Analysis of Neutron Stars Observations Using a Correlated Fermi Gas Model

Background: The nuclear symmetry energy is a fundamental ingredient in determining the equation of state (EOS) of neutron stars (NS). Recent terrestrial experiments constrain both its value and slope at nuclear saturation density, however, its value at higher densities is unknown. Assuming a Free Fermi-gas (FFG) model for the kinetic symmetry energy, the high-density extrapolation depends on a single parameter, the density dependence of the potential symmetry energy. The Correlated Fermi-gas (CFG) model improves on the FFG model by including the effects of short-range, correlated, high-momentum, nucleons in nuclear matter. Using the CFG model for the kinetic symmetry energy along with constraints from terrestrial measurements leads to a much softer density dependence for the potential symmetry energy. Purpose: Examine the ability of the FFG and CFG models to describe NS observables that are directly sensitive to the symmetry energy at high-density. Specifically, examine the ability of the CFG model, with its softer density dependence of the potential symmetry energy, to describe a two solar-mass NS. Methods: Using a Bayesian analysis of NS observables we compare the CFG and FFG models and examine the resulting parameters in the NS EOS and the density dependence of the potential symmetry energy. Results: Despite the large difference in the density dependence of the potential part of the symmetry energy, both models can describe the NS data and support a two solar-mass NS. The different density dependences has only a small effect on the NS EOS. Conclusions: While sensitive to the high-density values of the symmetry energy, NS observables alone are not enough to distinguish between the CFG and FFG models. This indicates that the NS EOS, obtain from Bayesian analysis of NS observables, is robust and is not sensitive to the exact nuclear model used for the kinetic symmetry energy.