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Long-lived magnetic fields are known to exist in upper main-sequence stars,white dwarfs, and neutron stars. In order to explore possible equilibriumconfigurations of the magnetic field inside these stars, we have performed3D-magnetohydrodynamic simulations of the evolution of initially randommagnetic fields in stably stratified and barotropic stars with an ideal-gasequation of state using the {\sc Pencil Code}, a high-order finite-differencecode for compressible hydrodynamic flows in the presence of magnetic fields. Inbarotropic (isentropic) stars, we confirm previous results in the sense thatall initial magnetic fields we tried decay away, unable to reach a stableequilibrium. In the case of stably stratified stars (with radially increasingspecific entropy), initially random magnetic fields appear to always evolve toa stable equilibrium. However, the nature of this equilibrium depends on thedissipation mechanisms considered. If magnetic diffusivity (orhyperdiffusivity) is included, the final state is more axially symmetric anddominated by large wavelengths than the initial state, whereas this is not thecase if only viscosity (or hyperviscosity) is present. In real stars, the mainmechanism allowing them to relax to an equilibrium is likely to be phasemixing, which we argue is more closely mimicked by viscosity. Therefore, weconclude that, depending on its formation mechanism, the equilibrium magneticfield in these stars could in principle be very asymmetric.

Evolution of random initial magnetic fields in stably stratified and barotropic stars