Observational constraints on quark matter in neutron stars

We estimate the constraints of observational mass and redshift on the properties of equations of state (EOS) for quark matter based on the quasiparticle description in the compact stars. We discuss two scenarios: strange stars and hybrid stars. We construct the equations of state utilizing an extended MIT bag model taking medium effect into account for quark matter and relativistic mean field theory for hadron matter. We show that quark matter may exist in strange stars and the interior of neutron stars. The bag constant is a key parameter that affects strongly the mass of strange stars. The medium effect can lead to the stiff hybrid-star EOS directing to the pure hadronic EOS due to the reduction of quark matter, and hence the existence of the heavy hybrid stars. We find that the intermediate coupling constant may be the best choice for compatibility with observational constraints in hybrid stars.