Bounds on the origin of extragalactic ultrahigh energy cosmic rays from the IceCube neutrino observations

Understand

We study general implications of the IceCube observations in the energy range from $10^{6}$ GeV to $10^{10}$ GeV for the origin of extragalactic ultrahigh energy cosmic rays assuming that high energy neutrinos are generated by the photomeson production of protons in the extragalactic universe.

• The PeV-energy neutrino flux observed by IceCube gives strong bounds on the photomeson-production optical depth of protons in their sources and the intensity of the proton component of extragalactic cosmic rays.
• The neutrino flux implies that extragalactic cosmic-ray sources should have the optical depth greater than $\sim 0.01$ and contribute to more than a few percent of the observed bulk of cosmic rays at 10 PeV.
• If the spectrum of cosmic rays from these extragalactic sources extends well beyond 1 EeV, the neutrino flux indicates that extragalactic cosmic rays are dominant in the observed total cosmic-ray flux at 1 EeV and above, favoring the dip transition model of cosmic rays.