Pairing in neutron stars

Abstract

Neutron star is an interesting object. It is dense with the mass of about the mass of the sun, while the radius of only about 10 km. This tremendous density may result in some unusual states of matter or lead to exotic many-body physics phenomena. For the discussion here we assume that a neutron star is a charge neutral system of nucleons and electrons in beta equilibrium at zero temperature. To sustain the stability, the neutron star must be in hydrodynamic equilibrium between gravity and Fermi degeneracy pressure. The mass, radius, pressure, and density profiles of neutron star are determined by general relativity and ydrodynamics of the neutron star matter consistently with its equation of state, via the so called Tolman-Oppenheimer-Volkov equation [1]. Given tremendous variations of density from almost zero on the surface to that of several times the nuclear density in the interior region the structure of neutron stars may be rich and diverse. In figure 1, we show the typical cross sections of the neutron star. Based on the increasing density of matter we roughly separate four different layers.