Formation and progenitor of PSR J0737-3039 : New constraints on the supernova explosion forming pulsar B

We investigate the formation of the double pulsar PSR $J0737\mathrm{\text{\ensuremath{-}}}3039$ and examine its most likely progenitors, taking into account the most recent and all currently available observational constraints. We show that the most likely kick velocity and progenitor parameters depend strongly on the consideration of the full five-dimensional probability distribution function for the magnitude and direction of the kick velocity imparted to pulsar B at birth, the mass of pulsar B's presupernova helium star progenitor, and the presupernova orbital separation rather than marginalized one- or two-dimensional distributions for the kick velocity and progenitor mass. The priors that enter the analysis are the age of the system, the minimum helium star mass required to form a neutron star, the transverse systemic velocity, and the treatment of the unknown radial velocity. Since the latter cannot be measured observationally, we adopt a statistical approach and use theoretical radial-velocity distributions obtained from population synthesis calculations for coalescing double neutron stars. We find that when the minimum presupernova helium star mass required for neutron star formation is assumed to be $2.1\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, the most likely kick velocity ranges from $70\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ to $180\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. When, on the other hand, masses lower than $2.1\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ are allowed as neutron star progenitors, the most likely kick velocity can reach very low values (as low as a few $\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$), although the majority of the models still yield most likely kick velocities of $50\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ to $170\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. Hence, we agree with Piran and Shaviv [T. Piran and N. J. Shaviv, Phys. Rev. Lett. 94, 051102 (2005).] that the observed system properties, including the low transverse systemic velocity, can indeed be compatible with low progenitor masses and low kick velocities. Equally important though, we show that this is not the only likely formation path of pulsar B, due to the role of different prior assumptions that are necessary in the analysis. Moreover, in contrast to earlier claims in the literature, we show that the proximity of the double pulsar to the Galactic plane and the small proper motion do not pose stringent constraints on the kick velocity and progenitor mass of pulsar B at all. Instead, the constraints imposed by the current orbital semimajor axis and eccentricity and the orbital dynamics of asymmetric supernova explosions turn out to be much more restrictive. We conclude that without further knowledge of the priors, the currently available observational constraints cannot be used to unambiguously favor a specific core-collapse and neutron star-formation mechanism. Both electron capture and neutrino-driven supernovae therefore remain viable formation mechanisms for pulsar B.