We find that the orbital period ( 2.4 hours ) , eccentricity ( 0.09 ) , dipole magnetic field strength ( 6.9 \times 10 ^ { 9 } Gauss ) and spin period ( 22 ms ) of the new highly relativistic double neutron star system PSR J0737–3039 can all be consistently explained if this system originated from a close helium star plus neutron star binary ( HeS-NS ) in which at the onset of the evolution the helium star had a mass in the range 4.0 to 6.5 \mathrm { M _ { \sun } } and an orbital period in the range 0.1 to 0.2 days .
Such systems are the post-Common-Envelope remnants of wide Be/X-ray binaries ( orbital period \sim 100 to 1000 days ) which consist of a normal hydrogen-rich star with a mass in the range 10 – 20 \mathrm { M _ { \sun } } and a neutron star .
The close HeS-NS progenitor system went through a phase of mass transfer by Roche-lobe overflow at a high rate lasting a few times 10 ^ { 4 } years ; assuming Eddington-limited disk accretion onto the neutron star this star was spun up to its present rapid spin rate .
At the moment of the second supernova explosion the He star had a mass in the range 2.3 to 3.3 \mathrm { M _ { \sun } } and in order to obtain the present orbital parameters of PSR J0737–3039 a kick velocity in the range 70 – 230 \mathrm { km s ^ { -1 } } must have been imparted to the second neutron star at its birth .