Modeling the Structure of a Neutron Star Using Relativistic Degeneracy Pressure
Abstract: The extreme density of neutron stars gives rise to exotic phenomena that cannot be found anywhere else in the universe. Modeling the structure of a neutron star can elucidate what processes keep a neutron star in hydrostatic equilibrium and their limits in doing so. The maximum mass of a neutron star is uncertain since the equation of state (EOS), which relates pressure as a function of density, is still uncertain for the extreme densities associated with neutron stars. We modeled the structure of a neutron star using the simplifying assumption that the pressure is solely due to a relativistic ideal Fermi fluid of neutrons. We numerically solved the general relativistic equation of hydrostatic equilibrium using Python. We compared our density profiles with nonrelativistic models as well as with previous work. For central densities on the order of or above 2.3 × 10 kg17 m−3 (roughly nuclear densities), both special relativistic effects and general relativistic effects become quite important. We confirm that, for a special relativistic EOS and Newtonian gravity, the predicted maximum mass for a neutron star is ≈ 5.6 M⊙. However, the inclusion of general relativistic hydrostatic equilibrium causes the density structure to become much more compact and causes the maximum mass to drop down to 0.85 M⊙. Since this maximum mass is considerably lower than the observed masses of several neutron stars, nucleon-nucleon interactions must significantly alter the EOS associated with real neutron stars.
