  The energy radiated in supernova neutrinos is a fundamental quantity that is
closely related to the gravitational binding energy of a neutron star. Recently
the tidal deformability of neutron stars was constrained by gravitational wave
observations. By considering several equations of state, we find a strong
correlation between the tidal deformability and neutron star binding energy. We
use this correlation to sharpen predictions of the binding energy of neutron
stars and the total neutrino energy in supernovae. We find a minimum binding
energy 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 this
value, it would strongly suggest new unobserved particles are carrying away
some of the supernova energy. Alternatively, if the neutrino energy is observed
above $\sim 6\times 10^{53}$ ergs, it would strongly imply the formation of a
(perhaps surprisingly) massive neutron star.
