Are there any stable magnetic fields in barotropic stars?

We construct barotropic stellar equilibria, containing magnetic fields with both poloidal and toroidal field components. We extend earlier results by exploring the effect of different magnetic field and current distributions. Our results suggest that the boundary treatment plays a major role in determining whether the poloidal or toroidal field component is globally dominant. Using time evolutions we provide the first stability test for mixed poloidaltoroidal fields in barotropic stars, finding that all these fields suffer instabilities due to one of the field components: these are localized around the pole for toroidal-dominated equilibria and in the closed-field line region for poloidal-dominated equilibria. Rotation provides only partial stabilization. There appears to be very limited scope for the existence of stable magnetic fields in barotropic stars. We discuss what additional physics from real stars may allow for stable fields.