In this paper, we explore whether or not quark deconfinement may occur in high-mass neutron stars such as J1614 $-${} 2230 ($1.97\ifmmode\pm\else\textpm\fi{}0.04\phantom{\rule{0.16em}{0ex}}{M}_{$\bigodot${}}$) and J0348 + 0432 ($2.01\ifmmode\pm\else\textpm\fi{}0.04\phantom{\rule{0.16em}{0ex}}{M}_{$\bigodot${}}$). Our study is based on a nonlocal extension of the SU(3) Nambu\char21{}Jona-Lasinio (n3NJL) model with repulsive vector interactions among the quarks. This model goes beyond the frequently used local version of the Nambu\char21{}Jona-Lasinio (NJL) model by accounting for several key features of QCD which are not part of the local model. Confined hadronic matter is treated in the framework of nonlinear relativistic mean field theory. We find that both the local as well as the nonlocal NJL model predict the existence of extended regions of mixed quark-hadron (quark-hybrid) matter in high-mass neutron stars with masses of 2.1 to $2.4\phantom{\rule{0.16em}{0ex}}{M}_{$\bigodot${}}$. Pure quark matter in the cores of neutron stars is obtained for certain parametrizations of the hadronic lagrangian and choices of the vector repulsion among quarks. The radii of high-mass neutron stars with quark-hybrid matter and/or pure quark matter cores in their centers are found to lie in the canonical range of 12 to 13 km.

The recent direct observation of gravitational wave event GW170817 and its GRB 170817 A signal has opened up a new window to studying neutron stars and heralds a new era of astronomy referred to as the multimessenger astronomy. Both gravitational and electromagnetic waves from a single astrophysical source have been detected for the first time. This combined detection offers an unprecedented opportunity to place constraints on the neutron star matter equation of state (EoS). The existence of a possible hadron–quark phase transition in the central regions of neutron stars is associated with the appearance of g modes, which are extremely important as they could signal the presence of a pure quark matter core in the centers of neutron stars. Observations of g modes with frequencies between 1 and 1.5 kHz could be interpreted as evidence of a sharp hadron–quark phase transition in the cores of neutron stars. In this article, we shall review the description of the dense matter composing neutron stars, the determination of the EoS of such matter, and the constraints imposed by astrophysical observations of these fascinating compact objects.

Strange quark matter could be found in the core of neutron stars or forming strange quark stars. As is well known, these astrophysical objects are endowed with strong magnetic fields that affect the microscopic properties of matter and modify the macroscopic properties of the system. In this article we study the role of a strong magnetic field in the thermodynamical properties of a magnetized degenerate strange quark gas, taking into account β-equilibrium and charge neutrality. Quarks and electrons interact with the magnetic field via their electric charges and anomalous magnetic moments. In contrast to the magnetic field value of ${10}^{19}$ G, obtained when anomalous magnetic moments are not taken into account, we find the upper bound $B\lesssim 8.6\times {10}^{17}$ G, for the stability of the system. A phase transition could be hidden for fields greater than this value.

We investigate the hadron-quark phase transition in cold neutron stars in light of (i) the observed limits on the maximum-mass of heavy pulsars, (ii) constraints on the tidal properties inferred from the gravitational waves emitted in binary neutron-star mergers, and (iii) mass and radius constraints derived from the observation of hot spots on neutron star observed with the Neutron Star Interior Composition Explorer instrument. Special attention is directed to the possible presence of $\mathrm{\Delta }(1232)$ baryons in neutron star matter. Our results indicate that this particle could make up a large fraction of the baryons in neutron stars and thus have a significant effect on the properties of such objects, particularly on their radii. This is partially caused by the low density appearance of $\mathrm{\Delta }\mathrm{s}$ for a wide range of theoretically defensible sets of meson-hyperon, SU(3) ESC08 model, and meson-$\mathrm{\Delta }$ coupling constants. The transition of hadronic matter to quark matter, treated in the $2\mathrm{SC}+\mathrm{s}$ condensation phase, is found to occur only in neutron stars very close to the mass peak. Nevertheless, quark matter may still constitute an appreciable fraction of the stars’ total matter if the phase transition is treated as Maxwell-like (sharp), in which case the neutron stars located beyond the gravitational mass peak would remain stable against gravitational collapse. In this case, the instability against gravitational collapse is shifted to a new (terminal) mass different from the maximum-mass of the stellar sequence, giving rise to stable compact objects with the same gravitational masses as those of the neutron stars on the traditional branch, but whose radii are smaller by up to 1 km. All models for the equation of state of our study fall comfortably within the bound established very recently by Annala et al. [ Nat. Phys., 10.1038/s41567-020-0914-9 (2020)].

In the first part of this paper, we use a nonlocal extension of the three-flavor Polyakov-Nambu-Jona-Lasinio model, which takes into account flavor-mixing, momentum dependent quark masses, and vector interactions among quarks, to investigate the possible existence of a spinodal region (determined by the vanishing of the speed of sound) in the QCD phase diagram and determine the temperature and chemical potential of the critical end point. In the second part of the paper, we investigate the quark-hadron composition of baryonic matter at zero as well as nonzero temperature. This is of great topical interest for the analysis and interpretation of neutron star merger events such as GW170817. With this in mind, we determine the composition of proto-neutron star matter for entropies and lepton fractions that are typical of such matter. These compositions are used to delineate the evolution of proto-neutron stars to neutron stars in the baryon-mass versus gravitational-mass diagram. The hot stellar models turn out to contain significant fractions of hyperons and $\mathrm{\Delta }$ isobars but no deconfined quarks. The latter are found to exist only in cold neutron stars.