The cumulative background of high energy neutrinos from starburst galaxies

We show that starburst galaxies efficiently convert cosmic rays into pions, which in turn decay into high energy neutrinos and photons. The cumulative background of GeV neutrinos is E ν 2 Φ ν ≈ 10 −7 GeV cm −2 s −1 sr −1 , and its extrapolation to higher neutrino energies depends on the energy spectrum of the injected cosmic rays, with E ν 2 Φ ν ∝ E ν - 0.15±0.1 up to E ν ∼ 0.3 PeV and possibly higher neutrino energies. This flux, which constitutes a lower limit to the high energy extra-Galactic neutrino flux, may be detectable with forthcoming kilometre-scale neutrino telescopes.