Accuracy of neutron star radius measurement with the next generation of terrestrial gravitational-wave observatories

In this paper, we explore the prospect for improving the measurement accuracy of masses and radii of neutron stars. We consider imminent and long-term upgrades of the Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo, as well as next-generation observatories—the Cosmic Explorer and Einstein Telescope. We find that neutron star radius with single events will be constrained to within roughly 500 m with the current generation of detectors and their upgrades. This will improve to 200, 100 and 50 m with a network of observatories that contain one, two or three next-generation observatories, respectively. Combining events in bins of $0.05M_{\odot }$ we find that for stiffer (softer) equations-of-state like ALF2 (APR4), a network of three XG observatories will determine the radius to within 30 m (100 m) over the entire mass range of neutron stars from $1M_{\odot }$ to $2.0M_{\odot }$ ($2.2M_{\odot }$), allowed by the respective equations-of-state. Neutron star masses will be measured to within 0.5% with three XG observatories irrespective of the actual equation-of-state. Measurement accuracies will be a factor of 4 or 2 worse if the network contains only one or two XG observatories, respectively, and a factor of 10 worse in the case of networks consisting of Advanced LIGO, Virgo KAGRA and their upgrades. Tens to hundreds of high-fidelity events detected by future observatories will allow us to accurately measure the mass-radius curve and hence determine the dense matter equation-of-state to exquisite precision.