On the Low Progenitor Mass of the Binary Pulsar J0737-3039B
  The observed orbital parameters of the recently discovered binary pulsar J0737-3039 are used to constrain the progenitor system. In particular, the small observed eccentricity and the small inferred peculiar velocity imply that during the formation of the second NS in the system, a very small mass Delta M <~ 0.15 Msun, was ejected. A progenitor more massive than 1.4 Msun is unlikely and a progenitor more massive than 2.3 Msun is practically ruled out. We therefore argue that the companion removed most of the progenitor envelope prior to its collapse. The second collapse may have been a SN of Type Ib, or more probably, of Type Ic. Alternatively, it could have been a bare collapse, an option which is kinematically favored. Future constraints on the peculiar motion could solidify this constraint on the mass loss. A future determination of the pulsars' spin vectors and proper motion could allow us the complete determination of the conditions during the second collapse. 
Tsvi Piran and Nir J. Shaviv