Theory of Nuclear Matter for Neutron Stars and ... - Graduate Physics

to explain the existence of quark matter but it’s still an open question. MIT bag modeldescribes the quarks are freely moving in a bag. If the distance between quarks is increases,the force increases so strong that they cannot get out of the bag. To maintain the bag,negative pressure is introduced, which is known as the bag constant (B). Since we cannot doany experiment to reveal the existence of quark matter at such high densities on the earthyet, the theoretical prediction of quark matter depends on the parameters, especially thebag constant in quark matter.One thing is for sure is that the densities of neutron stars are extremely high. It is believedthat the central density of the core in neutron stars is 4ρ 0 ∼ 10ρ 0 † , where a ρ 0 is the nuclearsaturation density, 3×10 14 g/cm 3 .The typical radius of neutron star is around 10km. The mass of neutron is about 1.2M ⊙ to2.0 M ⊙ . Since neutron stars are so compact, the surface gravity of neutron stars is extremelyhigh, about 2×10 11 times earth gravity. In these conditions, general relativity is essential tofind out the mass-radius relation of neutron stars. The Tolman-Oppenhimer-Volkov (TOV)equation solves the internal structure of spherically symmetric neutron stars. Thus, thenuclear physics and the TOV equation play together to give mass-relation of neutron stars.The nuclear physics beyond ρ 0 is not known well and the central density is much higher thanρ 0 , various nuclear force models give different mass-radius relation of neutron stars. Fig.Figure 1.1: Mass and radius relation of cold neutron stars [19]. Each nuclear force modelshows different mass-radius relation of neutron stars.1.1 shows the mass-radius relation of cold neutron stars using various nuclear force models.† ρ 0 ≃ 0.16fm −3 . ρ 0 denotes nuclear saturation density which is central density of heavy nuclei. But, ingeneral, it is a nuclear parameter to be determined from standard nuclear matter properties.2