We study the hadron-quark phase transition in the interior of hot protoneutron stars, combining the Brueckner-Hartree-Fock approach for hadronic matter with the MIT bag model or the Dyson-Schwinger model for quark matter. We examine the structure of
the mixed phase constructed according to different prescriptions for the phase transition, and the resulting consequences for stellar properties. We find important effects for the internal composition, but only very small influence on the global stellar properties.
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-b
ody 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.
We explore the relevance of confinement in quark matter models for the possible quark core of neutron stars. For the quark phase, we adopt the equation of state (EoS) derived with the Field Correlator Method, extended to the zero temperature limit. F
or the hadronic phase, we use the microscopic Brueckner-Hartree-Fock many-body theory. We find that the currently adopted value of the gluon condensate $G_2 simeq 0.006-0.007 rm {GeV^4}$, which gives a critical temperature $T_c simeq 170 rm MeV$, produces maximum masses which are only marginally consistent with the observational limit, while larger masses are possible if the gluon condensate is increased.
