| The energy production rate & the generation spectrum of UHECRs (2008) | |||||||||
Abstract | |||||||||
| We derive simple analytic expressions for the flux and spectrum of ultra-high energy cosmic-rays (UHECRs) predicted in models where the CRs are protons produced by extra-Galactic sources. For a power-law scaling of the CR production rate with redshift and energy, d\dot{n} /dE\propto E^-\alpha (1+z)^m, our results are accurate at high energy, E>10^18.7 eV, to better than 15%, providing a simple and straightforward method for inferring d\dot{n}/dE from the observed flux at E. We show that current measurements of the UHECR spectrum, including the latest Auger data, imply E^2d\dot{n}/dE(z=0)=(0.45\pm0.15)(\alpha-1) 10^44 erg Mpc^-3 yr^-1 at E. Comment: 9 pages, 11 figures, minor revisions | |||||||||
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