A remark on ``On the Formation and Progenitor of PSR J0737-3039: New   Constraints on the Supernova Explosion Forming Pulsar B" by Willems et al.,   astro-ph/0602024
  Shortly after the discovery of the binary system PSR J0737-3039 we predicted that it has a small proper motion and suggested that this implies that the progenitor mass of the younger pulsar (B) must be around 1.45M_sun. This is in contradiction to standard evolutionary scenarios that suggest a He-star progenitor with M >2.1-2.3M_sun and in sharp contrast to a velocity of ~100 km/s predicted by these models. It requires a new previously unseen type of gravitational collapse. Our (generally ignored) prediction of a low peculiar motion was confirmed later by pulsar timing observations that found v_\bot < 30 km/s. Recently Willems et al. put forward an elaborate simulation suggesting that in spite of these observations, the most likely natal kick is large (50-170 km/s) and the corresponding most likely progenitor mass is large as well. We refute this claim and show that Willems et al. implicitly assume the result that they obtain. 
Tsvi Piran & Nir J. Shaviv