Non-linear acceleration at supernova remnant shocks and the hardening in the cosmic ray spectrum

In the last few years several experiments have shown that the cosmic ray spectrum below the knee is not a perfect power-law. In particular, the proton and helium spectra show a spectral hardening by ~ 0.1-0.2 in spectral index at particle energies of ~ 200-300 GeV/nucleon. Moreover, the helium spectrum is found to be harder than that of protons by ~ 0.1 and some evidence for a similar hardening was also found in the spectra of heavier elements. Here we consider the possibility that the hardening may be the result of a dispersion in the slope of the spectrum of cosmic rays accelerated at supernova remnant shocks. Such a dispersion is indeed expected within the framework of non-linear theories of diffusive shock acceleration, which predict steeper (harder) particle spectra for larger (smaller) cosmic ray acceleration efficiencies.