Energy generation rate densities of ultrahigh-energy cosmic-ray nuclei

The origin of ultrahigh-energy cosmic-ray (UHECR) has been a mystery for many years. In order to identify candidate sources, it is crucial to figure out the energetics of cosmic-ray sources. By fitting the experiment data of cosmic-ray energy spectrum from Pierre Auger Observatory, we calculate the energy generation rate densities for different nuclei species via scanning over various parameters that are related to the source distribution models, injection properties as well as propagation of UHECR. Assuming UHECRs are protons and heavy nuclei produced by extragalactic sources, the energy generation rate density is estimated to be e²Q ~ 0.66_-⁺₀⁰₃⁸×10⁴⁴ erg Mpc^-3 yr^-1 averaging different nuclei species at power-law spectral index s = 2.0 and it varies on different fitting range. For a power-law scaling of the CR production rate with redshift, maximum energy and pure proton injection, dN/dE ? E^-sexp(-E/E_max)(1 + z)^m, best-fit parameters are s = 2.1, m = 5.0, E_max = 10^19.9eV. Hard spectra with strong source redshift evolution and low maximal source energy are slightly favored. We did not find a strong proof of the linear relationship between e²Q and s as shown in Katz et al 2009. We discuss cases of mixed composition models by analyzing the combined fit of spectrum and mass composition X_max data.