Quark Matter In Neutron-like Stars And The Structures Of Neutron-Like Stars

Neutron stars are the remnants of massive stars. Massive stars experience the core collapse supernova and neutron stars are left. The neutron stars are the densest objects in the universe. Physicists are also interested in neutron stars due to the properties of them. The study of particle physics can explain the structure of neutron stars. The neutron stars are the natural laboratories of cold, dense matter. According to Einstein’s general relativity, the space-time near a neutron star will be curved. The neutron stars also provide laboratories for general relativity.In 1934, Baade and Zwicky proposed the possibility of the existence of neutron star which is composed by degenerate neutrons after Chadwick had found neutron. In 1939, Oppenheimer and Volkoff first calculated the structures of the neutron stars. However, there were no observations at that time. The proposal were not noticed by many scientists until the pulsar was found Hewish adn J.Bell in 1967. According to the period of the pulsar, known objects can not account for the high frequency of pulsars. However, the model of neutron star could account for the observation.From the observational data of pulsars, the properties of neutron stars are clear, the mass of neutron stars are one solar mass or two, and their radii are about 10km to 20km. They have strong magnetic field and rapidly rotate.The study of neutron stars should from the observations. The observations of neutron stars cover the all bands:radio bands, X-ray,γ-ray, ultraviolet, optical and infrared bands. The observations can help us know the properties of neutron stars. In radio bands, the regular pulse was observed. Moreover, special phenomenon of neu-tron star called glitch was found. Glitches are sudden spin-ups periodically observed in most pulsars and are thought to be associated with unpinning of superfluid neutron vortices in the crust. Most neutron stars shining in X-ray belong to binary systems, and their bright emission is powered by the accretion from the companion. More than 100 isolated neutron stars are seen in X-rays, and they are phenomenologically quite heterogeneous. Among them, the most puzzling sources are magnetars. The high ener-gy emission of pulsars has been studied since the seventies,relying mostly on the data from two famous pulsars inside the Vela and Crab supernova remnants. The increas-ing statistics of high-energy pulsars helps to constrain the emission models, providing information about the region of magnetospheric emission and the involved electromag-netic processes, like curvature radiation and inverse Compton. Large Area Telescope undergo the observation of neutron stars. Neutron stars are intrinsically faint in the ul-traviolet, optical and infrared wavelengths. However, technological advances recently led to the identification of counterparts of a few tens of pulsars. Optical and ultraviolet observations can also help to infer the anisotropic thermal map of the surface and con-strain the cooling model, because these bands include the bulk of thermal emission of cold stars, and optical and infrared observations are useful to test the presence of debris disks surrounding isolated neutron stars.The study of the composition of neutron stars should base on the theory of cold, dense, strongly interacting matter. However, the properties of the cold, dense matter, especially that beyond the nuclear saturation, are not clear until now. Therefore, the composition of neutron stars are not clear too. Except nucleons, there may exist exotic composition, like koan and hyperon, even quarks. In 1984, Witten proposed that there may exist pure quark star due to the low energy. They are stable self bond system. The equation of state for strongly interacting matter at finite density can not be deduced from the first principle of QCD. The EoS should resort to phenomenological models. The models are cooperating with two basic features of QCD:confinement in low den-sity and asymptotic in high density. So far, most treatments that include quark matter in compact stars still employ the bag model. This model assumes that the quarks are free fermions in a bag with negative pressure B, which is known as the bag constant. The Nambu-Jona-Lasinio (NJL) model incorporates chiral symmetry and its breaking. The perturbative QCD model works well in the high-energy region due to asymptotic freedom.In 2010, using the National Radio Astronomy Observatory’s 100-meter-diameter telescope in Green Bank, West Virginia, NRAO’s Paul Demorest and coworkers have measured the highest neutron-star mass ever determined in a precision weighing. They reported that the neutron star in the binary-pulsar system J1614-2230 has a mass of 1.97 ± 0.04M(?).In 2013, the observation of PSR J0348+0432 gave another mass of 2.01 ± 0.04M(?). The mass-radii relation of neutron stars can be obtained if we know the equation of state. Conversely, the observation of mass-radii relation can be used to constrain the EoS. If the EoS is soft, the EoS will be excluded by the observation. In our work, the cold,dense matter is described by the quasi-particle model. There are some parameters is this model. The parameters can be constrained by the observation. However, the quasi-particle model is not self consistent. Therefore, we use the im-proved quasi-particle model to calculate the structure of pure quark star. We find that the obtained mass-radii relation is consistent with the observation.The hybrid star was inspired by the idea of the phase transition from quark matter to nuclear matter. The hybrid stars have quark cores and hadronic crusts. The phase transition can be modeled by Maxwell construction. We use Maxwell construction to calculate the mass-radii relation. We find that the masses of stable hybrid stars cannot exceed 2M(?). In 1992, Glendenning realized that a mixed phase of deconfined quark matter and hadronic matter inside a neutron-like star is not strictly excluded. It is called Gibbs criteria. It rearranges the electric charge between two phases to maintain global charge neutrality. The masses of stable hybrid stars can exceed 2M(?) while with mixed cores.