Upper critical field and (non)-superconductivity of magnetars

We construct equilibrium models of compact stars using a realistic equation of state and obtain the density range occupied by the proton superconductor in strong B-fields. We do so by combining the density profiles of our models with microscopic calculations of proton pairing gaps and the critical unpairing field H<inf>c2</inf> above which the proton type-II superconductivity is destroyed. We find that magnetars with interior homogeneous field within the range 0.1 ≤ B<inf>16</inf> ≤ 2, where B<inf>16</inf> = B/10¹⁶ G, are partially superconducting, whereas those with B<inf>16</inf> > 2 are void of superconductivity. We briefly discuss the neutrino emissivity and superfluid dynamics of magnetars in the light of their (non)-superconductivity.