Measuring the neutron star compactness and binding energy with supernova neutrinos

We investigate the precision with which a neutron star gravitational binding energy can be measured through the supernova neutrino signal, without assuming any prior such as the energy equipartition hypothesis, mean energies hierarchy or constraints on the pinching parameters that characterize the neutrino spectra. We consider water Cherenkov detectors and prove that combining inverse beta decay with elastic scattering on electrons is sufficient to reach $11\%$ precision on the neutron star gravitational binding energy already with Super-Kamiokande. The inclusion of neutral current events on oxygen in the analysis does not improve the precision further. We show that $3\%$ precision can be achieved if priors are introduced, such as energy equipartition. We discuss the implications of our findings on the properties of the newly formed neutron star, in particular concerning the assessment of the compactness or mass--radius relation.