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.
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