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

Chapter 1IntroductionStars give us light by burning hydrogen fuel. The simple Einstein’s equation, E = mc 2 isbehind sun’s energy. Hydrogen turns into helium and helium burns into carbon, nitrogen,and oxygen. Finally, the neutron rich elements iron is formed. After an iron core forms, astar begins to collapse since it cannot support itself against gravitational collapse. Duringthis process, which as known as a Type II supernova explosion, a neutron star is formed ifthe mass of main sequence star is about 8 ∼ 20 M ⊙ . Stars with greater than 20 M ⊙ arethought to form black holes. An enormous amount of energy (∼ 10 53 erg) is released fromsupernova explosion. The source of the energy is gravitational binding energy and the mostof the energy is carried away by neutrinos. Right after core collapse, the initial temperatureof neutron star is believed to be 10 11 K [38]. Neutron stars cool down quickly by neutrinoemission. After the temperature drops below the Fermi temperature, neutron star is cold.The existence of neutron stars was first suggested by Walter Baade and Fritz Zwicky in 1934[38] only a year after the discovery of neutrons by James Chadwick. Landau, Bohr, andRosenfeld discussed the idea of one giant nuclei in the core of a star before the discovery ofneutron [67] but their paper was not published.A neutron star has mostly neutrons (∼90%), protons and electrons. If the chemical potentialof electrons is greater than the rest mass of kaon, there might be kaon condensation sothe kaon replaces the role of electrons for charge neutrality. As the density increases, thechemical potential of neutrons and protons can be greater than the rest mass of hyperons,then hyperons (Σ +,−,0 , Λ, Ξ − ) might appear.A neutron star is divided into an inner core, outer core, inner crust and outer crust. Theouter crust consists of lattice nuclei with free gas of electrons. As density increase, the chemicalpotential of neutrons becomes greater than zero and neutrons drip out of heavy nuclei.Thus, the inner crust has a free gas of neutrons with lattice nuclei. Between the boundaryof inner crust and outer core, heavy nuclei become exotic. Because of high pressure, thespherical nuclei become oblate to minimize the energy, and as the density increases more,oblate nuclei merge together to become a cylindrical phase, a cylindrical phase becomes aslab phase, a slab phase turns into a cylindrical hole, and a cylindrical hole becomes a sphericalhole, and finally a spherical hole can become uniform nuclear matter. The outer corethus does not have any nuclei structure. The inner core, which is more dense than the outercore, is believed to have exotic nuclear matter. Some nuclear physicists argue that theremight be quark matter in the core of neutron stars. Many of them use the MIT bag model1