The Tayler Instability in the Anelastic Approximation
Abstract
The Tayler instability (TI) is a non-axisymmetric linear instability of an axisymmetric toroidal magnetic field in magnetohydrostatic equilibrium (MHSE). In a differentially rotating radiative region of a star, the TI could drive the Tayler-Spruit dynamo, which generates magnetic fields that can significantly impact stellar structure and evolution. Heuristic prescriptions disagree on the efficacy of the dynamo, and numerical simulations have yet to definitively agree upon its existence. The criteria for the TI to develop were derived using fully compressible magnetohydrodynamics, while numerical simulations of dynamical processes in stars frequently use an anelastic approximation. This motivates us to derive new anelastic Tayler instability criteria. We find that some MHSE configurations are unstable in the fully compressible case but become stable in the anelastic case. We find and characterize the unstable modes of a simple family of cylindrical MHSE configurations using numerical calculations, and we discuss the implications for fully nonlinear anelastic simulations.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- August 2019
- DOI:
- 10.3847/1538-4357/ab2a11
- arXiv:
- arXiv:1808.08958
- Bibcode:
- 2019ApJ...881...66G
- Keywords:
-
- dynamo;
- instabilities;
- magnetic fields;
- magnetohydrodynamics: MHD;
- stars: interiors;
- stars: magnetic field;
- Astrophysics - Solar and Stellar Astrophysics
- E-Print:
- 11 pages, 3 figures, 1 appendix