We present the first determination of the proper motion of the neutron star low mass X-ray binary Cen X-4 measured from relative astrometry of the secondary star using optical images at different epochs .
We determine the Galactic space velocity components of the system and find them to be significantly different from the mean values that characterize the kinematics of stars belonging to the halo , and the thin and the thick disc of the Galaxy .
The high metallicity of the secondary star of the system rules out a halo origin and indicates that the system probably originated in the Galactic disc .
A statistical analysis of the galactocentric motion revealed that this binary moves in a highly eccentric ( e \simeq 0.85 \pm 0.1 ) orbit with an inclination of \simeq 110 ^ { \circ } to the Galactic plane .
The large Galactic space velocity components strongly support that a high natal kick as a result of a supernova explosion could have propelled the system into such an orbit from a birth place in the Galactic disc .
The high Li abundance in the secondary , comparable to that of stars in star forming regions and young stellar clusters like the Pleiades , may suggest a relatively recent formation of the system .
Following the orbit backwards in time , we found that the system could have been in the inner regions of the Galactic disc \sim 100–200 Myr ago .
The neutron star might have formed at that moment .
However , we can not rule out the possibility that the system formed at a much earlier time if a Li production mechanism exists in this LMXB .