  Since the discovery of the first double neutron star (DNS) system, the number
of these exotic binaries has reached fifteen. Here we investigate a channel of
DNS formation in binary systems with components above the mass limit of type II
supernova explosion (SN II), i.e. 8 MSun. We apply a spherically symmetric
homologous envelope expansion model to account for mass loss, and follow the
dynamical evolution of the system numerically with a high-precision integrator.
The first SN occurs in a binary system whose orbital parameters are
pre-defined, then, the homologous expansion model is applied again in the newly
formed system. Analysing 1 658 880 models we find that DNS formation via
subsequent SN II explosions requires a fine-tuning of the initial parameters.
Our model can explain DNS systems with a separation greater than 2.95 au. The
eccentricity of the DNS systems spans a wide range thanks to the orbital
circularisation effect due to the second SN II explosion. The eccentricity of
the DNS is sensitive to the initial eccentricity of the binary progenitor and
the orbital position of the system preceding the second explosion. In agreement
with the majority of the observations of DNS systems, we find the system
centre-of mass velocities to be less than 60 km/s. Neutron stars that become
unbound in either explosion gain a peculiar velocity in the range of 0.02 - 240
km/s. In our model, the formation of tight DNS systems requires a
post-explosion orbit-shrinking mechanism, possibly driven by the ejected
envelopes.
