  The binary pulsar J0737-3039 is the only known system having two observable
pulsars, thus offering a unique laboratory to test general relativity and
explore pulsar physics. Based on the low eccentricity and the position within
the galactic plane, Piran & Shaviv (2004, 2005) argued that pulsar B had a
non-standard formation scenario with little or no mass ejection. They have also
predicted that the system would have a very slow proper motion. Pulsar timing
measurements (Kramer et al. 2006; Deller et al. 2009) confirmed this
prediction. The recent observations of the alignment between the spin of pulsar
A and the binary orbit is also in agreement with this scenario. Detailed
simulations of the formation process of pulsar B enable us to show that its
progenitor, just before the collapse, was a massive O-Ne-Mg white dwarf
surrounded by a tenuous, 0.1-0.16 M_sun, envelope. This envelope was ejected
when the white dwarf collapsed to form a neutron star. Pulsar B was born as a
slow rotator (spin period ~ 1 s) and a kick received when the pulsar formed
changed its spin direction to the current one. This realization sheds light on
the angular momentum evolution of the progenitor star, a process which is
strongly affected by interaction with the binary companion. The slow proper
motion of the system also implies that the system must have undergone a phase
of mass transfer in which Star A shed a significant fraction of its mass onto
B.
