We use a collection of 14 well-measured neutron-star masses to strengthen the case that a substantial fraction of these neutron stars were formed via electron-capture (e-capture) supernovae (SNe) as opposed to Fe core-collapse SNe. The e-capture SNe are characterized by lower resultant gravitational masses and smaller natal kicks, leading to lower orbital eccentricities when the e-capture SN has led to the formation of the second neutron star in a binary system. Based on the measured masses and eccentricities, we identify four neutron stars, which have a mean post-collapse gravitational mass of ~1.25?M ☉, as the product of e-capture SNe. We associate the remaining 10 neutron stars, which have a mean mass of ~1.35?M ☉, with Fe core-collapse SNe. If the e-capture SN occurs during the formation of the first neutron star, then this should substantially increase the formation probability for double neutron stars, given that more systems will remain bound with the smaller kicks. However, this does not appear to be the case for any of the observed systems and we discuss possible reasons for this.
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