Common Solution Of Three Cosmic Puzzles

The fluxes, spectra and sky distributions of the cosmic backgrounds of high energy neutrinos, gamma rays, and positrons, if produced in hadronic collisions of cosmic rays with matter inside their cosmic accelerators are simply related. Using these relations, we show that the flux of astronomical neutrinos above 35 TeV measured with IceCube is that expected from the sub-TeV gamma ray background measured with Fermi-LAT, and that the Galactic gamma ray background itself is that expected from the flux of sub-TeV CR positrons measured with AMS. This provides compeling evidence that the high energy neutrino, gamma ray, and positron backgrounds have a common origin - hadronic meson production by cosmic rays that takes place mostly inside the cosmic ray accelerators rather than in the interstellar medium of galaxies or through the decay/annihilation of dark matter particles.