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The cosmic ray (CR) energy spectra measured with ATIC, CREAM and PAMELAshowed that there is remarkable hardening for rigidity of several hundred GV.We propose that this hardening is due to the superposition of spectra from apopulation of sources, e.g., supernova remnants (SNRs), whose injectionspectral indices have a dispersion. Adopting proper model parameters theobservational data can be well explained. It is interesting that the injectionsource parameters are similar with that derived from gamma-ray observations ofSNRs, which may support the SNR-origin of CRs. Furthermore this mechanismprovides an alternative explanation of the "ankle-cutoff" structure of theultra high energy CR spectra.

Cosmic ray spectral hardening due to dispersion of source injection spectra