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Recent cosmic ray (CR) experiments discovered that the CR spectra experiencea remarkable hardening for rigidity above several hundred GV. We propose thatthis is caused by the superposition of the CR energy spectra of many sourcesthat have a dispersion in the injection spectral indices. Adopting similarparameters as those of supernova remnants derived from the Fermi $\gamma$-rayobservations, we can reproduce the observational CR spectra of differentspecies well. This may be interpreted as evidence to support the supernovaremnant origin of CRs below the knee. We further propose that the samemechanism may explain the "ankle" of the ultra high energy CR spectrum.

Cosmic ray spectral hardening due to dispersion in the source injection spectra