Gravity's role in taming the Tayler instability in red giant cores

Abstract

The stability of toroidal magnetic fields in radiative stellar interiors is a key open problem in astrophysics. We investigate the Tayler instability of purely toroidal fields $B_{\varphi }$ in a nonrotating, thermally stably stratified stellar region using global linear perturbation analysis and 3D direct numerical simulations in spherical geometry. Both approaches assume a magnetohydrostatic equilibrium where the Lorentz force is balanced by a pressure gradient, and include gravity and thermal diffusion. The simulations incorporate finite resistivity and viscosity and span the full range from stable to highly supercritical regimes for the first time. The global linear analysis reveals two classes of unstable nonaxisymmetric $m=1$ modes. High-latitude modes grow at Alfvénic rates with short radial scales, consistent with local WKB solutions. Low-latitude modes, missed by local analyses, show larger radial scales and reduced growth rates due to the stabilizing buoyancy. Simulations support these findings and yield field strength thresholds for both instability onset and the transition between global and WKB regimes. These thresholds correspond to the roots of two algebraic equations of the form $B_{\varphi }^{3/4}-a_1{\mathcal{A}}_1{B}_{\varphi }^{1/4}-a_0{\mathcal{A}}_0=0$, where ${\mathcal{A}}_0$, ${\mathcal{A}}_1$ depend on the fluid properties, and $a_0$, $a_1$ are simulation-derived coefficients. Combining our results with stellar evolution models of low-mass stars, we find that outer radiative cores of red giants are generally unstable, while deeper degenerate regions require toroidal fields above $10-100$ kG for instability. Our findings may help to constrain asteroseismic magnetic field detection and angular momentum transport in red giant cores, and provide a framework for identifying instability conditions in other stars with radiative interiors.

arXiv comment16 pages, 13 figures. Section 2 significantly revised and corrected. Section 3 updated with new numerical simulations and extended analysis. Sections 4-5 include a new discussion of stellar evolution model results. Accepted for publication in Astronomy & Astrophysics

References in corpus (29)

• Updated Electron-Conduction Opacities: The Impact on Low-Mass Stellar Models
• Stable magnetic fields in stellar interiors
• Slowing the Spins of Stellar Cores
• Efficient Spherical Harmonic Transforms aimed at pseudo-spectral numerical simulations
• Asteroseismology Can Reveal Strong Internal Magnetic Fields in Red Giant Stars
• On the Stability of Non Force-Free Magnetic Equilibria in Stars
• The age of the Sun and the relativistic corrections in the EOS
• 30 to 100-kG magnetic fields in the cores of red giant stars
• Strong magnetic fields detected in the cores of 11 red giant stars using gravity-mode period spacings
• The angular momentum transport by unstable toroidal magnetic fields
• Stability of Toroidal Magnetic Fields in Rotating Stellar Radiation Zones
• Excitation of gravity waves by fingering convection, and the formation of compositional staircases in stellar interiors
• 3D evolution of magnetic fields in a differentially rotating stellar radiative zone
• Stability of magnetic configurations containing the toroidal and axial fields
• Spin-down by dynamo action in simulated radiative stellar layers
• Interplay between magnetic fields and differential rotation in a stably stratified stellar radiative zone
• Numerical simulations of the Tayler-Spruit dynamo in proto-magnetars
• Global simulations of Tayler instability in stellar interiors: The stabilizing effect of gravity
• Stability of the toroidal magnetic field in stellar radiation zones
• Magnetohydrodynamic Simulations of the Tayler Instability in Rotating Stellar Interiors
• Resonance instability of axially-symmetric magnetostatic equilibria
• The Tayler Instability in the Anelastic Approximation
• Tayler-Spruit dynamo in stably stratified rotating fluids: Application to proto-magnetars
• Tayler Instability Revisited
• Critical fields and growth rates of the Tayler instability as probed by a columnar gallium experiment
• The Stability of Prendergast Magnetic Fields
• Global simulations of Tayler instability in stellar interiors: a long-time multi-stage evolution of the magnetic field
• Magnetic fields of Ap stars as a result of an instability
• Detectability of axisymmetric magnetic fields from the core to the surface of oscillating post-main sequence stars