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 ( 10 ^ { 13 } < B < 10 ^ { 14 } ~ { } G ; 3 < P < 12 ~ { } 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 } ~ { } yrs 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 , as well as calculate how the magnetic field and period evolve in a manner concurrent with RQINS observations .