We study the four double neutron star systems found in the Galactic disk in
terms of the orbital characteristics of their immediate progenitors and the
natal kicks imparted to neutron stars. Analysis of the effect of the second
supernova explosion on the orbital dynamics, combined with recent results from
simulations of rapid accretion onto neutron stars lead us to conclude that the
observed systems could not have been formed had the explosion been symmetric.
Their formation becomes possible if kicks are imparted to the radio-pulsar
companions at birth. We identify the constraints imposed on the immediate
progenitors of the observed double neutron stars and calculate the ranges
within which their binary characteristics (orbital separations and masses of
the exploding stars) are restricted. We also study the dependence of these
limits on the magnitude of the kick velocity and the time elapsed since the
second explosion. For each of the double neutron stars, we derive a minimum
kick magnitude required for their formation, and for the two systems in close
orbits we find it to exceed 200km/s. Lower limits are also set to the
center-of-mass velocities of double neutron stars, and we find them to be
consistent with the current proper motion observations.Comment: 25 pages, 6 figs (9 parts), 4 tables, AASTeX, Accepted in Ap