Magnetic fields within color superconducting neutron star cores

We discuss the Meissner effect for a color superconductor formed by cold dense quark matter. Though color and ordinary electromagnetism are broken in a color superconductor, there is a linear combination of the photon and a gluon that remains massless. Consequently, a color superconducting region may be penetrated by an external magnetic field. We show that at most a small fraction of the magnetic field is expelled, and if the screening distance is the smallest length scale in the problem there is no expulsion at all. We calculate the behavior of the magnetic field for a spherical geometry relevant for compact stars. If a neutron star contains a quark matter core, this core is a color superconductor. Our results demonstrate that such cores admit magnetic fields without restricting them to quantized flux tubes. Such magnetic fields within color superconducting neutron star cores are stable on time scales longer than the age of the universe, even if the spin period of the neutron star is changing.