Constraining the gravitational binding energy of PSR J0737-3039B using terrestrial nuclear data

We show that the gravitational binding energy of a neutron star of a given mass is correlated with the slope of the nuclear symmetry energy at 1\char21{}2 times nuclear saturation density for equations of state without significant softening (i.e., those that predict maximum masses ${M}_{\mathrm{max}}g1.44{M}_{\ensuremath{\bigodot}}$ in line with the largest accurately measured neutron star mass). Applying recent laboratory constraints on the slope of the symmetry energy to this correlation we extract a constraint on the baryon mass of the lower mass member of the double pulsar binary system, PSR J0737-3039B. We compare with independent constraints derived from modeling the progenitor star of J0737-3039B up to and through its collapse under the assumption that it formed in an electron capture supernova. The two sets of constraints are consistent only if $L\ensuremath{\lesssim}$ 70 MeV.