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The energy radiated in supernova neutrinos is a fundamental quantity that isclosely related to the gravitational binding energy of a neutron star. Recentlythe tidal deformability of neutron stars was constrained by gravitational waveobservations. By considering several equations of state, we find a strongcorrelation between the tidal deformability and neutron star binding energy. Weuse this correlation to sharpen predictions of the binding energy of neutronstars and the total neutrino energy in supernovae. We find a minimum bindingenergy for a neutron star formed in a supernova of $\sim1.5\times 10^{53}$ergs. Should the neutrino energy in a supernova be significantly below thisvalue, it would strongly suggest new unobserved particles are carrying awaysome of the supernova energy. Alternatively, if the neutrino energy is observedabove $\sim 6\times 10^{53}$ ergs, it would strongly imply the formation of a(perhaps surprisingly) massive neutron star.

Total Energy in Supernova Neutrinos and the Tidal Deformability and Binding Energy of Neutron Stars