Paramagnetism in colour superconductivity and compact stars

It is quite plausible that colour superconductivity occurs in the inner regions of neutron stars. At the same time, it is known that strong magnetic fields exist in the interior of these compact objects. In this paper we discuss some important effects that can occur in the colour superconducting core of compact stars due to the presence of the stars' magnetic field. In particular, we consider the modification of the gluon dynamics for a colour superconductor with three massless quark flavours in the presence of an external magnetic field. We show that the long-range component of the external magnetic field that penetrates the colour-flavour locked phase produces an instability for field values larger than the charged gluons' Meissner mass. As a consequence, the ground state is restructured forming a vortex state characterized by the condensation of charged gluons and the creation of magnetic flux tubes. In the vortex state the magnetic field outside the flux tubes is equal to the applied one, while inside the tubes its strength increases by an amount that depends on the amplitude of the gluon condensate. This paramagnetic behaviour of the colour superconductor can be relevant for the physics of compact stars