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Gravitational-wave observations of neutron star mergers can probe the nuclear equation of state by measuring the imprint of the neutron star’s tidal deformability on the signal. We investigate the ability of future gravitational-wave observations to produce a precise measurement of the equation of state from binary neutron star inspirals. Because measurability of the tidal effect depends on the equation of state, we explore several equations of state that span current observational constraints. We generate a population of binary neutron stars as seen by a simulated Advanced LIGO–Virgo network, as well as by a planned Cosmic Explorer observatory. We perform Bayesian inference to measure the parameters of each signal, and we combine measurements across each population to determineR_1.4, the radius of a 1.4M_⊙neutron star. We find that, with 321 signals, the LIGO–Virgo network is able to measureR_1.4to better than 2% precision for all equations of state we consider; however, we also find that achieving this precision could take decades of observation, depending on the equation of state and the merger rate. On the other hand, we find that with one year of observation, Cosmic Explorer will measureR_1.4to better than 0.6% precision. In both cases, we find that systematic biases, such as from an incorrect mass prior, can significantly impact measurement accuracy, and efforts will be required to mitigate these effects.

 

ABSTRACT Two binary neutron star mergers, GW170817 and GW190425, have been detected by Advanced LIGO and Virgo. These signals were detected by matched-filter searches that assume that the star’s orbit has circularized by the time their gravitational-wave emission is observable. This suggests that their eccentricity is low, but full parameter estimation of their eccentricity has not yet been performed. We use gravitational-wave observations to measure the eccentricity of GW170817 and GW190425. We find that the eccentricity at a gravitational-wave frequency of 10 Hz is e ≤ 0.024 and e ≤ 0.048 for GW170817 and GW190425, respectively (90 per cent confidence). This is consistent with the binaries being formed in the field, as such systems are expected to have circularized to e ≤ 10−4 by the time they reach the LIGO–Virgo band. Our constraint is a factor of 2 smaller that an estimate based on GW170817 being detected by searches that neglect eccentricity. However, we caution that we find significant prior dependence in our limits, suggesting that there is limited information in the signals. We note that other techniques used to constrain binary neutron star eccentricity without full parameter estimation may miss degeneracies in the waveform, and that for future signals, it will be important to perform full parameter estimation with accurate waveform templates.