Phenomenological Model Studies On Quark Matter And Quark Stars

In this thesis, we have investigated the properties of strange quark matter(SQM), quark symmetry energy and quark star within several phenomenological models. The thesis is composed of four parts and includes the results of quark matter and quark stars from density-dependent-mass models with/without considering strong magnetic ?eld, a con?ning quark model with Richardson potential and SU(3) Nambu–Jona-Lasinio(NJL)model with vector interaction under strong magnetic ?eld.Since it is di?cult to calculate the properties by using PQCD and Lattice QCD for strange quark matter with ?nite baryon density and zero temperature, phenomenological models are proposed to solve this problem. We extend the con?ned-density-dependent-mass(CDDM) model in Chapter 2 to include isospin dependence of the equivalent quark mass.Within the con?ned-isospin-density-dependent-mass(CIDDM) model, we study the quark matter symmetry energy, the stability of strange quark matter, and the properties of quark stars. We ?nd that including isospin dependence of the equivalent quark mass can signi?cantly in?uence the quark matter symmetry energy as well as the properties of strange quark matter and quark stars. While the recently discovered large mass pulsars PSR J1614.2230 and PSR J0348+0432 with masses around 2M⊙ cannot be quark stars within the CDDM model, they can be well described by quark stars in the CIDDM model. In particular, our results indicate that the two-?avor u–d quark matter symmetry energy should be at least about twice that of a free quark gas or normal quark matter within the conventional Nambu–Jona-Lasinio model in order to describe PSR J1614.2230 and PSR J0348+0432 as quark stars.In Chapter 3, we extend the con?ning quark matter(CQM) model, in which the con?nement is modeled by means of the Richardson potential for quark-quark interaction and the constituent quark mass is assumed to be density-dependent, to include isospin dependence of the constituent quark mass. Within this extended isospin-dependent con?ning quark matter(ICQM) model, we study the properties of strange quark matter and quark stars. We ?nd that including isospin dependence of the constituent quark mass can signi?cantly in?uence the quark matter symmetry energy, the stability of strange quark matter and the mass-radius relation of quark stars.An important aspect of the compact star physics is that compact stars could be endowed with strong magnetic ?elds. Within the con?ned isospin- and density-dependent mass model for simplicity, we study the properties of strange quark matter(SQM) and quark stars(QSs) under strong magnetic ?elds. The equation of state of SQM under a constant magnetic ?eld is obtained self-consistently and the pressure perpendicular to the magnetic ?eld is shown to be larger than that parallel to the magnetic ?eld, implying that the properties of magnetized QSs generally depend on both the strength and the orientation of the magnetic ?elds distributed inside the stars. Using a density-dependent magnetic ?eld pro?le which is introduced to mimic the magnetic ?eld strength distribution in a star,we study the properties of static spherical QSs by assuming two extreme cases for the magnetic ?eld orientation in the stars, i.e., the radial orientation in which the local magnetic ?elds are along the radial direction and the transverse orientation in which the local magnetic ?elds are randomly oriented but perpendicular to the radial direction. Our results indicate that including the magnetic ?elds with radial(transverse) orientation can signi?cantly decrease(increase) the maximum mass of QSs, demonstrating the importance of the magnetic ?eld orientation inside the magnetized compact stars.In Chapter 5, we construct quark magnetars in the framework of SU(3) Nambu–Jona-Lasinio(NJL) model, which is well accepted and more common to solve the properties of quark matter, with vector interaction under strong magnetic ?elds. The e?ects of vector-isoscalar and vectorisovector interaction on the equation of state(Eo S) of strange quark matter(SQM) is investigated, and it is found that the equation of state is not sensitive to the vector-isovector interaction, however, a repulsive interaction in the vector-isoscalar channel gives a sti?er equation of state for cold dense quark matter. In the presence of magnetic ?eld, gluons will be magnetized via quark loops, and the contribution from magnetized gluons to the Eo S is also estimated. For SQM under strong magnetic ?elds we consider anisotropic pressures and study the properties of SQM under a density-dependent magnetic ?eld pro?le which is introduced to mimic the magnetic ?eld distribution in a quark star(QS). The dependence of magnetar mass on the pressure of magnetized gluons has been discussed,and we study the parameter choice for the anisotropic pressures which can support 2 solar mass QSs by considering vector-isoscalar interaction and the magnetized gluon e?ect.