2006ApJ...646L..17N

We discuss a model wherein soft gamma-ray repeaters (SGRs), anomalous X-ray pulsars (AXPs), and radio-quiet isolated neutron stars (RQINSs) are all compact objects exhibiting superconductivity, namely, color-flavor-locked quark stars. In particular, we calculate the magnetic field decay due to the expulsion of spin-induced vortices from the star's superfluid-superconducting interior, and the resultant spin-down rate. We find that for initial parameters characteristic of AXPs/SGRs (10¹³G<B<10¹⁴G, 3s<P<12s), the magnetic field strengths and periods remain unchanged within a factor of 2 for timescales on the order of 5x10⁵ to 5x10⁷ yr given a quark star of radius 10 km. Within these timescales, we show that the observed period clustering in RQINSs can be explained by compactness, and we calculate how the magnetic field and period evolve in a manner concurrent with RQINS observations.