Since the discovery of the first double neutron star ( DNS ) system in 1975 by Hulse and Taylor , there are currently 8 confirmed DNS in our galaxy .
For every system , the masses of both neutron stars , the orbital semi-major axis and eccentricity are measured , and proper motion is known for half of the systems .
Using the orbital parameters and kinematic information , if available , as constraints for all system , we investigate the immediate progenitor mass of the second-born neutron star and the magnitude of the supernova kick it received at birth , with the primary goal to understand the core collapse mechanism leading to neutron star formation .
Compared to earlier studies , we use a novel method to address the uncertainty related to the unknown radial velocity of the observed systems .
For PSR B1534+12 and PSR B1913+16 , the kick magnitudes are 150 - 270 km/s and 190 - 450 km/s ( with 95 % confidence ) respectively , and the progenitor masses of the 2nd born neutron stars are 1.3 - 3.4 M _ { \sun } and 1.4 - 5.0 M _ { \sun } ( 95 % ) , respectively .
These suggest that the 2nd born neutron star was formed by an iron core collapse supernova in both systems .
For PSR J0737-3039 , on the other hand , the kick magnitude is only 5 - 120 km/s ( 95 % ) , and the progenitor mass of the 2nd born neutron star is 1.3 - 1.9 M _ { \sun } ( 95 % ) .
Because of the relatively low progenitor mass and kick magnitude , the formation of the 2nd born neutron star in PSR J0737-3039 is potentially connected to an electron capture supernova of a massive O - Ne - Mg white dwarf .
For the remaining 5 Galactic DNS , the kick magnitude ranges from several tens to several hundreds of km/s , and the progenitor mass of the 2nd formed neutron star can be as low as \sim 1.5 M _ { \sun } , or as high as \sim 8 M _ { \sun } .
Therefore in these systems , it is not clear which type of supernova is more likely to form the 2nd neutron star .