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

Recent cosmic ray (CR) experiments discovered that the CR spectra experience a remarkable hardening for rigidity above several hundred GV. We propose that this is caused by the superposition of the CR energy spectra of many sources that have a dispersion in the injection spectral indices. Adopting similar parameters as those of supernova remnants derived from the Fermi $\gamma$-ray observations, we can reproduce the observational CR spectra of different species well. This may be interpreted as evidence to support the supernova remnant origin of CRs below the knee. We further propose that the same mechanism may explain the "ankle" of the ultra high energy CR spectrum.