The diffuse supernova neutrino flux, supernova rate and SN1987A

I calculate the diffuse flux of electron antineutrinos from all supernovae using the information on the neutrino spectrum from SN1987A and the information on the rate of supernovae from direct supernova observations. The interval of flux allowed at 99% confidence level is ∼0.05-0.35 cm−2 s−1 above the SuperKamiokande (SK) energy cut of 19.3 MeV. This result is at least a factor of ∼4 smaller than the current SK upper limit of 1.2 cm−2 s−1, thus motivating the experimental efforts to lower the detection energy threshold or to upgrade to higher volumes. A Megaton water Cherenkov detector with ∼90% efficiency would record ∼2-44 inverse beta decay events a year depending on the energy cut.