Hadron-quark phase transition: the QCD phase diagram and stellar conversion

Abstract

Different extensions of the Nambu-Jona-Lasinio model, known to satisfy expected QCD chiral symmetry aspects, are used to investigate a possible hadron-quark phase transition at zero temperature and to build the corresponding binodal sections. We have shown that the transition point is very sensitive to the model parameters and that both pressure and chemical potential increase drastically with the increase of the vector interaction strength in the quark sector. Within the same framework, the possibility of quark and hybrid star formation is analyzed. The same conclusions drawn before with respect to the coexistence pressure and chemical potentials are reinforced. We conclude that even if a transition from a metastable hadronic star to a quark star is thermodinamically possible, it is either energetically forbidden or gives rise to a blackhole. Nevertheless, conversions from metastable to hybrid stars are possible, but the mass difference between both compact objects is very small, never larger than 0.2 M ⊙ .

Effects of Strong Magnetic Fields on the Hadron-Quark Deconfinement Transition

“…Following the stellar evolution scenario proposed by Refs. [8,9], we can assume the compact star as being initially a pure hadronic metastable star in the early stages after its emergence. In this stage, the equilibrium conditions are reached through the first deleptonization and cooling, and the resulting objects are the ones described by the black curve in Fig.…”

“…Although many works have already investigated the hadron-quark phase transition at zero temperature [5,6,7,8,9] with two different models, there are no works investigating the possible transition if matter is subject to strong magnetic fields. This is an interesting subject because of the existence of magnetars [10,11,12,13,14], which mani-fest themselves in quite different ways as compared to the traditional pulsars.…”

A Neutron Star Is Born

“…In this case, one would be dealing with what is known as hybrid star, and, from the theoretical point of view, its description requires a sophisticated recipe: a reliable model for the outer hadronic core and another model for the inner quark core. The ideal picture would be a chiral model that could describe both matters as density increases, but those models are still rarely used [117][118][119][120]. Generally, what we find in the literature are Walecka-type models such as the ones presented in Section 3.2 or density-dependent models, whose density dependence is introduced on the meson-baryon couplings as in [121,122] for the hadronic matter and the MIT bag model [123] or the Nambu-Jona-Lasinio (NJL) model [124] for the quark matter.…”

“…This hypothesis, later on also investigated by Witten, became known as the Bodmer-Witten conjecture, and it is theoretically tested with the search of a stability window, defined for different models in such a way that a two-flavor quark matter (2QM) must be unstable (i.e., its energy per baryon must be larger than 930 MeV, which is the iron-binding energy) and SQM (three-flavour quark matter) must be stable, i.e., its energy per baryon must be lower than 930 MeV [135,136]. As shown in the previous section, although the Nambu-Jona-Lasinio (NJL) model [124] can be used to describe the core of a hybrid star [120,126], it cannot be used in the description of absolutely stable SQM as shown in [137][138][139][140]. The most common model, the MIT bag model [123] satisfies the Bodmer-Witten conjecture, but cannot explain massive stars J0348+0432 [71], J1614-2230 [72] and J0740+6620) [8,70], as can be seen in Figure 20, from where one can observe that the maximum attained mass is 1.94 M obtained for a non-massive strange quark.…”

Modified MIT Bag Models -- part II: QCD phase diagram and hot quark stars

“…The description of stellar matter cannot be done using the two-flavor formalism presented in this section, since strangeness is necessary to fulfill the Bodmer-Witten conjecture. However, both hybrid and pure quark matter stars with the quark phase described by the three-flavor NJL model and NJL with a vector interaction model have been described in several studies [68][69][70]. It is worth noting, however, that these models do not produce stable quark matter at zero temperature and/or magnetic field [71], but they can certainly describe the inner matter of a hybrid star [25], which is enough to justify the applica-tion of this type of model in theoretical studies, mainly the ones involving phase transitions [68].…”