[abbreviated] Long-lived, large-scale magnetic field configurations exist in upper main sequence, white dwarf, and neutron stars. Externally, these fields have a strong dipolar component, while their internal structure and evolution are uncertain, but highly relevant for several problems in stellar and high-energy astrophysics. We discuss the main properties expected for the stable magnetic configurations in these stars from physical arguments, and how these properties may determine the modes

more »

... decay of these configurations. Stable magneto-hydrostatic equilibria are likely to exist in stars whenever the matter in their interior is stably stratified (not barotropic). These equilibria are not force-free and not required to satisfy the Grad-Shafranov equation, but they do involve both toroidal and poloidal field components. We argue that the main mode of decay for these configurations are processes that lift the constraints set by stable stratification, such as heat diffusion in main-sequence envelopes and white dwarfs, and beta decays or particle diffusion in neutron stars. In the former, heat diffusion is not fast enough to make these equilibria evolve over the stellar lifetime. In neutron stars, a strong enough field might decay by overcoming the compositional stratification through beta decays (at the highest field strengths) or through ambipolar diffusion (for somewhat weaker fields). These processes convert magnetic energy to thermal energy, and they occur at significant rates only once the latter is smaller than the former, and therefore they substantially delay the cooling of the neutron star, while slowly decreasing its magnetic energy.