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Supernovae are rare nearby, but they are not rare in the Universe, and allpast core-collapse supernovae contributed to the Diffuse Supernova NeutrinoBackground (DSNB), for which the near-term detection prospects are very good.The Super-Kamiokande limit on the DSNB electron {\it antineutrino} flux,$\phi(E_\nu > 19.3 {\rm MeV}) < 1.2$ cm$^{-2}$ s$^{-1}$, is just above therange of recent theoretical predictions based on the measured star formationrate history. We show that the Sudbury Neutrino Observatory should be able totest the corresponding DSNB electron {\it neutrino} flux with a sensitivity aslow as $\phi(22.5 < E_\nu < 32.5 {\rm MeV}) \simeq 6 $ cm$^{-2}$ s$^{-1}$,improving the existing Mont Blanc limit by about three orders of magnitude.While conventional supernova models predict comparable electron neutrino andantineutrino fluxes, it is often considered that the first (andforward-directed) SN 1987A event in the Kamiokande-II detector should beattributed to electron-neutrino scattering with an electron, which wouldrequire a substantially enhanced electron neutrino flux. We show that with therequired enhancements in either the burst or thermal phase $\nu_e$ fluxes, theDSNB electron neutrino flux would generally be detectable in the SudburyNeutrino Observatory. A direct experimental test could then resolve one of theenduring mysteries of SN 1987A: whether the first Kamiokande-II event reveals aserious misunderstanding of supernova physics, or was simply an unlikelystatistical fluctuation. Thus the electron neutrino sensitivity of the SudburyNeutrino Observatory is an important complement to the electron antineutrinosensitivity of Super-Kamiokande in the quest to understand the DSNB.Comment: 10 pages, 3 figure

New test of supernova electron neutrino emission using Sudbury Neutrino Observatory sensitivity to the diffuse supernova neutrino background