The contrasting magnetic fields of superconducting pulsars and magnetars

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 order ${10}^{15}$ 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 $B_{\text{pole}}\sim {10}^{14}$ 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.