  We use a collection of 14 well-measured neutron star masses to strengthen the
case that a substantial fraction of these neutron stars was formed via
electron-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 solar
masses, as the product of e-capture SNe. We associate the remaining ten neutron
stars, which have a mean mass of 1.35 solar masses, with Fe-core collapse SNe.
If the e-capture supernova 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.
