Global simulations of Tayler instability in stellar interiors: a long-time multistage evolution of the magnetic field

Magnetic fields are observed in massive Ap/Bp stars and are presumably present in the radiative zone of solar-like stars. To date, there is no clear understanding of the dynamics of the magnetic field in stably stratified layers. A purely toroidal magnetic field configuration is known to be unstable, developing mainly non-axisymmetric modes. Rotation and a poloidal field component may lead to stabilization. Here we perform global MHD simulations with the EULAG-MHD code to explore the evolution of a toroidal magnetic field located in a layer whose Brunt-Vaisala frequency resembles the lower solar tachocline. Our numerical experiments allow us to explore the initial unstable phase as well as the long-term evolution of such field. During the first Alfven cycles, we observe the development of the Tayler instability with the prominent longitudinal wavenumber, m = 1. Rotation decreases the growth rate of the instability and eventually suppresses it. However, after a stable phase, energy surges lead to the development of higher-order modes even for fast rotation. These modes extract energy from the initial toroidal field. Nevertheless, our results show that sufficiently fast rotation leads to a lower saturation energy of the unstable modes, resulting in a magnetic topology with only a small fraction of poloidal field, which remains steady for several hundreds of Alfven traveltimes. The system then becomes turbulent and the field is prone to turbulent diffusion. The final toroidal-poloidal configuration of the magnetic field may represent an important aspect of the field generation and evolution in stably stratified layers.