We study a family of equations of state (EOS) for hybrid neutron star matter. The hybrid EOS are obtained by a Maxwell construction of the first-order phase transition between a hadronic phase described by the relativistic density-functional EOS of the “DD2” class with excluded volume effects and a deconfined quark matter phase modeled by an instantaneous nonlocal version of the Nambu–Jona-Lasinio model in $\text{SU}{\left(2\right)}_f$ with vector interactions and color superconductivity. The form factor in the nonlocal quark matter model is fitted to lattice QCD results in the Coulomb gauge. Owing to strong coupling in the vector meson and diquark channels, a coexistence phase of color superconductivity and chiral symmetry breaking occurs. Our results show an approximately constant behavior for the squared speed of sound with values of 0.4–0.6 in the density region relevant for neutron star interiors. To simultaneously fulfill the constraints from the Neutron Star Interior Composition Explorer radius measurement for PSR $\mathrm{J}0740+6620$ and tidal deformability from GW170817 it is necessary to consider a $\mu$-dependent bag pressure that mimics confinement.

We present a hybrid equation of state (EoS) for dense matter in which a nuclear matter phase is described within the Dirac-Brueckner-Hartree-Fock (DBHF) approach and a two-flavor quark matter phase is modelled according to a recently developed covariant, nonlocal chiral quark model. We show that modern observational constraints for compact star masses ($M~2M_{\odot }$) can be satisfied when a small vector-like four quark interaction is taken into account. The corresponding isospin symmetric EoS is consistent with flow data analyses of heavy ion collisions and points to a deconfinement transition at about 0.55 fm${}^{-3}$.

We reconsider the problem of the hyperon puzzle and its suggested solution by quark deconfinement within the two-phase approach to hybrid compact stars with recently obtained hadronic and quark matter equations of state. For the hadronic phase we employ the hypernuclear equation of state from the lowest order constrained variational method and the quark matter phase is described by a sufficiently stiff equation of state based on a color superconducting nonlocal Nambu-Jona-Lasinio model with constant (model nlNJLA) and with density-dependent (model nlNJLB) parameters. We study the model dependence of the phase transition obtained by a Maxwell construction. Our study confirms that also with the present set of equations of state quark deconfinement presents a viable solution of the hyperon puzzle even for the new constraint on the lower limit of the maximum mass from PSR $\mathrm{J}0740+6620$. In this work we provide with model nlNJLB for the first time a hybrid star EoS with an intermediate hypernuclear matter phase between the nuclear and color superconducting quark matter phases, for which the maximum mass of the compact star reaches $2.2M_{\odot }$, in accordance with most recent constraints. In model nlNJLA such a phase cannot be realized because the phase transition onset is at low densities, before the hyperon threshold density is passed. We discuss possible consequences of the hybrid equation of state for the deconfinement phase transition in symmetric matter as it will be probed in future heavy-ion collisions at the GSI Facility for Antiproton and Ion Research, the Nuclotron-based Ion Collider fAcility, and corresponding energy scan programs at the CERN Large Hadron Collider and the BNL Relativistic Heavy Ion Collider.

We consider the phase diagram of two-flavor quark matter under neutron star constraints for two nonlocal, covariant quark models within the mean-field approximation. In the first case (Model I) the nonlocality arises from the regularization procedure, motivated by the instanton liquid model, whereas in the second one (Model II) a separable approximation of the one-gluon exchange interaction is applied. We find that Model II predicts a larger quark mass gap and a chiral symmetry breaking (CSB) phase transition line which extends 15–20% further into the phase diagram spanned by temperature ($T$) and chemical potential ($\mu$). The corresponding critical temperature at $\mu =0$, $T_c(0)\simeq 140\mathrm{MeV}$, is in better accordance to recent lattice QCD results than the prediction of the standard local NJL model, which exceeds 200 MeV. For both Model I and Model II we have considered various coupling strengths in the scalar diquark channel, showing that different low-temperature quark matter phases can occur at intermediate densities: a normal quark matter (NQM) phase, a two-flavor superconducting (2SC) quark matter phase and a mixed 2SC-NQM phase. Although in most cases there is also a gapless 2SC phase, this occurs in general in a small region at nonzero temperatures, thus its effect should be negligible for compact star applications.

We investigate the surface tension $\sigma$ and the curvature energy $\gamma$ of quark matter drops in the MIT bag model with vector interactions. Finite size corrections to the density of states are implemented by using the multiple reflection expansion (MRE) formalism. We find that $\sigma$ and $\gamma$ are strongly enhanced by new terms arising from vector interactions. With respect to the noninteracting case they are increased by a large factor, which can be as high as $\sim 10$ when the vector coupling constant $g$ varies within the range used in the literature. This behavior may have major consequences for the hadron-quark mixed phase speculated to exist at neutron star (NS) interiors, which may be totally suppressed or have its extension substantially reduced.

We review the properties of hybrid stars with a quark matter core and a hadronic mantle, focusing on the role of key micro-physical properties such as the quark/hadron surface and curvature tensions and the conversion speed at the interface between both phases. We summarize the results of works that have determined the surface and curvature tensions from microscopic calculations. If these quantities are large enough, mixed phases are energetically suppressed and the quark core would be separated from the hadronic mantle by a sharp interface. If the conversion speed at the interface is slow, a new class of dynamically stable hybrid objects is possible. Densities tens of times larger than the nuclear saturation density can be attained at the center of these objects. We discuss possible formation mechanisms for the new class of hybrid stars and smoking guns for their observational identification.