Measuring the neutron star equation of state with gravitational waves: The first forty binary neutron star merger observations

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 40 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 1 year at the sensitivity of the third-observation run, plus an additional 8 months of design sensitivity, we find that the radius of a 1.4 M neutron star can be constrained to better than ∼10% at 90% confidence. The pressure at twice the nuclear saturation density can be constrained to better than ∼45% at 90% confidence. We show that these results are robust to our choice of parametrization for the neutron star equation of state.