Neutron Star Matter Equation of State

Abstract

Neutron stars are highly compact objects with masses comparable to that of our Sun but radii of only about 10 km. The structure of neutron stars is encapsulated in the Tolman-Oppenheimer-Volkoff (TOV) equations, which represent the gen- eralization of Newtonian gravity to the domain of general relativity. Remarkably, the only input required to solve the TOV equations is the equation of state of cold, neutron-rich matter in chemical equilibrium. In this contribution we derive analytic expressions for the equation of state of an electrically neutral, relativistic free Fermi gas of neutrons, protons, and electrons in chemical equilibrium. Then, we introduce simple “scaling” concepts to rewrite the TOV equations in a form amenable to standard numerical algorithms. Finally, we highlight the ongoing synergy between astrophysics and nuclear physics that will need to be maintained, and indeed enhanced, to elucidate some of the most fascinating and challenging problems associated with the structure, dynamics, and composition of neutron stars.