The mass and radii of strongly magnetized neutron stars

It has been clear for some time now that super-critical surface magnetic fields, exceeding 4 x 10^13 G, exist on a subset of neutron stars. These magnetars may harbor interior fields many orders of magnitude larger, potentially reaching equipartition values. However, the impact of these strong fields on stellar structure has been largely ignored, potentially complicating attempts to infer the high density nuclear equation of state. Here we assess the effect of these strong magnetic fields on the mass-radius relationship of neutron stars. We employ an effective field theory model for the nuclear equation of state that includes the impact of hyperons, anomalous magnetic moments, and the physics of the crust. We consider two magnetic field geometries, bounding the likely magnitude of the impact of magnetic fields: a statistically isotropic, tangled field and a force-free configuration. In both cases even equipartition fields have at most a 30% impact on the maximum mass. However, the direction of the effect of the magnetic field depends on the geometry employed - force-free fields leading to reductions in the maximum neutron star mass and radius while tangled fields increase both - challenging the common intuition in the literature on the impact of magnetic fields.