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

TL;DR

This paper explores how non-linear diffusive shock acceleration at supernova remnants can explain the observed spectral hardening in cosmic rays around 200-300 GeV/nucleon, linking acceleration efficiency to spectral slope variations.

Contribution

It proposes that spectral hardening in cosmic rays results from dispersion in acceleration spectra predicted by non-linear shock acceleration theories.

Findings

Spectral hardening correlates with variations in shock acceleration efficiency.

Non-linear shock acceleration models can reproduce observed spectral features.

Heavier elements show similar hardening patterns, supporting the model.

Abstract

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.