Magnetic field configurations in neutron stars from MHD simulations

We have studied numerically the evolution of magnetic fields in barotropic neutron stars, by performing non-linear magnetohydrodynamical simulations with the code PLUTO. For both initially predominantly poloidal and toroidal fields, with varying strengths, we find that the field settles down to a mixed poloidal-toroidal configuration, where the toroidal component contributes between ${\rm 10}$ and $20 {{\ \rm per\ cent}}$ of the total magnetic energy. This is, however, not a strict equilibrium, as the instability leads to the development of turbulence, which, in turn, gives rise to an inverse helicity cascade, which determines the final 'twisted torus' setup. The final field configuration is thus dictated by the non-linear saturation of the instability, and is not stationary. The average energy of the poloidal and toroidal components, however, is approximately stable in our simulations, and a complex multipolar structure emerges at the surface, while the magnetic field is dipolar at the exterior boundary, outside the star.