Bayesian Inference of the Symmetry Energy of Super-Dense Neutron-Rich Matter from Future Radius Measurements of Massive Neutron Stars

Using an explicitly isospin-dependent parametric Equation of State (EOS) for the core of neutron stars (NSs) within the Bayesian statistical approach, we infer the EOS parameters of super-dense neutron-rich nuclear matter from three sets of imagined mass-radius correlation data representing typical predictions by various nuclear many-body theories, i.e, the radius stays the same, decreases or increases with increasing NS mass within $pm 15%$ between 1.4 M$_{odot}$ and 2.0 M$_{odot}$. The corresponding average density increases quickly, slowly or slightly decreases as the NS mass increases from 1.4 M$_{odot}$ to 2.0 M$_{odot}$. Using the posterior probability distribution functions (PDFs) of EOS parameters inferred from GW170817 and NICER radius data for canonical NSs as references, we investigate how future radius measurements of massive NS will improve our knowledge about the EOS of super-dense neutron-rich nuclear matter, especially its symmetry energy term, compared to what people have already learned from analyzing the GW170817 and NICER data. While the EOS of symmetric nuclear matter (SNM) inferred from the three data sets are approximately the same, the corresponding high-density symmetry energies at densities above about $2rho_0$ are very different, indicating that the radii of massive NSs carry reliable information about the high-density behavior of nuclear symmetry energy with little influence from the remaining uncertainties of the SNM EOS.