  The time-integrated luminosity and average energy of the neutrino emission
spectrum are essential diagnostics of core-collapse supernovae. The SN 1987A
electron antineutrino observations by the Kamiokande-II and IMB detectors are
only roughly consistent with each other and theory. Using new measurements of
the star formation rate history, we reinterpret the Super-Kamiokande upper
bound on the electron antineutrino flux from all past supernovae as an excluded
region in neutrino emission parameter space. A gadolinium-enhanced
Super-Kamiokande should be able to jointly measure these parameters, and a
future megaton-scale detector would enable precision studies.
