The contrasting magnetic fields of superconducting pulsars and magnetars

Abstract

We study equilibrium magnetic field configurations in a neutron star (NS) whose core has type-II superconducting protons. Unlike the equations for normal matter, which feature no special field strength, those for superconductors contain the lower critical field, of the order of 1015 G. We find that the ratio of this critical field to the smooth-averaged stellar field at the crust–core boundary is the key feature dictating the field geometry. Our results suggest that pulsar- and magnetar-strength fields have notably different configurations. Field decay for NSs with Bpole ∼ 1014 G could thus result in substantial internal rearrangements, pushing the toroidal field component out of the core; this may be related to observed magnetar activity. In addition, we calculate the magnetically induced ellipticities of our models.