Neutron star matter

Abstract

The matter in neutron stars is essentially in its ground state and ranges in density up to and beyond 3 × 1014 g/cm3, the density of nuclear matter. Here we determine the constitution of the ground state of matter and its equation of state in the regime from 4.3 × 1011 g/cm3 where free neutrons begin to "drip" out of the nuclei, up to densities ≈ 5 × 1014 g/cm3, where standard nuclear-matter theory is still reliable. We describe the energy of nuclei in the free neutron regime by a compressible liquid-drop model designed to take into account three important features: (i) as the density increases, the bulk nuclear matter inside the nuclei, and the pure neutron gas outside the nuclei become more and more alike; (ii) the presence of the neutron gas reduces the nuclear surface energy; and (iii) the Coulomb interaction between nuclei, which keeps the nuclei in a lattice, becomes significant as the spacing between nuclei becomes comparable to the nuclear radius. We find that nuclei survive in the matter up to a density ∼ 2.4 × 1014 g/cm3; below this point we find no tendency for the protons to leave the nuclei. The transition between the phase with nuclei and the liquid phase at higher densities occurs as follows. The nuclei grow in size until they begin to touch; the remaining density inhomogeneity smooths out with increasing density until it disappears at about 3 × 1014 g/cm3 in a first-order transition. It is shown that the uniform liquid is unstable against density fluctuations below this density; the wave-length of the most unstable density fluctuation is close to the limiting lattice constant in the nuclear phase.