Derivation of cosmic-ray source abundances above 10 GeV per nucleon and implications for air-shower measurements

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Abstract
The form of the energy spectra and the composition of cosmic rays on acceleration are important for illuminating the important question of the origin of cosmic rays at air-shower energies, a subject of considerable current interest following the recent detection of ultra-high-energy gamma rays from Cyg X-3 and Vela X-1. Source abundances of cosmic rays are usually calculated from data below approximately 1 GeV per nucleon and may not be applicable to air-shower energies. In this Letter, recent measurements of the energy spectra of cosmic-ray hydrogen, helium, oxygen and iron to energies greater than 104 GeV per nucleus are used, together with a recent determination of the mean escape length of cosmic rays from the galaxy, to obtain the energy spectra and composition of these components on acceleration. The source spectra at these energies are consistent with power laws in rigidity with exponents of -2.0, as expected for acceleration by strong shocks and also as inferred for acceleration in binary X-ray sources.