Magnetic Field Decay and Period Evolution of Anomalous X-Ray Pulsars in the Context of Quark Stars

Abstract

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&#39;s superfluid-superconducting interior, and the resultant spin-down rate. We find that, for initial parameters characteristic of AXPs/SGRs ($10^{13}<B<10^{14}~\rm{G}$; $3<P<12~\rm{s}$), the magnetic field strengths and periods remain unchanged within a factor of two for timescales of the order of $5\times 10^{5} - 5\times 10^{7}~\rm{yrs}$ given a quark star of radius $10~\rm{km}$. Within these timescales, we show that the observed period clustering in RQINSs can be explained by compactness, as well as calculate how the magnetic field and period evolve in a manner concurrent with RQINS observations.