On the rotation and magnetic field evolution of superconducting strange stars

Are pulsars made up of strange matter? The magnetic field decay of a pulsar may be able to give us an answer. Since Cooper pairing of quarks occurs inside a sufficiently cold strange star, the strange stellar core is superconducting. In order to compensate for the effect of rotation, different superconducting species inside a rotating strange star try to set up different values of London fields. Thus we have a frustrated system. Using Ginzburg-Landau formalism, I solved the problem of a rotating superconducting strange star: Instead of setting up a global London field, vortex bundles carrying localized magnetic fields are formed. Moreover, the number density of vortex bundles is directly proportional to the angular speed of the star. Since it is energetically favorable for the vortex bundles to pin to magnetic flux tubes, the rotational dynamics and magnetic evolution of a strange star are coupled together, leading to magnetic flux expulsion as the star slows down. I investigate this effect numerically and find that the characteristic field decay time is much less than 20 Myr in all reasonable parameter regions. On the other hand, the characteristic magnetic field decay time for pulsars is greater than or equal to 20 Myr. Thus, my finding casts doubts on the hypothesis that pulsars are strange stars.