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Contribution of starburst nuclei to the diffuse gamma-ray and neutrino flux

In nuclei of starburst galaxies, the combination of an enhanced rate of supernova explosions and a high gas density suggests that cosmic rays can be efficiently produced, and that most of them lose their energy before escaping these regions, resulting in a large flux of secondary products, including neutrinos. Although the flux inferred from an individual starburst region is expected to be well below the sensitivity of current neutrino telescopes, such sources may provide a substantial contribution to the diffuse neutrino flux measured by IceCube. Here we compute the gamma-ray and neutrino flux due to starburst galaxies based on a physical model of cosmic ray transport in a starburst nucleus, and accounting for the redshift evolution of the number density of starburst sources as inferred from recent measurements of the star formation rate. The model accounts for gamma-ray absorption both inside the sources and in the intergalactic medium. The latter process is responsible for electromagnetic cascades, which also contribute to the diffuse gamma-ray background at lower energies. The conditions for acceleration of cosmic ray protons up to energies exceeding $ \sim 10 \, \rm PeV$ in starburst regions, necessary for the production of PeV neutrinos, are investigated in a critical way. We show that starburst nuclei can account for the diffuse neutrino flux above $\sim 200 \, \rm TeV$, thereby producing $\lesssim 40 \%$ of the extragalactic diffuse gamma-ray background. Below $\sim 200 \, \rm TeV$, the flux from starburst appears to be somewhat lower than the observed one, where both the Galactic contribution and the flux of atmospheric neutrinos may account for the difference.