The Origin of the Binary Pulsar J0737-3039
  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. 
Tsvi Piran and Nir J. Shaviv