  It is generally accepted that neutron stars form in core collapse events that
are accompanied by a supernovae (types II or Ib or Ic). Typical progenitors
are, therefore, larger than $\sim 2.1 \Ms$. We suggest \cite{PS04,PS05} that
the binary pulsar J0737-3039 provides evidence for a new formation channel:
collapse of a light progenitor. This binary pulsar J0737-3039 has several
remarkable features including among others: a very tight orbit with a Keplerian
velocity of ~600km/sec, a low eccentricity, and a location ~50pc from the
Galactic plane implying that the system has, at high likelihood, a small
(compared to Keplerian) center of mass velocity. A significant mass loss during
the formation of the second pulsar would have lead either to an eccentric orbit
or to a large center of mass velocity or to both. Therefore, we can set a
strong upper limit on the progenitor's mass. A progenitor more massive than
1.9$\Ms$ is ruled out (at 97% confidence). The kinematically favored option is
of a progenitor mass around 1.45$\Ms$. Recent evidence for a rather low
velocity proper motion supports this prediction and decreases the likelihood of
the standard (high mass progenitor) scenario. Lack of variations in the pulses'
profiles (which indicate no significant geodetic precession) provides further
support for the no kick and low progenitor mass formation scenario.
