Stability of axially symmetric magnetic fields in stars

The magnetic fields observed in Ap-stars, white dwarfs, and neutron stars are known to be stable for long times. However, the physical conditions inside the stellar interiors that allow these states are still a matter of research. It has been formally demonstrated that both purely toroidal and purely poloidal magnetic fields develop instabilities at some point in the star. On the other hand, numerical simulations have proved the stability of roughly axisymmetric magnetic field configurations inside stably stratified stars. These configurations consist of mutually stabilizing toroidal and poloidal components in a twisted torus shape. Previous studies have proposed rough upper and lower bounds on the ratio of the magnetic energy in the toroidal and poloidal components of the magnetic field. With the purpose of mapping out the parameter space under which such configurations remain stable, we used the Pencil Code to perform 3D magnetohydrodynamic simulations of the evolution of the magnetic field in non-rotating, non-degenerate stars in which viscosity is the only dissipation mechanism, both for stars with a uniform (barotropic) and radially increasing (stably stratified) specific entropy. Furthermore, we considered different conditions regarding the degree of stable stratification and the magnetic energy in each component, roughly confirming the previously suggested stability boundaries for the magnetic field.