Hybrid stars in the light of the massive pulsar PSR J1614-2230

We perform a systematic study of hybrid star configurations using several parametrizations of a relativistic mean-field hadronic EoS and the NJL model for three-flavor quark matter. For the hadronic phase we use the stiff GM1 and TM1 parametrizations, as well as the very stiff NL3 model. In the NJL Lagrangian we include scalar, vector and 't Hooft interactions. The vector coupling constant $g_v$ is treated as a free parameter. We also consider that there is a split between the deconfinement and the chiral phase transitions which is controlled by changing the conventional value of the vacuum pressure $- Ω_0$ in the NJL thermodynamic potential by $- (Ω_0 + δΩ_0)$, being $δΩ_0$ a free parameter. We find that, as we increase the value of $δΩ_0$, hybrid stars have a larger maximum mass but are less stable, i.e. hybrid configurations are stable within a smaller range of central densities. For large enough $δΩ_0$, stable hybrid configurations are not possible at all. The effect of increasing the coupling constant $g_v$ is very similar. We show that stable hybrid configurations with a maximum mass larger than the observed mass of the pulsar PSR J1614-2230 are possible for a large region of the parameter space of $g_v$ and $δΩ_0$ provided the hadronic equation of state contains nucleons only. When the baryon octet is included in the hadronic phase, only a very small region of the parameter space allows to explain the mass of PSR J1614-2230. We compare our results with previous calculations of hybrid stars within the NJL model. We show that it is possible to obtain stable hybrid configurations also in the case $δΩ_0=0$ that corresponds to the conventional NJL model for which the pressure and density vanish at zero temperature and chemical potential.