Study Of Neutron Star Magnetic Field

A real neutron star model had been established in 1939, and its discovery was until 1967. The neutron star has a small radius about 10km, and its mass is about one unit mass of sun. These make the so compact, and have made our research so hard. For one thing, it isn't easy to be observed for a star which is little and far from earth. After the discovery 40 years passed, we still know little about its structure or composition. Some presume the neutron star must have hyperon and π condensate in its core, while some others consider that there is no "neutron star", but a "quark star". For another, the neutron star has a density high above in nuclei, and we have no experiment in such a density, so the relativistic quantum field theory of many bodies needs to be considered.For the complexities of this problem and its difficulties in mathematical' computations, some approximations are needed. The systematic method is called the relativistic mean field approximation (RMA). The main idea of the RMA is: the attraction and repulsion between nuclei are via the exchanges of mesons; the meson fields can be substituted by their expectation values under ground state while compute. The RMA theory had been proposed in 70 of last century. Via 30 years' development, this method has become a relatively completed theory, and it has being used in many fields, such as in nuclear physics and celestial physics. In this paper, we will use it to compute the magnetic fields in neutron star.Large magnetic fields B = 10¹²¹0¹⁴ G have been associated with the surfaces of neutron stars, while the interior field could be as high as ¹0¹⁸G. Such a strange property has attracted the scientists' attentions. However, because the structure and composition of this compact star still are unclear, the studies are so difficult. Besides, using the effective Lagrangian method, we meet another problem: photon is massless, and its effect may be canceled by the RMA. For this reason, some authors had to take magnetic field as external.A resent discover has showed that: in matter of high density, the U(1) local gauge symmetry of electric charge is spontaneously broken, and consequently, the photongains an effective mass through the Higgs mechanism. In this paper, we will take advantage of the result to discover the relations between magnetic field and density of neutron star. And in the end we will show you that with the increasing of density of density, the fraction of proton is increasing and the magnetic field is stronger. The variations of magnetic field in star are compatible with the variations of density. We also give a right order of magnitude of the field.