A consistent description of neutron stars with quark cores

We consider the equation of state of hadroninc and quark matter at finite density in mean field theory, through an effective chiral Lagrangian whose parameters (coupling constants) are all fixed by hadronic data. Between three to seven times nuclear density, for charge neutral quark matter in β equilibrium, we find the ground state to be a neutral pion condensate. With increasing baryon density we then expect nuclear matter, followed by pion condensed quark matter at intermediate density, and finally the diquark colour-flavour CFL condensate. These are all states with chiral spontaneous symmetry breaking (SSB). We find another remarkable feature and this is that the scalar (pseudoscalar) coupling, λ, has a crucial and unexpected influence on the physics of neutron stars. Neutron stars with pion condensed quark matter cores exist only in a small window, between, 5.7 <λ <6.45. Interestingly, this range is consistent with the value of λ derived from π,π scattering data and such stellar cores may carry magnetar strength magnetic fields