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We investigate the precision with which a neutron star gravitational bindingenergy can be measured through the supernova neutrino signal, without assumingany prior such as the energy equipartition hypothesis, mean energies hierarchyor constraints on the pinching parameters that characterize the neutrinospectra. We consider water Cherenkov detectors and prove that combining inversebeta decay with elastic scattering on electrons is sufficient to reach $11\%$precision on the neutron star gravitational binding energy already withSuper-Kamiokande. The inclusion of neutral current events on oxygen in theanalysis does not improve the precision further. We show that $3\%$ precisioncan be achieved if priors are introduced, such as energy equipartition. Wediscuss the implications of our findings on the properties of the newly formedneutron star, in particular concerning the assessment of the compactness ormass--radius relation.

Measuring the neutron star compactness and binding energy with supernova neutrinos