The formation of the double neutron star pulsar J0737-3039

We find that the orbital period (2.4 h), eccentricity (0.09), dipole magnetic field strength (6.9 x 10 9 G) 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 (HeS-NS) binary in which at the onset of the evolution the helium star had a mass in the range 4.0-6.5 M-circle dot and an orbital period in the range 0.1-0.2 d. Such systems are the post-common-envelope remnants of wide Be/X-ray binaries (orbital period 100 to 1000 d) which consist of a normal hydrogen-rich star with a mass in the range 10-20 M-circle dot 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) yr; assuming Eddington-limited disc accretion on to 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 2.3-3.3 M-circle dot, and in order to obtain the present orbital parameters of PSR J0737-3039 a kick velocity in the range 70-230 km s(-1) must have been imparted to the second neutron star at its birth.