Neutron stars and the transition to color-superconducting quark matter

We explore the relevance of color superconductivity inside a possible quark matter core for the bulk properties of neutron stars. For the quark phase we use an Nambu--Jona-Lasinio (NJL) type model, extended to include diquark condensates. For the hadronic phase, a microscopic many-body model is adopted, with and without strangeness content. In our calculations, a sharp boundary is assumed between the hadronic and the quark phases. For NJL model parameters fitted to vacuum properties we find that no star with a pure quark core does exist. Nevertheless the presence of color superconducting phases can lower the neutron star maximum mass substantially. In some cases, the transition to quark matter occurs only if color superconductivity is present. Once the quark phase is introduced, the value of the maximum mass stays in any case below the value of two solar masses.