The Cosmogenic Neutrino Flux Implied by the Observed Cosmic-Ray Spectrum and Composition

Every photopion interaction that taxes a cosmic-ray proton also mints neutrinos, so the observed cosmic-ray spectrum implies a diffuse neutrino flux whose size can be estimated from the same luminosity density that the source census requires. Accumulating a neutrino energy share of five percent of the cosmic-ray emissivity over a Hubble time with a redshift factor of 0.6 gives an all-flavour level of E squared times flux equal to 9.439e-10 GeV per square centimetre per second per steradian for a pure-proton flux. Scaling by the proton fraction implied by the composition analysis, about 0.3 at the highest energies, reduces the expectation to 2.832e-10, and an iron-dominated flux gives 9.439e-11. Current IceCube and Auger neutrino limits sit above even the pure-proton figure, so the non-observation of cosmogenic neutrinos is consistent with all three cases and already presses hardest on optimistic pure-proton, strong-evolution models. The density bound changes neither the emissivity nor the interaction physics. Simulated and computed; not a measurement.