ON THE INJECTION ENERGY-DISTRIBUTION OF ULTRA-HIGH-ENERGY COSMIC-RAYS

We investigate the injection spectrum of ultra-high-energy (>10(15) eV ) cosmic rays under the hypotheses that (1) these cosmic rays are prot ons and (2) the sources of these cosmic rays are extragalactic and are distributed homogeneously in space, although they may have had a diff erent strength in the past; furthermore, we assume that we are not unu sually close to any individual source(s). The most puzzling aspect of the observed ultra-high-energy cosmic-ray spectrum is the apparent non existence of a ''Greisen cutoff'' at about 10(19.8) eV. Such a cutoff would be expected owing to rapid energy loss from photopion production caused by interactions with the microwave background. We show that th is fact could be explained naturally if most (or all) of the cosmic ra ys presently observed above about 10(19.6) eV were initially injected with energy above the Greisen cutoff. However, we find that the inject ion of cosmic rays above the Greisen cutoff cannot account for the obs erved flux below about 10(19.6) eV Unless the injection rate of these particles was enormously higher in the past, as would be the case if t he injection resulted from the decay of an ultramassive particle with lifetime of order 10(9) yr. Even with such a rapid source evolution, t he observed cosmic-ray spectrum below about 10(18.5) eV cannot be expl ained by injection of particles above the Greisen cutoff in the distan t past. However, we show that a 1/E(3) injection spectrum can account for the observed spectrum below 10(18.5) eV, with the steepening obser ved by the Fly's Eye group between 10(17.6) and 10(18.5) eV being very naturally explained by e(+)e(-) production effects. This latter fact lends support to the hypothesis that the cosmic rays in this energy re gime are protons of extragalactic origin. However, owing to e(+)e(-) p roduction effects, a 1/E(3) injection spectrum cannot account for the observed flux above about 10(18.5) eV.