Study On Hadron-Quark Phase Transition In The Interior Of Hybrid Stars

During the nearly four decades since the observation of the first pulsar, the properties of nuclear matter under extreme conditions, as neutron star matter, have been the one of important subjects in astrophysics as well as in nuclear astrophysics. Using various models, many authors have studied the properties of neutron star so as to explore its deep interior where density is extremely high. However, it is still far from clearly known. In this paper, we shall study properties for neutron stars in several aspects. We study neutron star within hyperon level—Hyperon star. We employ several parameter sets including GL85, GL2, TM1 and TM2, in the framework of relativistic mean field theory to describe nuclear matter and calculate the particle fractions, equation of state(EOS) and corresponding mass-radius relations of neutron stars. The influence of the hyperon's coupling constant on the properties of neutron stars is discussed in detail. Our results show that the existence of hyperons in a neutron star can soften the EOS of nuclear matter, as a result, the corresponding mass and radius of the neutron star become smaller. But it is still bigger than the canonical mass of a neutron star, 1.4M⊙( M⊙is the solar mass). Studies on the influence of the model parameters on bulk properties of neutron star become very important in nuclear astrophysics owing to the uncertainty of the interior phase structure of neutron stars. In this paper, we study the influence of the model parameters on hadron-quark phase transition in the interior of hybrid stars and on their bulk properties. Here we employ several hadronic EOS for parameter sets GL85, GL2 , TM1 and TM2 in the framework of the RMFT to describe the hadronic phase(HP). We employ the effective mass bag model including medium effects to describe the quark phase(QP). To depict the mixed phase(MP) in which hadron and quark coexist, we use two components Gibbs phase equilibrium condition and global electric charge neutral constraint. We calculated the particle fractions, EOS and corresponding mass-radius relations of neutron stars. The influence of the coupling constants of hyperons χ, strong coupling constant between quarks g and bag constant B on the bulk properties of neutron stars are discussed in detail. The numerical analysis shows that the coupling constants of hyperons χhave a slight influence on the phase transitions and EOS, but an obvious influence on the particle fractions, while the coupling constant g and the bag constant B have an important influence on the phase transitions, the EOS and the corresponding mass-radius relations. With the increase of the two parameters, the EOS stiffen, the corresponding mass-radius curves raise. We find that both the bag constant B and coupling constant g play the same role in the description of the EOS and the corresponding mass-radius relations in a small parameter region . Medium effects may be described by a change of the original bag constant B may be able to approximately recover changes of the EOS and corresponding mass-radius relations due to mediumeffects parameterized by g. Furthermore we have determined both of the parameters for QP in the interior of hybrid stars by using the phase transition energy density, which can be considered compatible with the experimental data for high-energy heavy-ion collisions, so as to provide a gist for subsequence scientific calculations. The calculated maximum mass of hybrid star is between 1.4 M⊙--1.7 M⊙, the corresponding radius is R=9.3-12km, which are in the scope of the observable values. Using TM2 EOS, we have discussed the possibility of a third family of compact stars(TF) which might exist besides the two known families of neutron stars and white dwarfs. We find that a third family exists not only in the narrow parameter range of bag constant B1/4=175-180MeV and g=0, but also exists in the range of coupling constant g=0—1 and B1/4=175 MeV. Compared to stars of the neutron star family, the stars of the third family can have similar masses and smaller radii. These calculated results provide a signature for the observation of twins having the same masses but different composition and radius. The existence of a third family is equivalent to the existence of the hadron-quark phase transition at high densities. In this paper a new thermodynamic treatment is performed self-consistently in the effective mass bag model (EMBM). For convenience, we call this model thermodynamically self-consistent effective mass bag model. We employ the model to study the properties of hybrid and strange stars. From the average binding energy of each baryon calculated in this paper, we found that strange quark matter is the true ground state of QCD only with a small bag constant B. Itmeans that the hybrid stars may exist in a rather wide range of parameters. The EOS of strange stars described by our model are harder than the one described by the EMBM. The former EOS grow harder and the later EOS grow softer with the increase of the strong coupling constant g. The corresponding masses and radii of the former are larger than that of the later. It is interesting to note that the influence of strong coupling constant g on describing the EOS of hybrid stars is very different from that of the EMBM due to the additive pressure term brought by the thermodynamically self-consist treatment in the new model. At the same time the strong coupling constant g and the bag constant B will not have the same role in the new model as they do in the EMBM. The Gibbs condition for phase equilibrium can be easily satisfied by the pressure of quark phase due to the additive pressure term. The consequences are that the mixed phase (MP) start and end early. It also leads to a harder EOS of the high density pure quark phase when this model is used to describe a hybrid star. It can be concluded that the EOS of the MP described by this model is softer than that described by the EMBM and it becomes even softer with the increase of the strong coupling constant g, but the situation inversed in pure quark phase. These changes influence the mass-radius relations, as a results, the maximum masses of hybrid star described by our model are bigger than that of the EMBM, the corresponding radii are smaller than that of the latter. Furthermore, these differences grow more obviously with the increase of the coupling constant g. These results indicate again that two models are obviously different in description of both the strange stars and the hybrid stars.These also show that the thermodynamically self-consistent effective mass bag model is suitable to describe hybrid stars with bigger mass and smaller radius. This model may change one's opinion that the hybrid stars with small radii cannot be described within the present hybrid star theory. Chosen the appropriate model parameters, this model may describe a newly discovered X-ray pulsar, SAX J1808.4—3658. The mass-radius relations for hybrid and strange stars are also studied for the same parameter sets in our model. The masses of strange stars and hybrid stars described by the model with the same parameters are almost same, but they have different radii and these differences in radius will disappear with the increase of strong coupling constant g. So it is difficult to distinguish strange stars from neutron stars by their masses and radii for the big strong coupling constant g. These results can be theoretical evidence for the observation of pulsars.