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Gravitational waves from binary neutron star coalescences contain richinformation about matter at supranuclear densities encoded by the neutron starequation of state. We can measure the equation of state by analyzing the tidalinteractions between neutron stars, which is quantified by the tidaldeformability. Multiple merger events are required to probe the equation ofstate over a range of neutron star masses. The more events included in theanalysis, 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 arelikely to place on the neutron star equation of state by combining the firstforty binary neutron star detections, a milestone we project to be reachedduring the first year of accumulated design-sensitivity data. We carry outBayesian inference on a realistic mock dataset of binaries to obtain posteriordistributions for neutron star tidal parameters. In order to combine posteriorsamples from multiple observations, we employ a random forest regressor, whichallows us to efficiently interpolate the likelihood distribution. Assuming amerger rate of 1540 Gpc$^{-3}$ yr$^{-1}$ and a LIGO-Virgo detector networkoperating for one year at the sensitivity of the third-observation run, plus anadditional 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. Atthe same time, the pressure at twice the nuclear saturation density can beconstrained to $\sim 45$ % at 90% confidence. Finally, we add an appendixfollowing publication of the paper in the journal, showing the posteriordistribution 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.

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