The Formation of the Double Pulsar PSR J0737-3039A/B
  Recent timing observations of the double pulsar J0737-3039A/B have shown that its transverse velocity is extremely low, only 10 km/s, and nearly in the Plane of the Galaxy. With this new information, we rigorously re-examine the history and formation of this system, determining estimates of the pre-supernova companion mass, supernova kick and misalignment angle between the pre- and post-supernova orbital planes. We find that the progenitor to the recently formed `B' pulsar was probably less than 2 MSun, lending credence to suggestions that this object may not have formed in a normal supernova involving the collapse of an iron core. At the same time, the supernova kick was likely non-zero. A comparison to the history of the double-neutron-star binary B1534+12 suggests a range of possible parameters for the progenitors of these systems, which should be taken into account in future binary population syntheses and in predictions of the rate and spatial distribution of short gamma-ray burst events. 
I. H. Stairs, S. E. Thorsett, R. J. Dewey, M. Kramer, C. A. McPhee