We construct hydromagnetic neutron star equilibria which allow for a non-zero electric current distribution in the exterior. The novelty of our models is that the neutron stars interior field is in equilibrium with its magnetosphere, thus bridging th
e gap between previous work in this area which either solves for the interior assuming a vacuum exterior or solves for the magnetosphere without modelling the star itself. We consider only non-rotating stars in this work, so our solutions are most immediately applicable to slowly-rotating systems such as magnetars. Nonetheless, we demonstrate that magnetospheres qualitatively resembling those expected for both magnetars and pulsars are possible within our framework. The inside-out approach taken in this paper should be more generally applicable to rotating neutron stars, where the interior and exterior regions are again not independent but evolve together.
