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 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 \leq 0.024 and e \leq 0.048 for GW170817 and GW190425 , respectively ( 90 % confidence ) .
This is consistent with the binaries being formed in the field , as such systems are expected to have circularized to e \leq 10 ^ { -4 } by the time they reach the LIGO-Virgo band .
Our constraint is a factor of two 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 .