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Constraints on the Symmetry Energy Using the Mass-Radius Relation of Neutron Stars

The nuclear symmetry energy is intimately connected with nuclear astrophysics. This contribution focuses on the estimation of the symmetry energy from experiment and how it is related to the structure of neutron stars. The most important connection is between the radii of neutron stars and the pressure of neutron star matter in the vicinity of the nuclear saturation density $n_s$. This pressure is essentially controlled by the nuclear symmetry energy parameters $S_v$ and $L$, the first two coefficients of a Taylor expansion of the symmetry energy around $n_s$. We discuss constraints on these parameters that can be found from nuclear experiments. We demonstrate that these constraints are largely model-independent by deriving them qualitatively from a simple nuclear model. We also summarize how recent theoretical studies of pure neutron matter can reinforce these constraints. To date, several different astrophysical measurements of neutron star radii have been attempted. Attention is focused on photospheric radius expansion bursts and on thermal emissions from quiescent low-mass X-ray binaries. While none of these observations can, at the present time, determine individual neutron star radii to better than 20% accuracy, the body of observations can be used with Bayesian techniques to effectively constrain them to higher precision. These techniques invert the structure equations and obtain estimates of the pressure-density relation of neutron star matter, not only near $n_s$, but up to the highest densities found in neutron star interiors. The estimates we derive for neutron star radii are in concordance with predictions from nuclear experiment and theory.