The Model Study Of Quark Stars

The studies on compact stars have attracted astronomers and physicists'attention for a long time, because it plays a very important role in our understanding of the dynamical evolution of the stars, the constitution of matter, the development and veri-fication of the fundamental physical theory. The condition of large mass, high density, strong magnetic field and high temperature is never attained at the laboratory on earth. So, since the discovery of this compact star, the studies about it have continuous im-pelled the development of physical theories,and conversely the progress of the theory of physics promote our knowledge about the constitution, construction and the properties of the compact stars again. Up to now, we have discovered two kinds of compact stars: White Dwarf Star and Neutron Star from astronomical-observations.the White Dwarf Star was first found by astronomical-observations, and their properties were clarified by using the quantum theory. However, the existence of the Neutron Star was first predicted from the theories based on particle physics and general relativity, and three decades later was discovered accidentally. With the emergence of general relativity, a kind of exotic stellar object:Black Hole was predicted. But so far people have to deter-mined its existence by indirect method. Through the development of particle physics, various new particles were continuously discovered, and the quark was thought to be elementary particle of matter. So peoples presented a new kind of compact star:Quark Star. Because of its similarity on structure with Neutron Stars, it is very difficult to distinguish them from observation. The basic theory of Quark Star is Quantum Chro-modynamics(QCD),because the constitution of Quark Star is Quark. No matter what the Neutron Stars or Quark Stars, their matter density reaches 1014 sim1015g/cm3, the effects of general relativity are very remarkable. So we must consider the relativistic correction, that is the Tolman-Oppenheimer-Volkoff equation(TOV). Once the equation of state of the matter is known, we could understand the properties of these stars. So how to derive the equation of state of nuclear and super-nuclear dense matter become the key problem for studying the nature of these stars. The neutron star was found earlier. Its'main constitutions are neutrons, and the equation of state is under nuclear level. The relevant experiment parameters, for example, binding energy, saturation density, compression modulus, symmetry energy coefficient and so on, provid consid-erable information and restrictions for learning the equation of state. The quark stars' main constitutions are quarks, but peoples have never seen the individual quarks in all experiments since the emergence of the idea of quark. As is well known, the quarks have the properties of asymptotic freedom under the high energy and the confinement under the low energy region. So it is very difficult to understand the detailed proper-ties of state of the quark matter from the Quantum Chromodynamics(QCD). One has to use general principles of Quantum Chromodynamics(QCD) and resort to some con-crete models to describe their nature. For example:MIT bag model, NJL dynamical chiral symmetry breaking model, perturbative Quantum Chromodynamics(QCD) and Lattice QCD methods,and so on. For this reason, in this paper using the path integral formation of quantum field theory and the general property of Quantum Chromody-namics(QCD) we presented a new general method and obtained a model-independent expression of the equation of state of quark matter. The density, pressure of quark matter are determined by the quark propagator. For the study of the quark propagator, we have many approaches, including the perturbative and non-perturbative methods. Under the condition of high temperature and high density, the perturbative method is a suitable tool, but at finite temperature and density non-perturbative effects are dom-inant. In the study of non-perturbative Quantum Chromodynamics(QCD), the Dyson-Schwinger equation is a very efficient approach. We used the Ladder approximation of the Dyson-Schwinger equation to obtained the quark propagator at zero tempera-ture and finite density from the one at zero temperature and zero density. These results are model-independent. Because the Dyson-Schwinger equation are a set of infinite coupled integral equations, it is very hard to get the exact expression of quark propa-gator. So one usually use various kinds of approximation to obtain some approximate solutions. In this paper we adopt two approximate methods:the renormalized quark propagator model and the quark propagator model with character of dynamical chiral symmetry breaking. From these two models, we obtain the exact analytic expres-sions of quark propagator. In the re-normalized quark propagator model we adopt three groups of model parameters and differentiate two situations:without the bag model correction and with bag model correction. Without bag model corrections the equa- tion of state is stiff and leads to a little bigger mass and radius of quark star. The maximum mass is around 1.75M(?)～2.2M(?) and the radius R 22～26Km. The ob-tained mass-radius relationship is similar to the mass-radius relationship of the neutron stars. While with bag model corrections, the obtained equation of state is obviously soft. We choose the bag constant B1/4=65.5MeV,92MeV,108MeV respectively. The maximum mass is around 1.3M(?)～1.6M(?) and the radius R 9.5～14Km. The obtained mass-radius relationship is similar to the mass-radius relationship of a self-bound star, and the mass density is larger than the former(without bag model cor-rections). In the second type of quark propagator with character of dynamical chiral symmetry breaking, we also differentiate two situations:one with the pressure term un-der zero chemical potential Pressure(μ=0) and the other without this term. We can see from the results that the equation of state obtained without the Pressure(μ=0) term is stiffer than that obtained with this term. The maximum mass is around 1.3M(?) and the radius R 24Km. With Pressure(μ=0) term the maximum mass is around 0.8M(?) and the radius R 8Km. The mass density is larger than the former. In the above research of two kinds of quark star model, a comparison with other models is also made, for example, the perturbative Quantum Chromodynamics(QCD) model of Fraga, PisarskiandSchaffner-Bielich, the SQM model of Manju.Prakash,et al. For all these quark equation of state, the equation of state of SQM is stiffest. This is because it adopts the approximation of non-interacting free quarks. while in the model of Fraga, PisarskiandSchaffner-Bielich they added the perturbative effects of exchange of gluons and their equation of state is soft. In our models we considered the quarks'dynamic breaking effects. The coupling between quarks is very strong, so our equation of state is softest! this is consistent with the arguement that the interac-tion will lead the equation of state to be soft. We also consider the effect of the quark star rotation and the obtained maximum mass and radius are larger about 20% than the static stars. This point accords with the general arguement. Finally, we studied cooling process of interiors of quark stars, Our results show that the cooling process in our models were similar with previous conclusions. In the conclusion part, we give a summary of our research results, discuss some problems in this study, and made some further prospection.