Reconstructing the neutron-star equation of state with gravitational-wave detectors from a realistic population of inspiralling binary neutron stars

Gravitational-wave observations of inspiralling binary neutron-star systems can be used to measure the neutron-star equation of state (EOS) through the tidally induced shift in the waveform phase that depends on the tidal deformability parameter $\ensuremath{\lambda}$. Previous work has shown that $\ensuremath{\lambda}$, a function of the neutron-star EOS and mass, is measurable by Advanced LIGO for a single event when including tidal information up to the merger frequency. In this work, we describe a method for stacking measurements of $\ensuremath{\lambda}$ from multiple inspiral events to measure the EOS. We use Markov chain Monte Carlo simulations to estimate the parameters of a four-parameter piecewise-polytrope EOS that matches theoretical EOS models to a few percent. We find that, for ``realistic'' event rates ($\ensuremath{\sim}40$ binary neutron-star inspiral events per year with signal-to-noise ratio $>8$ in a single Advanced LIGO detector), combining a year of gravitational-wave data from a three-detector network with the constraints from causality and recent high-mass neutron-star measurements, the EOS above nuclear density can be measured to better than a factor of 2 in pressure in most cases. We also find that in the mass range $1{M}_{\ensuremath{\bigodot}}--2{M}_{\ensuremath{\bigodot}}$, the neutron-star radius can be measured to better than $\ifmmode\pm\else\textpm\fi{}1\text{ }\text{ }\mathrm{km}$ and the tidal deformability can be measured to better than $\ifmmode\pm\else\textpm\fi{}1\ifmmode\times\else\texttimes\fi{}1{0}^{36}\text{ }\text{ }\mathrm{g}\text{ }{\mathrm{cm}}^{2}\text{ }{\mathrm{s}}^{2}$ (10%--50% depending on the EOS and mass). The overwhelming majority of this information comes from the loudest $\ensuremath{\sim}5$ events. Current uncertainties in the post-Newtonian waveform model, however, lead to systematic errors in the EOS measurement that are as large as the statistical errors, and more accurate waveform models are needed to minimize this error.