The Formation of the Most Relativistic Pulsar PSR J0737-3039

We present an updated set of constraints for the progenitor of PSR J0737-3039 and for the natal kicks imparted to pulsar B taking into account both the evolutionary and kinematic history of the double neutron star. For this purpose, we use recently reported scintillation velocity measurements to trace the motion of the system in the Galaxy backwards in time as a function of the unknown orientation Omega of the systemic velocity projected on plane of the sky as well as the unknown radial velocity Vr. The absolute limits on the orbital separation and the mass of pulsar B's helium star progenitor just before its supernova explosion are 1.2Rsun < A0 < 1.7Rsun and 2.1Msun < M0 < 4.7Msun. The kick velocity is constrained to be between 60km/s and 1660km/s and to be misaligned from the pre-SN orbital angular axis (which could be associated with pulsar B's spin axis) by least 25 degrees. We also derive probability distribution functions for the kick velocity imparted to pulsar B and for the misalignment angle between pulsar A's spin and the post-supernova orbital angular momentum for both isotropic and polar kicks. The most probable values of both quantities depend sensitively on the unknown radial velocity. In particular, tilt angles lower than 30-50 degrees tend to be favored for current radial velocities of less than 500km/s in absolute value, while tilt angles higher than 120 degrees tend to be associated with radial velocities in excess of 1000km/s in absolute value.