Stellar Magnetic Equilibria with the Pencil Code

Stable magnetic fields have been observed in intermediate-mass stars in the main-sequence (Ap/Bp stars) and in degenerate stars (white dwarfs and neutron stars). Despite the important role that the magnetic field plays in the stellar evolution, its origin, internal structure and the way it can survive timescales as long as the star's lifetime are not still completely understood.

In the past years, important steps have been made in this line of research. For example, purely toroidal and poloidal magnetic fields are known to develop instabilities at some point in the star. Numerical simulations have shown that random initial magnetic fields in stably stratified stars can evolve into a roughly axisymmetric stable equilibrium configuration consisting of both toroidal and poloidal components of comparable strength in a twisted-torus shape. Additionally, different studies have put rough upper and lower bounds on the ratio of the magnetic energy in the toroidal and poloidal components of the magnetic field. 

 In order to contribute to the study of the stability of magnetic field configurations, we perform 3D-MHD simulations of the evolution of magnetic field configurations with the Pencil Code, a high-order-finite-difference code for compressible hydrodynamics flows. We first validate the use of the  Pencil Code, confirming that a random magnetic field evolves, in a few Alfven timescales, to an ordered magnetic configuration in a stratified star while it decays away in a barotropic one. Then, we test the stability of different axially symmetric magnetic field configurations by following their dynamical evolution inside the star. We have evolved linked configurations of poloidal and toroidal magnetic fields under different initial conditions (i.e. the star's stratification and magnetic field strengths) and mapped the parameter space where the configuration evolves to a stable equilibrium.