The Curvature Parameter of the Symmetry Energy and a Modified Polytropic Equation of State

The nuclear symmetry energy is a key component of the equation of state of neutron stars, controlling their macroscopic parameters and internal structure. Currently, it remains an unknown issue in both experimental and theoretical studies within the density range relevant to the interiors of neutron stars. This paper aims to investigate the density dependence of the symmetry energy, analyzing it in terms of the curvature parameter Ksym. The analysis is based on a neutron star matter equation of state constructed using the proposed modified polytropic form. The polytropic equations of state used approximate the complex, realistic ones. The realistic equations of state selected for the analysis in this paper are those derived using the relativistic mean-field approach. The proposed method exploits the existing strong correlations between the incompressibility of both symmetric and asymmetric nuclear matter and the calculated values of the neutron star crust–core transition density. Starting from the experimental constraint on the incompressibility of symmetric nuclear matter K0 and based on observationally determined parameters, such as the mass and radius of PSR J0740+6620 pulsar, the formulated method allows for a selection of the range of Ksym values acceptable by both the constraints on K0 and the results of astrophysical observations.