Spectrum of the Supernova Relic Neutrino Background and Metallicity
  Evolution of Galaxies
  The spectrum of the supernova relic neutrino (SRN) background from past
stellar collapses including black hole formation (failed supernovae) is
calculated. The redshift dependence of the black hole formation rate is
considered on the basis of the metallicity evolution of galaxies. Assuming the
mass and metallicity ranges of failed supernova progenitors, their contribution
to SRNs is quantitatively estimated for the first time. Using this model, the
dependences of SRNs on the cosmic star formation rate density, shock revival
time and equation of state are investigated. The shock revival time is
introduced as a parameter that should depend on the still unknown explosion
mechanism of core collapse supernovae. The dependence on equation of state is
considered for failed supernovae, whose collapse dynamics and neutrino emission
are certainly affected. It is found that the low-energy spectrum of SRNs is
mainly determined by the cosmic star formation rate density. These low-energy
events will be observed in the Super-Kamiokande experiment with
gadolinium-loaded water.
