs into slow-magnetosonic (SM) waves that damp at magnetic cutoff heights. Here, we extend these results to the non-axisymmetric case, for which the IGWs and SM waves are coupled to a continuous spectrum of Alfven waves (AWs). We consider a Cartesian model of the radiative interior with uniform stratification and a spatially-varying, current-free magnetic field. Using a Wentzel-Kramers-Brillouin approximation to solve for the vertical mode structure, corroborated with numerical simulations, we show that IGWs convert to up-going SM waves, which resonate with the Alfven spectrum and produce mixed SM-AW modes. We find cutoff heights (as in the axisymmetric case), above which the SM/SM-AWs convert to AWs. Latitudinal variations of the background magnetic field lead to phase mixing of the AWs, resulting in rapid damping. Our results suggest that energy in both axisymmetric and non-axisymmetric IGWs is lost via interactions with a strong magnetic field.

Figures (8)

• Figure 1: (a) Schematic cross-section of the inner portion of a RGB star with convective envelope and stably-stratified radiative core. Convective turbulence in the envelope excites acoustic waves which convert to internal gravity waves (IGWs) in the radiative core. In the presence of a strong remnant core magnetic field, non-axisymmetric IGWs convert to slow magnetosonic (SM) and resonant Alfvén waves (AWs). These magnetohydrodynamic waves develop fine vertical and horizontal scales as they propagate outwards, damping via diffusion. (b) Idealized Cartesian model formed by "unwrapping" the radiative core, with $x$, $y$, $z$ corresponding to latitude, azimuth, and radius, respectively. The field lines for the current-free background magnetic field $\boldsymbol{B}_0$ used in this study are plotted in purple. The opacity of the plotted field lines increases with $\lvert \boldsymbol{B}_0 \rvert$. Numerical simulations employ a sinusoidal wavemaker ($k_x = k_y = 2\pi/L$) located at the dotted line and damping layers indicated by the hatched areas.
• Figure 2: Snapshots of the latitudinal ($x$) and azimuthal ($y$) velocity perturbations ($u_{\text{IVP}}$, $v_{\text{IVP}}$) from IVP I ($\textit{Lu} = 6.25 \times 10^4$, $\textit{Fr} = 0.025$, $\Gamma =0.1$) after the simulation has equilibrated. (a) Plot of $u_{\text{IVP}}$ over ($x$,$z$) plane located at $y = 0$. IGWs are forced at the dotted line and damp in the hatched regions. (b)–(c) Sine and cosine-parity components of $u_{\text{IVP}}$, respectively. (d) The azimuthal velocity component, $v_{\text{IVP}}$. (e)–(f) Cosine and sine-parity components of $v_{\text{IVP}}$, respectively. An animated version of this figure (temporarily available https://drive.google.com/file/d/1EDDOsur0UWkQmlARIUjvauWUp812lZXa/view?usp=share_link) shows the transient behavior of IVP I; the fine shingle-like features (associated with AWs) in panel e (above $z/L \approx 0.17$) and panel f (above $z/L \approx 0.1$) propagate upwards.
• Figure 3: Three-dimensional rendering of magnetic field lines $B_{0 z}\boldsymbol{e}_z + b_y\boldsymbol{e}_y$ perturbed by AWs in an axisymmetric ($k_y = 0$) toy problem where the background magnetic field strength varies according to $B_{0 z}^2 = \cos^2(2\pi x) + 0.01$; darker shades of purple correspond to higher $\lvert B_{0 z} \rvert$. The open field lines are sinusoidally forced in the azimuthal ($y$) direction at their base with fixed frequency $\omega$. Each field line oscillates with a different vertical wavenumber given by (\ref{['eqn:toyalfvenwavenumber']}), leading to phase mixing that increases with height ($z$). Profiles of the azimuthal fluid displacement $\xi_y$ as a function of $x$ are overlaid in orange. An animated version of this figure (temporarily available https://drive.google.com/file/d/1RWIsRjlpe2CvuDbXAnPc7m2d7-niEQx5/view?usp=share_link) shows the oscillation of the magnetic field lines according to (\ref{['eqn:toydisplacement']}).
• Figure 4: Snapshots of the latitudinal ($x$) and azimuthal ($y$) velocity perturbations ($u_{\text{IVP}}$, $v_{\text{IVP}}$) from IVP II ($\textit{Lu} = 6.25 \times 10^5$, $\textit{Fr} = 0.025$, $\Gamma =0.1$) after the simulation has equilibrated. Panel descriptions are the same as in Figure \ref{['fig:casei']}. An animated version of this figure (temporarily available https://drive.google.com/file/d/19pU_GKMCCUQNPBcTSMLIC9d3OF1ZB3Bi/view?usp=share_link) shows the transient behavior of IVP II.
• Figure 5: (a) The real part of the local vertical wavenumber $k_z(z)$ versus height $z$ in the axisymmetric WKB problem ($k_y=0$, $\Gamma = 0.1$) in Section \ref{['sec:wkb:axi']}. Solid curves correspond to five discrete wave modes (IGW-0, IGW-1, evan.-0, evan.-1, SM-1) while the gray shaded region indicates the continuous spectrum of AWs (\ref{['eqn:alfvenbdry']}) at each height. Arrows indicate the direction of the WKB group velocity, computed using (\ref{['eqn:groupvel']}). IGW modes closely follow the wavenumber prediction for pure IGWs (vertical gray dash-dotted line) based on (\ref{['eqn:lowFrigwdisprel']}). A SM cutoff height (horizontal gray dashed line) at $z/L = \ln(6\pi \Gamma)/(2\pi) \approx 0.101$ bounds the upward path of SM-1. Note that two SM modes may exist above $z=0$ for higher values of $\Gamma$ (cf. Figure 5 of lecoanet_conversion_2017). (b) The real part of $k_z(z)$ in the resistive non-axisymmetric WKB problem ($k_y=2\pi/L$, $\Gamma = 0.1$) in Section \ref{['sec:wkb:nonaxi']}. The five waves present in the axisymmetric case are now accompanied by a sine-parity SM wave (SM-0), two AWs (AW-0 and AW-1), and a mixed SM-AW mode (SM-AW-1). The latter refracts as it approaches the same SM cutoff height (dashed gray line) as in panel a. (c) The imaginary part of the WKB wavenumber $k_z(z)$ for $k_y = 2\pi/L$ and $\Gamma = 0.1$. For the up-going SM, SM-AW, and AW modes, $\Im\{k_z\} > 0$ implies locally exponential damping and is due to Ohmic dissipation.