Constraints on the quark matter equation of state from astrophysical observations

We calculate the structure of neutron star interiors comprising both the hadronic and the quark phases. For the hadronic sector we employ a microscopic equation of state involving nucleons and hyperons derived within the Brueckner-Hartree-Fock many-body theory with realistic two-body and three-body forces. For the description of quark matter, we use several different models, e.g. the MIT bag, the Nambu--Jona-Lasinio (NJL), the Color Dielectric (CDM), the Field Correlator method (FCM), and one based on the Dyson-Schwinger model (DSM). We find that a two solar mass hybrid star is possible only if the nucleonic EOS is stiff enough.