The energy production rate density of cosmic rays in the local universe is $\sim10^{44-45}\rm erg~Mpc^{-3}~yr^{-1}$ at all particle energies

Abstract

The energy output (per logarithmic interval of particle energies) of Cosmic Rays (CRs) with energies $10{\rm GeV}\lesssim\varepsilon_p\lesssim100{\rm GeV}$ is $\sim 10^{47}\rm erg$ per solar mass of star$-$formation, based on the CR production rate in the Milky Way and in starburst galaxies, implying a generation rate of $\varepsilon_p^2Q\sim 10^{45}\rm erg~Mpc^{-3}~yr^{-1}$ in the local universe. It is only $\sim 10$ times larger than the output, $\varepsilon_p^2 Q=0.5\pm0.2\times 10^{44}\rm erg~Mpc^{-3}~yr^{-1}$, of Ultra High Energy CRs (UHECRs) at energies $10^{10.5}{\rm GeV}<\varepsilon_p<10^{12}\rm GeV$ (obtained assuming they are mostly protons), which in turn is comparable to the lower limit of $\varepsilon_p^2 Q\ge 0.5\times 10^{44}\rm erg~Mpc^{-3}~yr^{-1}$ of high energy CRs with $10^6{\rm GeV}\lesssim\varepsilon_p\lesssim 10^{8}\rm GeV$ implied by the saturation of the Waxman-Bahcall bound by the neutrino excess recently discovered by IceCube. These similarities are consistent with a flat production spectrum, $\varepsilon_p^2 Q\sim \text{const}$ for CRs at all observed energies. If a flat production spectrum is generated by our galaxy, the observed CR flux in the range $10^{6.5}-10^{9.5}\rm GeV$, above the "knee", is suppressed compared to lower energies due to propagation effects rather than acceleration upper limits. As suggested by Parizot and Aublin, the most exciting possibility is that cosmic rays at all energies are emitted from a single type of (unknown) sources, which can not be supernova remnants.