Revisiting the Contributions of Supernova and Hypernova Remnants to the Diffuse High-Energy Backgrounds: Constraints on Very-High-Redshift Injections

Star-forming and starburst galaxies are considered as one of the viable candidate sources of the high-energy cosmic neutrino background detected in IceCube. We revisit contributions of supernova remnants (SNRs) and hypernova remnants (HNRs) in such galaxies to the diffuse high-energy neutrino and gamma-ray backgrounds, in light of the latest Fermi data above 50GeV. We also take into account possible time dependent effects of the cosmic-ray (CR) acceleration during the SNR evolution. CRs accelerated by the SNR shocks can produce high-energy neutrinos up to $\sim100$ TeV energies, but CRs from HNRs can extend the spectrum up to PeV energies. We show that, only if HNRs are dominant over SNRs, the diffuse neutrino background above 100 TeV can be explained without contradicting the gamma-ray data. However, the neutrino data around 30 TeV remain unexplained, which might suggest a different population of gamma-ray dark CR sources. Alternatively, we consider possible contributions of Pop-III HNRs up to $z\lesssim10$, and show that they are not constrained by the gamma-ray data, and thus could contribute to the diffuse high-energy backgrounds if their explosion energy reaches ${\mathcal E}_{\rm POP-III}\sim{\rm a~few}\times10^{53}$erg. More conservatively, our results suggest that the explosion energy of POP-III HNRs is ${\mathcal E}_{\rm POP-III}\lesssim7\times{10}^{53}$erg.