  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 star's interior field is in equilibrium with its
magnetosphere, thus bridging the 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.
