Energetics of ultrahigh-energy cosmic-ray nuclei

Energetics of the ultrahigh-energy cosmic rays (UHECRs) generated in the Universe is crucial for pinning down their candidate sources. Using the recent Auger data on UHECR spectra, we calculate the UHECR energy generation rate density for different species of nuclei at the injection, considering intermediate and heavy nuclei as well as protons, through scanning over source parameters on the spectral index, maximum energy and redshift evolution. We find the resulting UHECR energy generation rate density to be $\ensuremath{\approx}(0.2--2)\ifmmode\times\else\texttimes\fi{}{10}^{44}\text{ }\text{ }\mathrm{erg}\text{ }{\mathrm{Mpc}}^{\ensuremath{-}3}\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$ at ${10}^{19.5}\text{ }\text{ }\mathrm{eV}$ with a nontrivial dependence on the spectral index. Nuclei other than protons and irons favor hard spectral indices at the injection, and the required value of energy budget is smaller for intermediate nuclei. Given significant uncertainties in hadronic interaction models and astrophysical models for the Galactic-extragalactic transition, our results can be regarded as conservative. The composition data on ${X}_{\mathrm{max}}$ give additional constraints, but the results are consistent within the model uncertainties.