  Six of the eight double neutron stars known in the Galactic disk have low
orbital eccentricities (< 0.27) indicating that their second-born neutron stars
received only very small velocity kicks at birth. This is similar to the case
of the B-emission X-ray binaries, where a sizable fraction of the neutron stars
received hardly any velocity kick at birth (Pfahl et al. 2002). The masses of
the second-born neutron stars in five of the six low-eccentricity double
neutron stars are remarkably low (between 1.18 and 1.30 Msun). It is argued
that these low-mass, low-kick neutron stars were formed by the electron-capture
collapse of the degenerate O-Ne-Mg cores of helium stars less massive than
about 3.5 Msun, whereas the higher-mass, higher kick-velocity neutron stars
were formed by the collapses of the iron cores of higher initial mass. The
absence of low-velocity single young radio pulsars (Hobbs et al. 2005) is
consistent with the model proposed by Podsiadlowski et al. (2004), in which the
electron-capture collapse of degenerate O-Ne-Mg cores can only occur in binary
systems, and not in single stars.
