Evolution of a magnetic field in a differentially rotating radiative zone

Abstract

Recent spectropolarimetric surveys of main-sequence intermediate-mass stars have exhibited a dichotomy in the distribution of the observed magnetic field between the kG dipoles of Ap/Bp stars and the sub-Gauss magnetism of Vega and Sirius. We would like to test whether this dichotomy is linked to the stability versus instability of large-scale magnetic configurations in differentially rotating radiative zones. We computed the axisymmetric magnetic field obtained from the evolution of a dipolar field threading a differentially rotating shell. A full parameter study including various density profiles and initial and boundary conditions was performed with a 2D numerical code. We then focused on the ratio between the toroidal and poloidal components of the magnetic field and discuss the stability of the configurations dominated by the toroidal component using local stability criteria and insights from recent 3D numerical simulations. The numerical results and a simple model show that the ratio between the toroidal and the poloidal magnetic fields is highest after an Alfvén crossing time of the initial poloidal field. For high density contrasts, this ratio converges towards an asymptotic value that can thus be extrapolated to realistic stellar cases. We then consider the stability of the magnetic configurations to non-axisymmetric perturbations and find that configurations dominated by the toroidal component are likely to be unstable if the shear strength is significantly higher than the poloidal Alfvén frequency. An expression for the critical poloidal field below which magnetic fields are likely to be unstable is found and is compared to the lower bound of Ap/Bp magnetic fields.

13 pages, 10 figures

References in corpus (7)

• Seismic constraints on the radial dependence of the internal rotation profiles of six Kepler subgiants and young red giants
• Weak magnetic fields in Ap/Bp stars: Evidence for a dipole field lower limit and a tentative interpretation of the magnetic dichotomy
• Angular momentum transport within evolved low-mass stars
• The stability of poloidal magnetic fields in rotating stars
• The angular momentum transport by unstable toroidal magnetic fields
• 3D evolution of magnetic fields in a differentially rotating stellar radiative zone
• On obliquely magnetized and differentially rotating stars

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• Global simulations of Tayler instability in stellar interiors: The stabilizing effect of gravity
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• Tayler-Spruit dynamo in stably stratified rotating fluids: Application to proto-magnetars
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• Fossil magnetic fields in intermediate-mass and massive stars
• A decade-long magnetic monitoring of Vega
• Axisymmetric investigation of differential rotation in contracting stellar radiative zones
• Secular dipole-dipole stability of magnetic binaries
• Exploring the probing power of gamma-Dor's inertial dip for core magnetism: case of a toroidal field