Quark matter in high-mass neutron stars?

The recent measurements of the masses of the pulsars PSR J1614-2230 and PSR J0348-0432 provide independent proof for the existence of neutron stars with masses in range of 2 $M_\odot$. This fact has significant implications for the physics of high density matter and it challenges the hypothesis that the cores of NS can be composed of deconfined quark matter. In this contribution we study a description of quark matter based on the Nambu--Jona-Lasinio effective model and construct the equation of state for matter in beta equilibrium. This equation of state together with the hadronic Dirac-Brueckner-Hartree-Fock equation of state is used here to describe neutron star and hybrid star configurations. We show that compact stars masses of 2 $M_\odot$ are compatible with the possible existence of deconfined quark matter in their core.