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

TL;DR

This paper investigates whether the internal composition of neutron star cores can be determined from observable data, revealing fundamental ambiguities and the limited impact of current empirical constraints.

Contribution

It demonstrates that multiple core compositions are possible under beta equilibrium, even with simplified assumptions, and highlights the limited effectiveness of high-density symmetric matter data.

Findings

Multiple solutions to beta-equilibrium equations exist.

Empirical data on symmetric matter at high densities have limited constraining power.

Constraints on symmetry energy at high densities are crucial for deciphering NS core composition.

Abstract

General relativity guarantees a unique one-to-one correspondence between static observables of neutron stars (NSs) accessible by multi-messenger 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 in principle 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.