Can we decipher the composition of the core of a neutron star?

General relativity guarantees a unique one-to-one correspondence between static observables of neutron stars (NSs) accessible by multimessenger astronomy, such as mass-radius or tidal deformability, and the equation of state (EoS) of beta equilibrated matter. It is well known that these static properties are not enough to discern conventional NSs from hybrid stars. However, if one assumes that hadrons present in the neutron star core are only neutrons and protons, the lepton fraction is expected to be determined unequivocally by the condition of chemical equilibrium. Using a simple analytical method based on a polynomial expansion of the EoS, we show that multiple solutions are possible to the beta-equilibrium equation, leading to a characteristic indetermination on the composition of the interiors of NSs, even in the purely nucleonic hypothesis. We further show that additional empirical information on symmetric matter at high densities are not very efficient to pin down the composition, if uncertainties on measurements are accounted for. We conclude that constraints on the symmetry energy at high densities only, can make meaningful impact to decipher the composition of neutron star core. Our results give a lower limit to the uncertainty on the NS core composition that can be obtained with astrophysical and terrestrial experiments.

Automated summary

General relativity ensures a unique correspondence between static observables of neutron stars accessible by multimessenger astronomy and the equation of state (EoS) of beta-equilibrated matter. However, even in the purely nucleonic hypothesis, multiple solutions to the beta-equilibrium equation can lead to indeterminacy in the interior composition of neutron stars. Additional empirical information regarding high-density symmetric matter is not very efficient in determining the composition, considering measurement uncertainties. Constraints on the symmetry energy at high densities can make a meaningful impact on deciphering the composition of neutron star cores.