Optimal neutron-star mass ranges to constrain the equation of state of nuclear matter with electromagnetic and gravitational-wave observations

Exploiting a very large library of physically plausible equations of state (EOSs) containing more than $10^{7}$ members and yielding more than $10^{9}$ stellar models, we conduct a survey of the impact that a neutron-star radius measurement via electromagnetic observations can have on the EOS of nuclear matter. Such measurements are soon to be expected from the ongoing \textit{Neutron Star Interior Composition Explorer} mission and will complement the constraints on the EOS from gravitational-wave detections. Thanks to the large statistical range of our EOS library, we can obtain a first quantitative estimate of the commonly made assumption that the high-density part of the EOS is best constrained when measuring the radius of the most massive, albeit rare, neutron stars with masses $M\gtrsim2.1\,M_\odot$. At the same time, we find that radius measurements of neutron stars with masses $M\simeq1.7-1.85\,M_\odot$ can provide the strongest constraints on the low-density part of the EOS. Finally, we quantify how radius measurements by future missions can further improve our understanding of the EOS of matter at nuclear densities.