Double neutron star systems and natal neutron star kicks

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 (less than or similar to 10 R.), we find it to exceed 200 km s(-1). 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.