Measuring the neutron star equation of state with gravitational waves: the first forty binary neutron star mergers

Gravitational waves from binary neutron star coalescences contain rich information about matter at supranuclear densities encoded by the neutron star equation of state. We can measure the equation of state by analyzing the tidal interactions between neutron stars, which is quantified by the tidal deformability. Multiple merger events are required to probe the equation of state over a range of neutron star masses. The more events included in the analysis, the stronger the constraints on the equation of state. In this paper, we build on previous work to explore the constraints that LIGO and Virgo are likely to place on the neutron star equation of state by combining the first forty binary neutron star detections, a milestone we project to be reached during the first year of accumulated design-sensitivity data. We carry out Bayesian inference on a realistic mock dataset of binaries to obtain posterior distributions for neutron star tidal parameters. In order to combine posterior samples from multiple observations, we employ a random forest regressor, which allows us to efficiently interpolate the likelihood distribution. Assuming a merger rate of 1540 Gpc$^{-3}$ yr$^{-1}$ and a LIGO-Virgo detector network operating for one year at the sensitivity of the third-observation run, plus an additional eight months of design sensitivity, we find that the radius of a 1.4 $M_\odot$ neutron star can be constrained to $\sim 10$% at 90% confidence. At the same time, the pressure at twice the nuclear saturation density can be constrained to $\sim 45$ % at 90% confidence. Finally, we add an appendix following publication of the paper in the journal, showing the posterior distribution of the maximum neutron star mass allowed by the equation of state. We find that the maximum mass can be constrained to $\sim 0.3$ $M_\odot$ at 90% confidence.