Magnetic fields of compact stars with superconducting quark cores

The behavior of the magnetic field of a rotating neutron star with a superconducting color-flavor-locked (CFL) quark matter core is investigated in the framework of the Ginzburg-Landau theory. We take into account the simultaneous coupling of the diquark condensate field to the magnetic and gluomagnetic gauge fields. We solve the Ginzburg-Landau equations by properly taking into account the boundary conditions, in particular the gluon confinement condition. The rotation of the CFL condensate produces neutral vortices with normal cores. We find the distribution of the magnetic field in both the quark and the hadronic phases and show that a magnetic field penetrates into quark phase through normal cores of the rotational vortices. As a result, equivalent "magnetic vortices" are formed due to the induced Meissner currents.